THE FLOW OF GASES
IN FURNACES
BY
W. E. GROUME-GRJIMAILO
Professor of Iron Manufacturing at the Polytechnic Institute ofPetrograd
Translated from Russian into French
By LEON DLOUGATCH and A. ROTHSTEIN
With a Preface
By HENBY LE CHA/TELIEE
Translated from the French
By A. D. WILLIAMS
With an Appendix upon
THE DESIGN OF OPEN-HEARTH FURNACES
NEW YOEK
JOHN WILEY & SONS, inc.
london: CHAPMAN <fe HALL, limited
1923

COPYKIGHT,  1922
BY
A. D. WILLIAMS

PREFACE  BY TRANSLATOR INTO ENGLISH
moke or less mystery has enveloped the designing and con-
struction of metallurgical furnaces. Blue-prints with the titles
removed and tables of supposedly important features have been
carefully treasured. When new furnaces were to be designed
an extensive analysis was frequently made of what was known
of the work of others, and an endeavor was made to "improve"
upon them. During construction other plants were visited and
further improvements were frequently made, with the result that
the finished furnace departed widely from the drawings. Not
infrequently the starting up of a new furnace was signalized by an
acrid meeting of the lodge of sorrow and by expensive reconstruc-
tion and loss of product. During the campaign of the furnace the
question, "What can be done to change it?" was a live issue.
Certain parts of the furnace had to be rebuilt from time to time,
and this afforded a certain amount of opportunity to correct
early errors, provided they had been rightly diagnosed.
Some years ago, the writer became convinced that the flow
of gases in a furnace was entirely devoid of mystery, being gov-
erned by the laws of elementary physics. Several furnace design-
ers were asked, as the occasion offered, whether they based their
design upon experience and upon the proportions of working
furnaces or used formulas for the flow of the gases. The replies
received were interestingly noncommittal. The physical laws of
flowing fluids, however, were found to agree very closely with
practical observations. They explained, with remarkable clarity,
some mysterious troubles.
Later, the writer got in touch with the work of Professors
Grourne-Grjimailo and Yesmann. Professor Groume-Grjimailo
had gone over the ground very thoroughly several years before the
writer became interested in furnace work, and had conducted
numerous experiments with model furnaces. He had simulated
the flow of the gases and the effects of the atmosphere by immers-

vi	PREFACE BY TRANSLATOR INTO  ENGLISH
ing his models in water and circulating colored kerosene oil through
them, the models being built with glass sides to permit observation.
A great many illustrations and drawings of furnaces, with
more or less detail, have been printed from time to time. Atten-
tion was occasionally called to certain differences, generally to an
increase in the size of certain parts above those of some well-known
furnace. The reasons for changes not being stated, it was possible
to make many inferences.
While the title of this work, "The Flow of Gases in Furnaces/7
explains its purpose, it is an abbreviation of the title of the
French edition, which may be rendered into English as "An
Essay upon a Theory concerning Hot Gases in Furnaces based
upon the Laws of Hydraulics/7 The work treats of the develop-
ment of the flow laws of heated gases and the application of those
laws to the rational design of furnaces. Primarily, a furnace,
considered as an elementary structure, is merely a hollow structure
of refractory material, within which heat may be released. A
great many furnaces show that their designers had very elementary
ideas concerning the application and utilization of heat. Damour
has given the following definition of industrial heating, which
sums up the question:
" Industrial heating has for its objective the realization of a
temperature more or less high, with economy, within an enclosure of
known dimensions, making use of a selected combustible (or form
of heat energy), for effecting a certain operation or chemical reaction.
"High temperature, economy, various combustibles, fixed
dimensions of the furnace or its heating chamber, a certain
industrial operation—such are the five variables of the problem.
Industrial heating operations present an infinite variety of results
to be accomplished. The engineer must be able to see all sides
of the problem; he must understand the various furnaces required,
their proper operation, the correction of their defects, and above
all the rational solution of each particular case. Each phase of
the question calls for many different forms of knowledge, with
each of which the engineer must be equally familiar; but it is
essential that he carefully distinguish between them, lest he
become confused or fall into those errors which frequently retard
the progress of the science of furnaces."
In a preceding paragraph Damour states: "All forms of energy
may be converted into heat, either directly by a single apparatus

PREFACE BY TRANSLATOR INTO ENGLISH	vii
or indirectly by the successive use of two forms of apparatus.
The only difficulty consists in obtaining this heat in such form,
or at a thermal potential (temperature), which will permit its
utilization, or in finding the methods of recuperation^ which will
avoid the waste of the energy."
According to these conditions the problem may be stated as
follows: "To find the most advantageous means of transforming
energy under any of its various forms, chemical, thermal, electrical,
mechanical, etc., either singly or in combination, within the chamber
of a furnace, into heat, utilizable for effecting a particular industrial
operation."
All industrial heating operations fall within four principal
classes :
" (./) Those in which the temperature at which the particular
reaction occurs is sufficiently low, and the chemical energy of the
reaction is sufficient, to release enough heat for the propagation of the
reaction and to more than cover all radiation and other cooling effects"
This case covers the burning of sulphur to sulphur dioxide, the
combination of nitrogen with calcium carbide in the manufacture
of cyanamicle, the making of steel in the Bessemer converter.
" (#) Those industrial operations in which a certain amount of
heat is released, but whose heat energy is not sufficient to maintain
the ruling temperature necessary for the reaction"
This case is the most general one: Nearly all operations release
some heat. A characteristic example in this class is the open-
hearth furnace.
" (3) The operation possesses no special chemical energy or is
inert."
This case comprises many reheating and some melting opera-
tions.
"(4) The chemical energy peculiar to the operation is negative.71
All the heat must be supplied from an external source.
In translating this work, no effort has been made to transform
the formulas and tables from the metric to the English system, of
units. Such a transformation would introduce many complicated
constants into the formulas and, in addition, would greatly
increase the numerical work required in computation. Moreover,
by translator. — As used here, this does not necessarily mean regene-
ration, but the economic utilization of the heat by direct or indirect recov-
ery of waste heat.

viii	PREFACE BY TRANSLATOR INTO ENGLISH
the Continental practice of stating metric values has been fol-
lowed, as it obviates the use of the decimal point. The use of the
metric system in work of this character is practically compulsory
and practically all of the basic data are available in metric units.
The results, if desired, may readily be transformed into English
units, the transformation factors, in many cases, being simple and
easily memorized numbers.
The translator holds no brief for the metric system. Its
logical and simple numerical constants supply a most potent
argument for its use in all technical work. It reduces many of
the problems of engineering from the tedious computations of the
English system to exceedingly simple mental computations.
It is unfortunate that German methods are much more widely
known than the extremely simple methods used in France, as a
result of German propaganda which has been spread over the
world and accepted without due investigation. The Germans
have claimed as their own many technical discoveries for which
credit is really due to men of other nations.
The purpose of this translation is to convey the ideas of the
original author. In order to enhance the usefulness of the work,
some additions have been made in the shape of appendices supply-
ing methods not elsewhere available in English.

PREFACE FOR THE ENGLISH EDITION
this work was originally published in the Journal of the
Russian Metallurgical Society, in 1911.
During the past six years, a large number of furnaces have been
designed and placed in operation by my pupils, by the technical
bureau .working under my direction, and by myself; but I do
not know of a single instance in which we have met with a failure.
The hydraulic theory of the flow of hot gases has proved to be
correct. This method of establishing the design of furnaces by
computations has given good results and may be followed without
fear.
This is not all; the new idea, that of examining each furnace
as a hydraulic recipient or reservoir, has exercised a deep influence
upon the working out of new forms of furnaces. During the last
six years I have worked out a number of new forms of furnaces,
the greater proportion of which have already been controlled by
working experience. There is no doubt that we are on the eve of
a radical change in the technical utilization of the heat generated
by the combustion of fuel.
When the war is over, I hope to publish my work in regard to
the establishment of the design of new types of furnaces. In the
mean time, I limit myself to the following remarks:
During the last few years, it has happened more than once
that a furnace construction thought out by me, solving a problem
placed before me by a client, has proved, after some research,
to have been described in an American patent. This tends to show
that the technique of the United States has approached very close
to the solution of many of the problems connected with the design
of furnaces. With a little more theory, the American engineers
will fully master the science of building furnaces. I am, therefore,
extremely obliged to Mr. A. D. Williams for his offer to translate
this work. I am convinced that it will prove very useful to our
esteemed allies, the Americans.
W.-E. geotjme-geimailo.
pethograd, May, 1917.

PREFACE TO THE FRENCH EDITION
the researches of Professor Groume-Grjimailo bring to us a
new idea. Conceptions of this character are very rarely presented
to us in the numerous publications of the day, and we sincerely
compliment the author in that he has opened the way for us into
a very broad field which merits our careful consideration. He
has set forth a principle in regard to the circulation of the hot
gases within furnaces—a very simple principle, but one that has
not heretofore been recognized. We have always considered that
gases, by reason of their absolute elasticity, completely fill the
chamber in which they are enclosed. Then, by a process of
unconscious induction, without any sound basis, we conclude that
in circulating through a series of successive chambers or flues,
they fill equally the entire cross-section of those chambers through
which they pass and that their current sweeps uniformly through
all the passages or flues which are open to them in proportion to the
area of these passages. Perhaps we should not formulate this
erroneous principle in such exact terms; nevertheless, we pro-
ceed as though we firmly believed that it was correct. And it
certainly follows, notably in the construction of furnaces, that
very serious errors are made. Professor Groume-Grjimailo cites
numerous examples of these errors.
A phenomenon is more readily understood when it is compared
with something that we have always before us. Wo see a stream
of water flowing in its bed, resting upon the soil and bounded upon
three sides by the surface of the ground. Its upper surface is
separated from the atmospheric air above by a horizontal plane,
the position of which is not fixed and which varies in accordance
with the volume of water flowing. The hot gases in a furnace
tend to circulate in exactly the same manner, with this single
difference, that the plane of separation is below, and the profile
of the bed of the stream is formed by the roof and the walls of the
furnace. As this comparison shows, we have heretofore errone-
ously considered that the flame filled the entire furnace and heated

xii	PREFACE  TO THE FRENCH EDITION
it uniformly, when in reality the hot gases may circulate only in
I	the upper portion of the heating chamber, without coming into
I	any contact with the material which has been placed upon the
I	hearth.    The utilization of the heat in this case will be very
'	inefficient.    The stream of fire which flows against the roof will
I	carry all of its heat to the chimney.
|	The reason for this lies in the high coefficient of expansion of
'	gases, that is to say, in the fact that their density diminishes
I	very  rapidly  as   their   temperature  increases.    Therefore,   the
I	hydrostatic equilibrium of the different layers of gases, which are
«	at different temperatures, is accomplished with great rapidity,
f	and the hottest gases tend to accumulate at the highest point in
,'	the furnace.    Take, for example, the case of a kiln for bricks,
I	having a height of 5 meters and an average temperature of 1000°
f	and assume that the hot gas issuing from the fireboxes has, where
I	it enters the kiln, a temperature 500° higher, or 1500°.    The
motive pressure caused by this difference in temperature, acting
upon a column of gases 5 meters in height, tends to produce, in the
column of hot gases a vertical velocity of 5 meters per second,
while the average velocity of the gases, as referred to the total
area of the kiln chamber, is perhaps one-fiftieth of this velocity.
The gases, therefore, have ample time to arrange themselves in
layers according to their relative density. If the opening for the
escape of the waste gases is located at the highest point of the
roof of the furnace, the greatest portion of the heat will be lost.
It is necessary, in order to avoid such heat loss, to employ the
downdraft principle of heating, which has been employed for a
long time in the manufacture of porcelain and faience, but which
still remains unknown in a great many other industries.
By numerous examples, the author of this volume shows that
at least one-half of the furnaces designed for high-temperature
heating are arranged in such a manner that the currents of hot
gases tend to isolate themselves in the heating chamber, thus
giving an extremely poor utilization of the heat released by the
combustible.
The formation of these streams of hot gases in the furnace is
the cause of another difficulty; they tend to retard the completion
of the reaction of combustion. Above a fire burning upon a
grate, there are a number of parallel currents of gas, some of which
contain an excess of oxygen, while others contain an excess of

PREFACE TO THE FRENCH EDITION	xiii
combustible gas. In order that the latter may burn it must be
mixed intimately with the oxygen; this requires a certain period
of time, and the mixture must be made at a temperature sufficiently
high to permit the gases to react upon each other.
In steam-boiler settings, an arch of refractory materials is
frequently built over the fire. But if this arch does not form a
pocket in which the hot gases may accumulate and remain for a
time, the unburned gases will flow too rapidly from beneath the
arch, and the effect of the arch will be only imaginary. The work
of Professor Groume-Grjimailo is filled with similar examples,
with complete information regarding the works in which the
observations were made. This work is not, therefore, purely
theoretical; it is a thoroughly practical treatise based upon actual
observations and experiments.
Not content with having developed these new ideas, the
author has endeavored to place them before his readers in a man-
ner which will make them absolutely clear, just as he has been
doing for a long time in the instruction of his classes. In order to
present in a visible manner the circulation of the hot gases within
the furnace, he has employed small models of furnace sections,
enclosed between two plates of glass, and within these models he
has arranged to circulate .two liquids of different densities, water
serving as the heavier liquid and colored kerosene as the lighter
liquid, representing the hot gases or flame. The localization of
the current of kerosene shows very clearly whether the furnaces
are of poor design or not. This method is particularly applicable
for presenting this subject before those who may not be well
informed regarding the technical principles of the great industries;
but it has the inconvenience of giving, to a certain extent, an
erroneous view of the actual phenomena. During its circulation,
the colored kerosene cannot be changed into water or mixed with
it, while the light or hottest gases, having given up their heat, are
transformed into colder and heavier gases. This introduces very
essential differences which must be clearly understood. The
only purpose of this method of representation is to present to the
eye a very strong impression which will stimulate the imagination;
in practical application it is necessary that we consider these
phenomena as they really occur and study the gas itself, which
can only be conceived in the abstract and of which no visible
representation can be made.

xiv	PREFACE TO  THE FRENCH EDITION
The reading and study of this small volume will present these
principles to the eyes of many engineers and should lead to many
improvements in the art of heating and utilizing heat. In this
it will be of service; this is the highest recognition which can
be given to an author.
henry le chatelier.
note.—The foregoing was written by Henry Le Chatelier for the French
edition, which appeared in 1914.

FOREWORD
in his celebrated Traite de Metallurgie in 1875, Gruner gave
this definition:
" Metallurgy is the Art which treats of the preparation of
metals."
To-day, the application of the laws of physical chemistry, and
above all the application to metallurgical processes of the prin-
ciples set forth by M. Le Chatelier, have enabled us to uncover
the mysteries of this art. Metallurgy has become a science.
The dense fog of empiricism, which formerly enveloped all of the
metallurgical processes, has been dispersed, and everything has
become simple and clear, as it does in all other branches of human
knowledge, when they become part of the domain of science.
It is true that we now require a much more profound theoretical
preparation than was required in former times of those who took
up metallurgical work. As a result, the young engineer at the
termination of his studies enters the workshop with such a clear
idea of its processes that after a few months of practical experience
he is much better able to make himself the master of the situation
than are the older students of Gruner—who acquired the metal-
lurgical art—after ten years of practice and assiduous work in the
shops.
The young man of our day, who is well prepared theoretically,
becomes familiar with his work ten times as rapidly and works to
better advantage than those who studied under the old system.
Armed with scientific truths, he copes much more readily with
the difficulties which arise, and he does not experience the feeling
of helplessness which overcame the older metallurgists when they
found it impossible to better working conditions and save the
plant from a serious loss—a feeling which often paralyzed our
efforts at the time when all of our energies were vitally necessary.
The book which we present to our readers is dedicated to the
methods of constructing more efficient fuel-fired furnaces. Here-

xvi	FOREWORD
i	tofore, this field has been solely the field of practical experience
I	and of empiricism.    How were we able to acquire knowledge of
/	this veritable art?    I will speak from my personal experience.
*	After I had finished my studies at the Institute of Mines, at
Petrograd, I left the schoolroom to enter the Salda Works of
I	.	M. Demidow, one of the best plants in the Oural.    The supervision
t	of furnace work of all kinds was entrusted to an old employee,
s	Pierre Chicarine, a man of very great intelligence, but illiterate,
j	unable even to sign his own name.    This did not prevent him in
^	any way from undertaking to design new furnaces of many types,
\	and he always succeeded in obtaining good working results.
/	He was unable to state the principles by which he was guided,
despite a sincere desire upon his part to make me understand the
I	reasons for the various features of the designs.    This, however,
I	was beyond his power of expression.    His only argument was,
|	"It must be done in this way;   otherwise, you do not get any-
I       :	thing."
"Why?"
f	To this he was never able to reply.
|       i	I still remember many of his constructions, and I am per-
suaded that he really knew nothing of the fundamental principles,
or more exactly, that he did not have any very clear comprehen-
sion of them. He made many big mistakes, which he finally
corrected after many trials. Meanwhile, from time to time, in
discussing the various furnaces, and in placing new furnaces in
operation, he gave me much important information, calling to my
attention the phenomena which took place in the furnace, teaching
me not only where to look, but also how to see that which took place.
I became greatly interested in the furnaces. I studied them
very closely, making great efforts to solve their mysteries; but
I did not make very rapid progress in so doing. It was only after
ten years that I commenced to make suggestions to my instructor
for his criticism. It was only after fifteen years that I ventured to
design a new furnace for myself. My master reported after some
days upon my design; fully half of it had been erased and redrawn.
"It is necessary to do it in this manner; otherwise you will not be
able to make it work." Thereupon my dignity as director of the
works—the position which I occupied at this time—was deeply
wounded; at the same time, I recognized that the veteran had
reasons for acting in this manner.

FOREWORD	xvii
After about twenty years I was able to solve the mysteries of
furnace construction and discovered how to make furnaces which
would work properly. I finally comprehended that each furnace
could be represented as a hydraulic recipient or reservoir, that the
problem of designing a furnace was nothing more than a problem
in hydraulics, and that the circulation of the hot gases in the
furnace was similar to the circulation of a light liquid within a
heavier liquid.
Having arrived at this knowledge of furnaces, I found much
pleasure in conveying it to my co-workers. I was thus confirmed
in my belief that the hydraulic theory was clear, and presented to
the human mind an exact and precise view of the problem, a true
point of attack. The time necessary to acquaint a young engineer
with the principles of furnace design was reduced to one month.
An old employee \vho worked in the rolling mill and was well
posted in regard to shop practice was able to understand the
science of furnaces in a single evening, and I am satisfied that the
subject was thoroughly understood by him.
Nevertheless rny problem was not completely solved; under-
standing the mechanism of the circulation of the hot gases was not
sufficient. It still remained to establish the mathematical
formulas for those laws, in order to compute the dimensions of the
furnace. M. J. Yesmann, Professor of Hydraulics at the Poly-
technic Institute of Petrograd, came to my assistance at this point.
Professor Yesmann's formula for the inverted dam or weir W has
been verified by me by its application to twenty existing furnaces.
Having convinced myself that it was correct, I inserted the com-
putation of reverberatory furnaces into the metallurgical course of
the Polytechnic Institute of Petrograd.
It is true that the problem has not been entirely solved. A
large amount of research work must be done in order to determine
the coefficients which are necessary to reduce these formulas to
practice. I understand perfectly that my work is nothing more
than the first step toward the solution of the problems of furnaces.
It has caused and, I hope, will cause many others to undertake
the tests which are required to complete the work.
For example, one objection which has been made is that I have
made an error in assuming that a current of flame is similar to a
current of incandescent gas. It is perfectly true that this is an
(1) Refer to pages 40 and 53.

I
i	xviu	FOREWORD
error; but it is impossible to do everything at the same time and
in a single step. It was necessary to establish the fundamental
idea firmly, and in doing this the minor details were temporarily
neglected. When it has been firmly established that the circula-
tion of the hot gases in a furnace is a problem in hydraulics,
when the fog which has obscured these problems and appeared
to make them insoluble has been cleared away, then it will become
possible to settle the various details in a suitable manner.
The complete working out of the laws governing the theory of
the circulation of the hot gases, which has been commenced by
Professor Yesmann, should be continued by experts in hydraulics.
It is our province, as men of deeds, to check the working methods
of existing furnaces and to deduce therefrom the practical rules
which it is necessary for us to know in determining their design.
I am at present engaged in this work, as are many of my
students who are constructing furnaces in numerous workshops in
Russia. When sufficient progress has been made, it will be
possible to give the methods for the design computations of all
types of furnaces.
The very simplicity of the conclusions to which I was led were
rather disconcerting. But their approval by my colleagues at the
Polytechnic Institute—M. Kir pitch ow, Professor of Applied
Mechanics, and M. Mechtchersky, Professor of Theoretical
Mechanics—encouraged me to publish the original of the present
volume.
It was only natural that I should desire to submit my work to a
high authority, such as M. Le Chatelier;  the translation of the
work into French afforded such an opportunity, and I am greatly
I i -j	pleased by the honor which he has conferred upon me in introduc-
| ' |]	ing me, in such flattering terms, to my new readers.
W.-E. grotjme-gkjimailo.
petrograd,
February, 1914.

TABLE OF CONTENTS
preface by translator into english	!		v
preface to the english edition by W.-E. groume-grjimailo		ix
preface to the french edition, by henry le chatelier		xi
foreword, by W.-E. groume-grjimailo		xv
PART I
THE APPLICATION OF THE LAWS OF HYDRAULICS TO THE
COMPUTATIONS FOR A REVERBERATORY FURNACE
CHAPTER
I. the fundamental viewpoint	      1
II. experiments which serve to show the analogy between the
circulation of the flame and the movement of a light
liquid within a heavy liquid	      3
First Experiment	      4
Second Experiment	      7
III.	the current of hot gases may be compared to a stream
op water turned upside down, or inverted	      8
IV.	application of the laws of hydrostatics to hot gases	    11
(a) The Draft Fallacy of Metallurgical Furnaces	 16
(ft) Hydrostatic Pressure within Metallurgical Furnaces and
Their Flues	 21
(c) Hydrostatic Pressure in Open-top Chambers Filled with
a Light Gas	 25
V. the application to hot gases op the laws for the flow of
LIQUIDS THROUGH AN   ORIFICE IN THE  BOTTOM OF THE RESER-
VOIR	    27
VI. relation between the head, the pressure and the velocity
of currents of liquids and gases	    32
VII.  the application to hot gases of the theory of hydraulic
flow over thick-crested weirs	    40
VIII. velocity under inverted weirs.   rational construction
of furnaces of this type	    52

XX	CONTENTS
CHAPTER	PAGE
IX. reverberatory furnaces considered as inverted weirs
with a cistern or reservoir.    dimensions  upon which
their correct operation depends	    56
X. the application to hot gases of the theory of jets of
water	    63
XI. methods of computation for furnaces of various types. ..    72
PART II
principles for the rational construction of furnaces ...	87
The Subdivision of a Current of Hot Gas		88
I.   vertical regenerators		93
II.   horizontal regenerators		95
III.	hot-blast stoves		97
Construction of the Combustion Chamber of a Hot-blast
Stove	  102
IV.	hot-blast temperature equalizers	  107
V.   iron tube hot-blast or air heaters	 108
VI.	steam boilers		109
VII.	chamber furnaces, brick and pottery kilns		112
VIII.	cementation furnaces		115
IX.	furnaces for annealing malleable iron castings		116
X.	continuous or multiple chamber kilns, ring furnaces. .	116
XI.	muffle furnaces		121
XII.	vertical furnaces for tempering, annealing and heat
treating		123
XIII.	horizontal tempering furnaces,		126
XIV.	annealing and heating furnaces for boiler plates		128
XV.	ordinary reverberatory furnaces for reheating		129
XVI.   siemens type reheating furnaces		131
XVII.   pit furnaces		135
XVIII.   continuous heating furnaces		138
XIX.   tunnel furnaces or kilns		144
conclusion		149
APPENDICES
I. formula for the inverted weir, according to the com-
putation of professor J.-C. yesmann	  153
II.  gas factors, volumetric and weight	  160
III. velocity heads required for different velocities	  163

CONTENTS	xxi
CHAPTER	PAGE
IV. friction or gases flowing through brick flues or mains. 168
V. muffle furnace for tempering and annealing steel at
the petrograd arsenal	   171
VI. arch brick work	  177
Miscellaneous Tables	  183
Metric Conversion Table	  189
Conversion of Metric Formulas	  192
VII. design of open-hearth furnaces	  194
VIII.  design of hot-blast stoves	 300
IX. steam boilers, combustion and boiler settings	 320
X. heat capacity and calorific intensity curves	 348

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THE FLOW OF GASES IN FURNACES
Based upon the Laws of Hydraulics
part I
THE APPLICATION  OF THE LAWS  OF HYDRAULICS
TO THE COMPUTATIONSF OR A REVERBERATORY
FURNACE
I. THE FUNDAMENTAL VIEWPOINT
heretofore reverberatory furnaces have been constructed
with very little, or without any, computation; and the designer has
always met with more or less difficulty in establishing the lines
for a new furnace or in improving an old furnace which was
defective, and forcing it to work in the right manner. This was
due to the fact that the technical considerations governing the
design of these furnaces had not advanced sufficiently to give
any very exact point of view regarding the mechanism of the
circulation of the gases within the furnace. If the viewpoint
which is proposed below is accepted, the working processes of
these furnaces will become completely clear:
We are surrounded, as is everything else amidst which we live,
by a liquid w ocean, the air; the reverberatory furnace, which is
under consideration, is also immersed in this ocean of air. As
the density of this liquid, the air, is 770 times less than that pf
water, its presence is hardly noticeable and is very rarely con-
sidered. At the same time, it must be admitted that we do not
(1)ATo£e by the French translators.—While the word " fluid " would be more
appropriate, the word " liquid " has been retained as conveying more exactly
the thoughts of the author.

'-f
2	APPLICATION OF THE LAWS OF HYDRAULICS
live and exist in a vacuum. It is this neglect of the part played
by the air which causes error; it is this which prevents a clear
conception of the mechanism of the circulation of the hot gases
within a reverberatory furnace. When the presence of the air
is taken into consideration, the problem becomes very clear.
What is it that forms the flame? It is a mixture of gases at a
high temperature, reacting upon each other (combustion) and
releasing in this manner a sufficient amount of heat to raise the
products of their combustion to incandescence. The solid par-
tides of carbon, by their incandesence, give to the flames that
especial appearance which impresses the imagination and causes
the flame to be attributed to some infernal power. But, in
reality, the idea which the author desires to convey in regard to
the " flame " may be better understood if the flame is considered
as a current of incandescent gas. This approximation is suffi-
ciently accurate for the purpose.
The reverberatory furnace is accordingly considered as an
apparatus immersed in a liquid, the air, which weighs 1 kg 29
per cubic meter, in the interior of which there circulates a current
of incandescent gases, that is to say, a liquid much lighter than
the air.
It is known that the coefficient of expansion of gases is -5--^-;
if, therefore, the specific weight of air at 0° is considered as unity:
at   273° its specific weight will be £
546°	i
819°	i
1092°	i
1365°	$
1638°	i
1911°	£
and as the specific weight of air at 0° is 1 kg 29:
'?	at   273° its specific weight will be 0 kg  645
;«	546°	0	430
\	819°	0	323
J	1092°	0	258
|	1365°	0	215
jj	1638°	0	184
i<	1911°	0	161

EXPERIMENTS WHICH SERVE TO SHOW THE ANALOGY     3
A very clear idea of the differences in density which are caused
by great differences in temperature may be obtained by a con-
sideration of the air (gases) in an open-hearth furnace, of which
the temperature is in the neighborhood of 1638° while that of
the air is 0°. If it is assumed that the density of the gases in the
furnace is equal to water, the density of the air at 0° will be
relatively equal to that of molten iron.
A furnace in its regular working condition may be considered
as being immersed in a glass tank filled with water, the heavy
liquid, while the interior of the furnace is traversed by a lighter
liquid; the action of the flame within the furnace may in this
manner be considered as similar to that of the lighter liquid
flowing within the heavier liquid.
A complete representation of the circulation of the flame or
hot gases within a furnace may be made in the following manner;
A model to scale of the longitudinal section of a reverberatory
furnace is constructed and immersed in a tank with glass sides; if
a stream of a lighter liquid, as for instance, kerosene, is now
passed through the model of the furnace, the movement of this
liquid will reproduce exactly the movement of the flames within
the furnace.
II. EXPERIMENTS WHICH SERVE TO SHOW THE ANALOGY
BETWEEN THE CIRCULATION OF THE FLAME AND THE MOVE-
MENTS OF A LIGHT LIQUID WITHIN A HEAVY LIQUID.(1)
A white metal model reproducing to scale a brick kiln is placed
between two sheets of glass and submerged in a glass tank; by
means of pipes a stream of colored kerosene is passed into the
model^ through the firebox from which the gases of combustion
enter the furnace.
(1)	The photographs for Figs. 1, 2, 4, 10, 19, 24, 29, 30; 31,32,116, and 117
were supplied by the Sotiet6 russe de metallurgie, whom the author desires to
thank for the same.
(2)	The illustration (Fig. 2) shows the general arrangement of the apparatus
which has been used in conducting the experiments made before the classes at
the Polytechnic Institute of Petrograd.    The model is a scale reproduction
of a brick kiln of the Motovillikha works, the drawing of which is shown in
Fig. 3.   This is submerged in a tank filled with water.   Tubes with control
valves serve to introduce streams of colored kerosene through the fireboxes
of the kiln, the kerosene flowing from a large bottle which acts as a high-
level reservoir.   The kerosene, having passed through the furnace, rises to

FT
1    A

4	APPLICATION OF THE LAWS OF HYDRAULICS
First Experiment.—Study of the older, or updraft, type of
brick kiln (Fig. 1), which has the opening for the escape of the
waste gases at the highest part of the arched roof.
Small streams of colored kerosene are introduced through the
fireboxes and flow up to the central orifice, which is wide open.
The streams of kerosene may be seen as fine threads flowing up
close to the walls of the kiln and are not of sufficient volume to
fill the kiln chamber. Increasing the flow of the kerosene, or, as
it may be expressed, firing the kiln more heavily, does not affect
the result, It is very clear that the burning of the brick in a

fig. 1.
kiln working in this manner will be defective. The brick in the
lower portion of the kiln will be soft and only partially burned.
In order to improve this condition it will be necessary partially to
stop up or close the smoke hole. The poor working conditions
which exist in the updraft brick kiln are shown in Fig. 1. When
the smoke hole is partially closed, the kerosene is forced to accumu-
late in the upper portion of the kiln; it fills more and more of the
the surface of the water; thence by a trough it flows to the large bottle below.
A small pump driven by a motor of -^ hp draws the kerosene from the lower
bottle and delivers it to the upper bottle, enabling the kerosene to circulate
by gravity as long as desired.

EXPERIMENTS WHICH SERVE  TO  SHOW TIIK ANALOGY      5
kiln chamber; until an equilibrium is established between its
inflow and its outflow. When this equilibrium is established, the
lower surface of the layer of colored kerosene assumes a permanent
level.
It can be seen in Fig. 2 that only the upper portion of the

fig. 2.
kiln, above its mid-height, is filled with hot gitBen, and that the*
space between the lower surface of the layer of kerosene and the
hearth of the kiln contains none at alL Thin space, therefore, will
only be heated by such eddy currents as form, and the«e are due
entirely to the differences in density which exist between the

r

6	APPLICATION OF THE  LAWS OF HYDRAULICS
flame and the cooler gases with which they come in contact.
Immediately below the roof of the kiln the hot gases are
relatively at rest. The burning of bricks does not permit
of sudden or quick changes of temperature, as bricks will
crack and spawl if subjected to such changes; therefore it
would not be advantageous to use a kiln which worked in this
manner.
By still further obstructing the smoke hole of the kiln, the
lower surface of the layer of hot gases can be driven downward

IfPPIPiW^

fig, 3.

!P
'W

until it comes into contact with the sole of the kiln, thus giving
the maximum efficiency which is possible with kilns working on the
updraft system. Under these conditions, the brick can be burned
to an extent which is fairly satisfactory, but they will not be of
extra good quality, because, in spite of all, the currents of hot
gases have a tendency to flow directly to the highest opening.
The equalization of the temperature will be affected very little by
the eddy currents which will be formed. These eddy currents
will be of very slight intensity when the hot gases in the kiln are
as shown in Fig. 1, but nevertheless they do not disappear entirely

EXPERIMENTS WHICH SERVE TO SHOW THE ANALOGY     7
while the temperature at the solo is less than that which exists
immediately below the roof of the kiln.
Note by /ra//,.s7<7/or.—A considerable portion of the equalization of the heat
in the updraft kiln is due to conduction of the heat, through the kiln structure
and the brick set iu the kiln. This heat is carried downward in this manner
and imparted to the cooler layers of j^aseH at the bottom of the kiln, healing
them and promoting eddy currents. The updraft kiln, however, heats very
slowly at the bottom, and the upper portion of the sotting will he overburned
while the lower portion is underburned. As compared with the downdmft
kiln, the updraft kiln consumes a larger amount of fuel per unit of output,
and requires a longer time to complete a kiln round.
Direct or updraft brick kilns were the only ones built up to
about twenty years ago. They are still found in many potteries,

fhj. 4.
as in the works of Korniloff Brothers, at Petrognul. A brie.k
kiln of this type is still in use at the Oboukoff works, and it is
only a short (line since one* was in use at the Poutiloff works.
These arc not the last updraft kilns in use, but most of thorn have
been replaced by downdraft kilns.
tiecond Experiment.—VonimMud study of updraft kiln. Method
of operating downdraft kiln. For this experiment the smoke
hole at the top of the kiln is completely closed. The; chimney
of the apparatus, as shown in Fig. 4, is filled with kerosene, which

f

8	APPLICATION OF THE LAWS OF HYDRAULICS
is also introduced as before, through the fireboxer, It follows that
when the damper or stopper at the top of the chimney is opened
slightly, the model will represent a downdraft brick kiln in
operation.
It is seen that in the downdraft kiln the hottest gases rise to
the highest point under the roof, where they accumulate, forcing
the cold gases to the chimney through the ports in the hearth of
the kiln. Descending little by little toward the sole of the kiln,
the flames or hot gases finally fill the entire kiln chamber and
maintain themselves throughout it, only passing to the chimney
as they are displaced by hotter gases. In this manner the free
lower surface of the hot layer of gases is very nearly stationary,
which insures a practically uniform burn to the brick. In this
atmosphere, which varies very little, the reactions of combustion
are readily effected until only very slight traces of the combustible
elements and free oxygen can be found in the gases. That is,
combustion takes place with very nearly the theoretical supply of
oxygen. The flames of this combustion traverse the entire mass
of the gases and there are no definite points at which high tem-
peratures may be found. For this reason the downdraft kiln
is successfully employed when it is desired to obtain slow and
uniform heating.
These experiments with a model of a furnace immersed in
water confirm, with sufficient clearness, the fundamental principle
that the circulation of the hot gases within a furnace is similar
to the circulation of a light liquid within an enclosure filled with a
heavy liquid.
III. THE CURRENT OF THE HOT GASES MAY BE COMPARED TO
A STREAM OF WATER TURNED UPSIDE DOWN OR
INVERTED
Streams composed of a heavy fluid in motion within a lighter
fluid are seen everywhere. Do not all rivers represent the dis-
placement of a light fluid—the air—by a heavy fluid—the water?
In this case, it is very well known that the stream is confined
on the bottom and the sides.
If the flame and the hot gases within the furnace were fluids
heavier than the air, it would be found that they flowed in the
same manner as the stream of water. But as they are much lighter

THE  CURRENT OF HOT  GASES

than the air, it is found necessary to confine them%g><m-; the top
and the sides.
This may be more
clearly comprehended
by means of the fol-
lowing laboratory ex-
periment :
It is possible to
pour a gas from one
container to another
by employing a slop-
ing trough to guide
its  flow.     This  may	FlG  5
be done with carbon -
dioxide gas, which is heavier than air, and also with hydrogen,
which is lighter than air.    When the carbon dioxide is being

poured, the stream of gas must be
confined below and upon its sides
(Fig. 5). The hydrogen, on the
other hand, must be confined
upon the top and the sides (Fig. 6).
There is evidently nothing
which confines the current of car-
bon dioxide upon the top and the
stream of hydrogen on the bottom.
These experiments require care,
but are easy to make if the
surrounding air is absolutely still
and free from currents. & The
gases may be poured equally well
whether there is a fourth wall or
not.
fig. g.	These experiments lead to the
following conclusions:
Streams of incandescent gas need be confined only upon the
top and sides, and, in effect, all reverberatory furnaces confine
the stream of hot gases in this manner, at the top (the roof) and
(1)A condition which is neglected in the above experiment, is the tendency
of all gases to form homogeneous mixtures by diffusion. In both experiments
there will be a slight mixing with the air, as a result of this tendency.

10

APPLICATION OF THE LAWS OF HYDRAULICS

upon the sides (the walls of the furnace) (Fig. 7). The confining
boundary upon the bottom may be present or not. In the same
manner, a stream of water may be confined by walls below and

upon both sides, while
its upper surface is
entirely free. In a
similar way the gase-
ous stream has to be
confined upon the top
and the two sides,
while upon the bottom
its surface is entirely
free.
fig. 7.

It would reveal a
serious error in this
theory, if, for exam-
ple, the breeching, or
smoke flue, common to four boilers was found to be completely
filled with gases without regard to the number of boilers which
were in service. This, however, will not be the case. In a
correctly proportioned smoke
flue the free lower surface of
the gaseous stream will be
found in the neighborhood of
the bottom A A (Fig. 8). If
the volume of the gases flow-
ing decreases to one-fourth its
former volume, the thickness
of the stream decreases two
and one-half times <1} or to 0.40
its former thickness, and the
lower free surface of the gases
will be found at the level BB]
within the space A ABB, no
circulation of the gases will
be found. (2)
(1)	Where 2.5 = V4^ as may be seen further on, p. 40.
(2)	This statement is not absolutely correct, as eddy currents will exist in
the space A ABB due to the cooling effect of the walls upon the flowing stream
of heated gases.

APPLICATION  OF THE LAWS  OF  HYDROSTATICS       11
Just as a river has a depth which is a function of the volume
of water flowing, it is evident that a stream of gases will have a
thickness which is a function of the volume of gases flowing. If,
on this basis, water is used to simulate the cold air and colored
kerosene to simulate the hot gases flowing in the flue, it would not
be difficult to show a smoke flue filled or partially filled with a
stream of kerosene. This demonstration is considered useless
as it has been thoroughly established that flowing streams of hot
gases do not require anything to confine their lower surface and
that the thickness or depth of the stream is a function of the
volume of the gases which are flowing.
Therefore, when currents of hot gases are dealt with, they will
always be represented as inverted streams of water.
IV. APPLICATION   OF   THE   LAWS   OF   HYDROSTATICS   TO   HOT
GASES.
The weight per cubic meter of the products of combustion of
the ordinary combustibles varies from 1 kg 29 to 1 kg 33 at 0°
and 760 mm. The computations may be simplified, and will be
sufficiently exact, if the first of these values is assumed as the
weight of the products of combustion, because this value is also
the weight of a cubic meter of air. At any temperature t the
1 29
weight of 1 cu m of the hot gases will be, therefore,  /' '    kg, in
--
which a =      = 0.00367.
By reason of this large coefficient of expansion of gases, the
difference between the weight of a cubic meter of atmospheric air
(1 kg 29) and a cubic meter of the gases of combustion, taking,
for example, those in an open-hearth furnace (0 kg 17) is quite
large, being equal to 1.29—0.17 = 1 kg 12. It is this difference
between the weight of the air and the weight of the flame or hot
gases which causes the hydrostatic pressure of the latter.
The following experiments will serve to make this clear (Fig. 9).
The upper surface of the water in a beaker is at aa; and B is a
lamp chimney into which kerosene has been poured until its
lower surface is at the bottom of the lamp chimney. It can be
seen that the upper surface of the kerosene 66 in the lamp chim-
ney is higher than the surface of the water in the beaker.
The difference in level between aa and 66 can be computed in

12

APPLICATION OF THE LAWS  OF HYDRAULICS

the following manner. The column of water h is balanced by the
column of kerosene H. The specific weight of water is 1.0 and
that of kerosene is 0.80; it follows that :
and the difference in level will be 0.25/i, equivalent to a column
of water of 0.25/1 X0.8 = 0.2/i.
This experiment may be modified as follows:   take a beaker
1'

~T

x

\ 		
A
i 	— 	/rv-~>\ 	- dL^r 	
i
i 	_ - 		_ 	
<? 				
i 				
i 	— __ 		 		
i 				
1 	B-> 		V 	

 

fig. 9.

fki. 10.

I
I
J*
II
l
i

of water and immerse therein a test-tube filled with kerosene,
until the bottom of the test-tube is even with the surface of the
water, the test-tube being inverted (Fig. 10), and determine the
hydrostatic pressure which it supports. It is evident that at the
level B the pressure exerted by the water upon the kerosene and
the pressure reciprocally exerted by the kerosene upon the water
are equal, because they are in equilibrium.
The pressure of the water per unit of surface in millimeters of
water column is that given by the height h:
-Pwater = h X density of water = AXl = fe mm.
The pressure of the kerosene is measured, first, by the weight

APPLICATION OF THE LAWS  OF  HYDROSTATICS         13
of the column of kerosene, and, second, by a certain hydrostatic
pressure 5 to be determined. From which:
Pkerosene== AX density of kerosene+ 8 = 0.8fe+ <5 mm of water.
But Since Pwater = Pkerosene,  it follows that:
h = Q.8h+8    and    5 = +0.2h mm of water
If it is considered that the water in this experiment represents
the cold air and that the kerosene represents the incandescent
gases in the furnace, the following law may be established with
regard to the hydrostatic pressure which will be produced at the
different parts of a furnace chamber containing hot gases:
The hydrostatic pressure 8 in kilograms per square meter at a
point in a chamber bathed by the incandescent gases, located at
a distance H above the free surface of those gases, is equal to the
difference A between the weight in kilograms of a cubic meter of the
external air and a cubic meter of the incandescent gases, multiplied
by the height H, from which
8= HA.
Example.—If 77 = 0 m 70 and the weight W of 1 cu m of hot
gases at 1200°,
1 33
Pi2oo=1+i|200 kg = 0 kg 25,
from which
8 = 0.7 (1.29 - 0.25) = 0 kg 728 per square meter,
or 0 mm 728 of water, since the pressure of 1 kg per square meter
is equal to the pressure exerted by a column of water 1 mm in
height.
Experiments which may be readily made will show that the
light hot gases which fill the furnace are actually exerting a pres-
sure greater than that of the atmosphere.
Open the register connected with any hot-air house-heating
system. A jet of hot air escapes with some force. What is it
that sets this air in motion? What is it that provides the
energy necessary for this motion?
Open the sight hole located at the upper part of an open-
hearth regenerator chamber. If the regenerator is not connected
(1) Refer to Appendix II.

14         APPLICATION OF THE LAWS OF HYDRAULICS

with the chimney, a jet of incandescent gas or air will escape with
considerable force.    What is it that sets this in motion?
Open the bell of a gas producer working with natural draft;
the producer gas will escape. What is the force which causes the
air to pass through the bed of wood or coal, where it is transformed
into gas, and which, in addition, has sufficient pressure to produce
the jet of gas?
From the fact that enclosures filled with a cold gas, but one
which is lighter than the air, always exert a pressure higher than
that of the atmosphere, it follows that the preceding phemonena
are due not to the temperature of the gas, but to the fact that it
weighs less than the air.
Take, for example, a balloon 10 m in diameter, filled with

hydrogen (Fig. 11). Com-
pute the hydrostatic pressure
of the gas at the top of the
sphere. This balloon being
open at the bottom, at the
level A A the gas is in equilib-
rium with the air, their pres-
sures being equal.
Consequently the weight
of a column of cold air 10 m
in height (1 kg 29 X10 = 12 kg
90) is held in equilibrium by
the weight of a column of
hydrogen 10 m in height plus
a certain hydrostatic pressure 5 which may be determined.
The weight of a cubic meter of hydrogen being equal to 1.29X
0.06927, the following equation is obtained:
1.29X10 = 1.29X0.06927X10+5; 5 = 12 kg 006,
which is in the neighborhood of 12 mm of water.
It is on account of this hydrostatic pressure of the hydrogen
at the top of the balloon that it is necessary to employ a very
strong material in the making of this envelope. It is this pressure
which causes the balloon filled with hydrogen to ascend and
which furnishes the energy for the flow of the hydrogen when the
valve at the top of the balloon is opened to permit it to escape.
Furthermore, children are often amused by making small hot-air

APPLICATION  OF THE LAWS OF HYDROSTATICS

15

balloons of paper, which are then filled by the hot air rising from a
samovar or a lamp. Many readers will undoubtedly recall the
circumstances attending the launching of such a balloon; the
hot air enters the balloon, expanding its envelope, and the balloon
tends to fly. This would not happen if the pressure in the balloon
were not higher than the atmospheric pressure.
The question of this hydrostatic pressure, existing in all
enclosures filled with a gas which is hot and for that reason lighter
than air, is the basic one of the hydraulic theory of reverberatory
furnaces. It is therefore desirable to give another example which
occurs in daily life.
In a building piped for both gas and water it is very evident
that the hydrostatic pressure of the water will be greater upon
the lower floors than it will be upon the upper floors. Will it be
the same for the gas? If, for example, the gas upon one floor has
a pressure of 25 mm of water, what will be the gas pressure 10 m
higher?

Assume that at the stopcock R (Fig.
12) the gas pressure is equal to that of the
atmosphere. The pressure of the column
of air per unit of surface, which is equal
to (1.29 X10) kg, will be held in equilibrium
by the weight of the column of gas 10 m	L
in height, increased by the hydrostatic
pressure 6 of the gas; the weight of a cubic
meter of the gas is equal to 1.29X0.4, from
which

1.29X10 = 1.29X0.4X10+6,
d = 7 kg 74 per square meter.
fig. 12.
But the pressure of the gas at the point
R is not only equal to the atmospheric
pressure, but exceeds it by 25 mm.
It is therefore necessary to add to both sides of the equation
+25 mm. It follows that the gas pressure at the point B (since
1 kg per square meter is equivalent to 1 mm of water) may be
expressed as follows:
5+25 = 32 mm 74,
that is to say, the pressure of the gas at the higher floors of the

16         APPLICATION OF THE LAWS OF HYDRAULICS
building is always greater than it is on the lower floors. The
increase of the pressure in the case of gas is the inverse of that
which occurs with water.
In Hutte, in the chapter upon illuminating gas, the following
statement occurs: " A rise (or a drop) of 10 m in height in the
mains corresponds to an increase (or a loss) in pressure in the
neighborhood of 7 mm of water column." <X)
The following rule, to be followed in the location of a gas
works is given in order that there may be a uniform pressure in
the holder and throughout the distributing system: " The gas
works, should be installed at the lowest point in the system and
should be so located that the highest point in the supply system
is furthest from the works, and the lower parts are closer to the
works; under such conditions the loss of gas pressure due to
friction in the mains is compensated for by the increase of the
hydrostatic pressure in the piping, in proportion to its distance
from the works and its elevation above their level/7
The existence of hydrostatic pressure in the gas having been
established, it is now possible to take into exact account those
phenomena which are presented in metallurgy.
(a) The Draft Fallacy of Metallurgical Furnaces.—It was
believed for a long time that furnaces having a natural current
of air through them operated through the effect of their chimneys.
This is an error due to a poor interpretation of the facts. One
of the first principles which must never be forgotten is that the
only furnaces which operate by the draft provided by the chimney
are those which have no working doors or openings for the charging
of material to be heated. Furnaces of this sort include boilers,
entirely enclosed in a setting built of brick or other material,
crucible melting furnaces which are very nearly hermetically closed
up, iron tube air heaters (formerly used for heating the air at
blast furnaces), the Cowper hot blast stove, etc.
Furnaces which have working doors to their laboratories or
heating chambers, such as reverberatory furnaces, melting fur-
naces, puddling furnaces, brick kilns, Siemens furnaces of all
kinds (open-hearth and others), do not operate by the draft of the
chimney. The chimney connected with these furnaces is only an
apparatus for removing the products of combustion from the
laboratory. The colossal chimneys which are very often seen are
C1) Vol. II, p. 869, French edition of 1911.

APPLICATION  OF THE LAWS OF HYDROSTATICS        17
frequently unnecessary for this purpose. Therefore all of those
furnaces which are provided with working openings or doors
operate without " draft.77 This fact will be established.
Consider any reverberatory furnace (Fig. 13) when in operation.
The doors are never hermetically tight to the walls, and a flame
or sting escapes from the interstices at the top of the door. If a

fig. 13.

lighted torch is held close to the upper part of the door its flame
will incline away from the crack. On the contrary, if the. torch
is held close against the crack at the lower part of the door, it will
be noticed that the flame will be drawn into the furnace. It can
be stated, therefore, that immediately below the roof of the
furnace the pressure of the hot gases inside the furnaces is higher
than the atmospheric pressure at that level; whereas, at the level
corresponding to the lower
part of the furnace the pressure
of the hot gases is less than
the atmospheric pressure, that
is to say, negative with regard
to the pressure at the roof of
the furnace.
i
If two openings are made
in the walls of this furnace
(Fig. 14), one at the level of
the sole, the other at the level	fig. 14.
of the roof, the phenomena
will be the same.    By the lower opening the external air will be

18         APPLICATION OF THE LAWS OF HYDRAULICS
drawn into the furnace, whereas from the upper opening a tongue
of flame will escape. From this it might be concluded that if
an opening m were made halfway between the top and the
bottom of the wall of this furnace, there would be no tendency for
the air to be drawn into the furnace nor for tongues of flame to
escape.
In reality the phenomenon which occurs is slightly different.
At this opening m, the outer air will sometimes be drawn into the
furnace and at other times small jets of flame will escape, as the
pressure within the furnace varies. That is, the level at which
the pressure in the furnace is in equilibrium with the atmospheric
pressure shifts vertically, now above and now below the level of
the opening m.
These simple observations show that the pressure of the hot
gases within the laboratory of a metallurgical furnace provided
with working openings or doors is, on the average, equal to
atmospheric pressure. These pressures may be directly measured
by the use of a manometer.(1)
Let it now be considered whether it would be possible for a
metallurgical furnace to work in a regular and uniform manner if
the pressure of the hot gases within the furnace were less than the
atmospheric pressure. If the foregoing occurred, an enormous
quantity of cold air would be drawn in through the working doors.
When this occurred, the depression due to the chimney draft
would be entirely overcome. And, further, by reason of this
inrush of cold air, the temperature of the furnace would be lowered
to such an extent as to produce a very bad effect upon the working
of the furnace. In addition, this would be likely to damage the
brickwork of the furnace.
In order to understand the working of those furnaces which
operate with a natural current of air it is not necessary to take
into account what is called the " draft of the chimney," the only
function of the chimney being to remove the burned gases from the
heating chamber, in order to provide space for the new or burning
gases. By placing this construction upon the question of chimney
(1) Extensive observations covering the temperatures and the pressures at
various points in an open-hearth furnace have been made by E. Juon, at the
Donetz-Jurjewka works, Russia. M. Juon's paper appeared in Stahl und
Eisen, Oct. 24 and Nov. 7,1912. It was abstracted in The Iron Age, Dec. 26.
1912.

APPLICATION OF THE LAWS  OF HYDROSTATICS

19

draft, it becomes possible to take into account the manner in
which metallurgical furnaces operate.
The pressure of the gas within the laboratory of the furnace
is zero. The firebox acts to pump the elements necessary for the
formation of the flame into the furnace, and the chimney acts to
remove the products of combustion. This is the case with all
such furnaces and with all systems of heating, whether simple
coal-fired or using producer gas with or without the recuperation
of the heat. This rule is also applicable to coke ovens, to kilns
for the burning of brick or for the calcining of ores.
Each firebox acts as a force pump, functioning in the following
manner: assume that the firebox A (Fig. 15) is filled with gas at a
temperature of 1200°, that is to say, the specific weight of this

fig. 15.
gas will be about one-fifth the weight of air. Under these condi-
tions each particle of air which is near the grate is acted upon,
on the side of the furnace, by the pressure of a column of gas h,
which is only one-fifth the weight of that which acts upon it on the
side exposed to the outside air. It is evident that a current
of air will be established by the action of this positive pressure,
which will be equal to the difference between the weight of a
column h of the outside or cold air and the same column of hot
gases.
The height of the column has been taken as h and not as 7iT,
because, in the furnace chamber, the current of hot gases rising
from the firebox must always be taken with regard to the hearth
level.
The positive pressure which is measured by the height of the
column h is expended: (a) in overcoming the resistance of the
bed of fuel to the passage of the air and the gas; (6) in creating

20

APPLICATION OF THE LAWS OF HYDRAULICS

the velocity with which the gases and the flame flow, and which
also acts as a reserve force through their inertia.
In a number of types of furnaces this live force or velocity
is utilized to direct and force the flame or hot gases from the top
down upon the hearth of the furnace. It has been shown that
the cold external air has a tendency to enter the furnace through
the cracks or openings below the working doors; since this cold
air settles upon the hearth it acts as a heavy liquid flowing within
a chamber filled with a light liquid, the hot gases. However, the
material to be heated (ingots, faggots, billets, bars, etc., in the
furnaces for the reheating of small pieces of metal, the molten
metal of the open-hearth furnace, etc.) is always placed upon- the

fig. 16.
hearth.    Therefore it is necessary to overcome the formation of
such a current of cold air.   There are two means of doing this:
1.	Increasing the velocity of the   flame by increasing the
height h.
2.	Bending the flame sharply down upon the hearth as it issues
from the firebox, and in this way pushing back the cold air and
preventing it from entering the furnace through the openings below
the doors.
A furnace constructed to employ this second method is shown
in Fig. 16. The increasing of the head h provides a possibility
of increasing the thickness of the bed of fuel and of obtaining in
the firebox a producer gas at a slightly lower temperature. This
increase in the head of the column of gases also permits the mixing
of the producer gas from the firebox with a supply of preheated
secondary air, supplied through channels in the bridge wall.

APPLICATION  OF THE LAWS OF  HYDROSTATICS         21
Boetius and Bichcrou have utilized this method of firing in a
furnace invented by them and bearing their names.
When many of the various existing types of furnaces, such as
the continuous furnaces, Siemens furnaces, brick kilns, etc., an;
analyzed, it will be noted that their construction is such as to
preclude, in reality, the draft action of the chimney in drawing
in outside air and to limit the action of the chimney to the removal
of the waste gases. The drawing in of the cold outside air would
have an injurious effect upon the working of the; furnace, par-
ticularly in the case of brick kilns. Those furnaces, therefore,
constitute a perfect illustration of the fundamental principle of
the method in which metallurgical furnaces operate. It is well
known that the pressure of the hot gases in the; heating chamber
of such furnaces is practically equal to the pressure of the atmos-
phere. The gases coining from the; firebox and the supply of
secondary air, if such is necessary for the operation of the furnace,
enter the heating chamber under a pressure head which may br
measured by the difference in level between the grate bars and
the hearth of the furnace. The chimney for a metallurgical
furnace should be designed to provide for the removal from the
heating chamber of the burned gases, but it should riot, in addi-
tion, provide any further draft depression. On the; contrary, it is
always desirable that there should be a slight positive pressure1
in the heating chamber of metallurgical f urnacos.
(6) Hydrostatic Pressure within Metallurgical Furnaces and
their Flues.—1. All revcrberatory furnaces comprise a chamber
of some fixed height filled with incandescent gases. Ai, each
point in the interior of this chamber there will be a different
pressure, according to the height of the point. Therefore, in
a reheating furnace, having working doors with a height of
700 mm, with a pressure equal to that of the; atmosphere acting
at the hearth level, there; will be a pressure +0 mm 728 of water,
at the level of the top of the door, as has been shown previously
on page 13.
This pressure, in excess of that of the atmosphere, causes, as
is well known, the formation of a great aureole or " sting " of
flame due to the hot gases which escape through the crevices at
the top of the door. In order to diminish the loss of gases through
these crevices, the following means may be employed. By a slight
increase in the chimney draft, the level at which the pressure in

22

APPLICATION OF THE LAWS OF HYDRAULICS

the furnace is in equilibrium with the atmospheric pressure may be
changed to about the mid-height of the working door. This will
produce the following results: the pressure at the level of the
hearth of the furnace will be reduced below that of the atmosphere
and will be (— 0 mm 36), and air from outside the furnace will
commence to flow into it under the door; the pressure at the top
of the door will be diminished by one-half, becoming (+0 mm 36),
and the loss of hot gases will be diminished correspondingly.
2.	Hydrostatic pressure readily explains the irregular working
of sloping grates in gas producers fired with wood.    There is a
current of gas with such a grate, as indicated by the arrow at the
17.
right of Fig. 17. The
negative pressure which
exists at the level of
the horizontal grate
bars varies gradually
until it becomes posi-
tive at the top of the
sloping grate (compare
with page 141), under
which some of the gas
commences to escape
and burn, a pure loss of
energy. C1) The decrease
in the draft produced in
this manner also occurs with the sloping grates used under boilers.

This is the reason why
this type of   grate has
never   been   considered
satisfactory with natural
draft.
3.	The  existence   of
this hydrostatic pressure
readily explains the draft
of gas  producers which
operate without forced
draft, with the Siemens
siphon (Fig. 18).   The gas from the producer passes up through
(1) With forced draft and a closed ash pit, sloping grates work compara-
tively well.

L,

t     i

APPLICATION OF  THE LAWS OF  HYDROSTATICS        23
the masonry gas uptake with an average temperature of 600°,
thence into a long horizontal main constructed of steel plates,
where its temperature drops to approximately 300°. The gas then
flows down a vertical gas downtake to the underground gas flue,
which it reaches with a temperature of 200°.
Assuming that the height of the masonry gas uptake is 9 m
above the grate of the producer and that the producer gas has a
weight of 1 kg 07 per cubic meter at 0°, the hydrostatic pressure
of the gas at the top of the uptake will be
$coo = 9  1 . 29 ~Tinr) = 8 mm 64 of water.
\	-L T~ YY 3V
The average temperature of the gases in the downtake will be
In order to force the hot gas down through the vertical downtake
there must be an initial pressure at the head of the downtake
sufficient to overcome the hydrostatic pressure of the gases in
the downtake with an average temperature of 250°.
The resistance due to the hydrostatic pressure in the downtake
is
5250 = 9 (l . 29 - ^~^} = 6 mm 57 of water.
According to the foregoing the hydrostatic pressure of the gas
within the underground flue will be equal to
d= 5Goo--525o = 8. 64-6.57= +2 mm 07 of water.
As the frictional resistance of the gas mains and flues to the
passage of the gas is generally less than 2 mm 07 of water, the
Siemens " siphon " favors the " draft " of the gas producer. It is
evident that the draft on the gas producer would be stronger if
the length of the conduit were increased, as in this case the drop
in temperature in the horizontal section would be greater.
The position of the horizontal gas main, at a considerable
height above the grate of the gas producer, assures a pressure in
the main somewhat higher than that of the atmosphere, and this
constitutes a guarantee against the risk of explosions with gas
producers operating without forced draft. On the contrary, a

f	24	APPLICATION OF THE  LAWS OF  HYDRAULICS
V
J?
construction in which the gas flows directly from the producer
I	into the underground conduit or gas flue will always possess latent
v      '	possibilities of an explosion, because the gas in the producer will
*	be at such a low pressure that there will be a negative pressure in
the underground flue,  with producers working without forced
draft.
A gas producer with mains connected in this manner was
installed at the Alapayevsky works.    The producer was worked
without forced draft and the gas main was long.    When placed in
!|	operation this proved so dangerous that it became necessary to
replace the gas main with a metal main forming a Siemens siphon.
When this was done there were no more explosions.
4. This method of computing hydrostatic pressure may be
t	applied to the gas mains of a blast furnace producing charcoal iron.
These furnaces have very large bells for charging and the volume
of gas is relatively small.    The percentage of the gas lost by the
!	bells is considerable and increases rapidly as the pressure of the gas
i ;,	in the mains increases.    For this reason it is very important that
I"'	the mains should be designed to require the minimum of gas pressure
j	to overcome the unavoidable resistance to the flow of the gas.
I /	It is also possible to determine the excess of pressure required to
•;'	overcome the resistance created by poorly designed gas main, too
j|	small for the volume of gas flowing, having sharp bends, etc.
!''!	Assuming that the height of the furnace is 20 m, the height of a
I	cubic meter of the gas being 1 kg 22 and the temperature in the
!	main 200°, the hydrostatic pressure required at the top of the
|'i	furnace can be determined.    Assuming, on the other hand, that
I f	the gas is to be burned under boilers located 3 meters below the
!	hearth level of the blast furnace, the pressure in the gas mains
]	or the burners at the boiler after regulation and control, must not
1	be less than the atmospheric pressure.
The gas mains form an enclosure or chamber 23 meters in
height, filled with a' light gas which has the following weight per
cubic meter:
1 22
The hydrostatic pressure will be, therefore,
3 = 23 (1 .29 - 0.705) = 13 kg 45 per square meter,

APPLICATION  OF  THE LAWS  OF  HYDROSTATICS

25

or 13 mm 45 of water. This pressure of 13 mm 45 is absolutely
necessary, as well as a slight additional pressure to overcome the
friction in the mains and impress upon the gas the necessary
velocity of flow. In the case of a blast furnace producing char-
coal iron, the pressure at the head of the furnace was 35 mm of
water, the gas mains being too small and poorly designed. This
bad construction of the gas mains could not be corrected without
a general reconstruction. The method of arriving at the resistance
caused by friction in the gas mains will be given later,
(c) Hydrostatic Pressure in Open-top Chambers Filled with a
Light Gas.—If an inverted test-tube is held vertically (Fig. 1.9)

O
T

H,2

T

fig. 19.

fig. 20.

and filled with hydrogen the pressure at the level 00 will be equal
to that of the atmosphere, and at the upper part there will be a
positive pressure + <5. This experiment may bo modified by using
a vessel filled with hydrogen (Fig. 20) which has a capillary
strangulation at the top surmounted by a thistle, and a U tube
at the bottom. The capillary tube is sealed with a drop of water,
permitting the hydrogen to escape, when its pressure exceeds
that of the atmosphere, without, at the same time, giving free
communication between the interior of the vessel and the air.
It necessarily follows that the pressure in the interior of the vessel
at the level 00 is equal to that of the atmosphere. What will
be the pressure indicated by the manometer U tube filled with
water at K connected with the lower part of the vessel? Upon

26

APPLICATION OF THE LAWS  OF HYDRAULICS

the free surface of the water the pressure will be equal to the
pressure of a column of air whose height is measured by H+5
and whose weight is 1.29X(H+d) kg. This column of air is
in equilibrium with a column of hydrogen whose height is H
and with a column of water with a height <5, the existence of
which can only be explained by a rarefaction of the hydrogen in
the bottom of the vessel B. It is on account of this rarefaction
that the equilibrium at the top may be maintained by the drop
of water.
It is not difficult to compute the value of this depression by
	means of the general formula:
O	0
- 5 = #-1.29-0.06927-(ff+S)-1.29.

I
i    I

fig. 21.
It may be noted that this is what
takes place in all chimneys (Fig. 21),
which are simply open-topped en-
closures filled with a light gas. As in
the preceding case, the waste gases at
the base of the chimney have a pressure
less than the pressure of the atmos-
phere. This phenomenon is well known
as the depression produced by the
chimney. (1)
The following problem remains to be considered:
In the heating chamber of an open-hearth furnace the pressure
of the hot gases is in equilibrium with the atmospheric pressure.
From the heating chamber the gases at a temperature of 1600°
pass to the regenerators. There they give up a portion of their
heat and are finally reduced to a temperature of 400° at the
chimney. The weight of a cubic meter of these gases being 1 kg 30,
what is the hydrostatic pressure which will be found at the level
of the bottom of the regenerators, when the distance down from
the heating chamber is 6 m? From what has gone before it may be
seen that the pressure at the level of the bottom of the regenerators
will be negative. In order to set the hot and light gases in motion
and cause them to descend through the regenerator, the chimney
must draw these gases from the heating chamber and accordingly
C1) Note by English translator. — Very often the waste gases in the chimney
do not fill the entire area of the stack, due to their high ascensional velocity.

FLOW   THROUGH   ORIFICE	27
produce a depression at the bottom of the regenerator which will
be equal, neglecting the resistance to their flow, to

2.X 273
To sum the matter up, when a chamber is filled with a light
gas and the line at which its pressure is in equilibrium with the
atmospheric pressure is at or below the lowest point of the chamber,
the pressure in the upper part of the enclosure will be higher
than atmospheric pressure. If the line of equilibrium with the
atmospheric pressure passes through or above the upper part of
the chamber, the pressure at the lowest point in the chamber will
be negative. In other words: when a light gas ascends it will
create a pressure; conversely, to force a light gas to pass down-
ward, it is necessary to create a depression.
V. THE APPLICATION TO HOT GASES OF THE LAWS FOR THE
FLOW OF LIQUIDS THROUGH AN ORIFICE IN THE BOTTOM
OF THE RESERVOIR.
For water flowing into air the formula is:
in which Q= the volume of liquid flowing;
h= the head of the liquid above the orifice;
= the theoretical velocity of flow;
co = the area of the orifice;
/ci = the coefficient for the contracted vein, that is, the
ratio between the area of the contracted vein and
co (generally ki = 0.64) ;
/C2=the coefficient of velocity, that is, the ratio between
the actual velocity at the contracted vein and the
theoretical velocity (generally /C2 = 0.97).
If it is desired to apply this formula to the flow of kerosene
through an orifice in the top of a bell glass immersed in a vessel of
water, it is necessary to determine exactly what is meant by the
head A.

28	APPLICATION OF THE LAWS OF HYDRAULICS
Assume that a bell glass with an orifice of an area w, within
Water
which the kerosene is con-
stantly maintained at a
height PI (Fig. 22), is im-
mersed in water. Neglect-
ing, for the moment, the
coefficients of contraction /q
and of velocity /C2, which, for
this case, have not been de-
termined, the formula for
the flow will be simplified.
The hydrostatic pressure at
the orifice co will be equal
F    2r>	"k° ^ne weight of a column of
water H less the weight of
a column of kerosene of the same height, that is to say:
8 = H (Awater — Aj
A designates the specific weights corresponding to the indices.
But as this head must be given in meters of height of the liquid
which is flowing, the expression for the head will be

r —A;
^kerosene — *

kerosene
Aker<

Introducing this value of h in the formula for the volume
flowing, will give, for the volume of a light liquid (kerosene)
flowing through an orifice into a heavy liquid (water), the following
expression:

AWater —2

(A)

Passing to the case of the air and the gases in furnaces, this
expression will become

Q =

r — Ag
Agas

in which H designates the distance from the lower free surface
of the gas to the opening in the roof, or, as it may be said, the
thickness of the layer of gas.

FLOW   THROUGH   ORIFICE	29
This may be clearly seen by a reference to Fig. 2, in which is
given the orifice at the highest portion of the roof of the kiln
having an area «, such that the lower free surface of the layer of
kerosene in the model has become stationary at a distance H
below the smoke hole or orifice.
It is evidently desirable that the values of the coefficients
ki and *2 should be determined in order that they may be used in
the equation (B). The values of Q, o> and h may be determined
experimentally. Unfortunately this has not been done up to the
present.
For gases, in the case of comparatively large orifices, these
coefficients will probably approximate unity. This is the value
which has been assigned to these coefficients for the purpose of
solving the problems presented in this work.
The case shown in Fig. 2 may be especially called to the
attention of those who are operating reverberatory furnaces.
The author had the opportunity to verify this in the works of
Korniloff Brothers, at Petrograd, accompanied by Professor
J. G. Yesmann.W In the second story of the porcelain kiln (Fig.
85, page 114) where the waste gases passed out through the roof,
the lower free surface of the gases was clearly seen at a height of
from 1 to If meters above the hearth of the kiln. This lower
free surface of the layer of gases evidently might be forced down
as far as the hearth of the upper chamber by the obstructing of the
smoke hole in the roof of the kiln, as with the experimental models
which have been shown.
When the lower free surface of the layer of gases is brought
down into contact with the hearth of the kiln, it gives the nearest
approach to a uniform burn that it is possible to obtain with a
furnace operating in this manner, which is old and irrational.
Complete regularity of the burn cannot be attained, as has been
shown, except by the use of the downdraft system (Fig. 4).
Getting rid of the waste gases of combustion by means of an
opening in the highest part of the furnace was a method very
much in favor in former times ;<2> but in later furnaces this method
has been completely supersede*!. However, an example is given
C1) Professor of hydraulics at the Polytechnic Institute of Petrograd.
[Refer to p. 153 and following.
(2) Updraft furnaces are frequently employed in the manufacture and
smelting of copper, lead, and certain other metals.

8GG

8

30	APPLICATION OF THE  LAWS  OF  HYDRAULICS
of the  method of  computation which is used  for  an updraft
furnace.
From a reheating furnace at the Lougansk works (Russia) the
products of combustion, at a temperature of 600°, pass to a boiler
by an outlet port in the roof. The volume of these gases, based
upon the actual coal consumption per second, is computed as being
equal to $500 = 8 m3 58 per second, with an air supply equal to
one and one-half times the theoretical amount required. The
port in the roof of the furnace had a section of 2.5X0.6= 1 m2 50.
With these conditions fixed, at what distance below the roof will
the free surface of the layer of gases in the furnace be located?

8.58 = KHC2

Assuming /ci/c2 = l, V2g = 4A3, it will be found that
And therefore, according to these calculations, the distance
from the free lower surface of the gas layer to the port, in the
case of the gases flowing into the air, would be 896 mm. In the
furnace this distance actually was 800 mm.
This shows that the designers of this furnace had taken into
account a very old rule which says that if a reverbatory furnace is
to work well, the flame must KcA the hearth of the furnace. The
height of 896 mm not only assures the contact of the flame with
the sole of the furnace, but also permits, by the increase or diminu-
tion of the draft through the boiler, of the regulation of the
thickness of the gaseous current; that is to say, it provides a
means of drawing the flame up from the hearth or of forcing it
down against it.
Although the above computation has already been given, it is
repeated here that the port for the waste gases should never be
placed in the roof of the furnace. It is a bad system and one that
is now out of date. In the operation of those furnaces where

FLOW  THROUGH  ORIFICE	31
the waste gases are taken off by a port through the roof, the hot
gases cannot distribute themselves uniformly; the hottest currents
tend to rise and pass out of the waste gas port in the roof, and
there will be currents of cold and therefore heavy gases in the neigh-
borhood of the ingots on the hearth, which accordingly will not
be well heated.
Therefore the waste gases should always be carried away from
the heating chamber by a port at the level of the hearth of the fur-
nace; the colder currents of gases will then pass out of the heat-
ing chamber and their place will be taken by currents of hot gases;
under these conditions the ingots will be well heated. These
remarks apply to furnaces of all kinds, and are a general rule for
the construction of all furnaces of rational design. It has been
well established that the port for the waste gases must be located
at or below the level of the hearth of the furnace.
Returning to the computations, the equation (B) may be
considerably simplified, if it is assumed that the weight of a cubic
meter of waste gases is the same as the specific weight of air
(1 kg 29). This is very nearly true. Therefore,
1.29-1^-
Aair — Agas	1 +orf         .
""vr"=—iw—^-
l+at
Q = k-i *2co '\/2gIIott	((7)
The expression Hat is that of the velocity head ft, because
Therefore	h = Hat}
h_   t
and	#~273'
Therefore the ratio of the head required to generate the velocity
to the height H is equal to the ratio of the temperature t to 273.
This expression will be found used later in connection with
jets of gas, page 65.

32

APPLICATION OF THE LAWS OF HYDRAULICS

VI. RELATION BETWEEN THE HEAD, THE  PRESSURE AND  THE
VELOCITY  OF  CURRENTS   OF  LIQUIDS  AND   GASES
If the velocity of flow of any current is considered, as in a canal
or a river, it is a function of the head expended. As the bottom
or bed of a torrent of water is never smooth, the velocity of flow
is only maintained by the expenditure of a velocity head sufficient
to compensate for the velocity lost at the obstructions. The
water in a stream flows only when its free upper surface has a
sufficient slope or hydraulic gradient to cover the loss of velocity
due to the friction against the bottom and sides of the stream.
Therefore, there will be no flow or current unless there is a
corresponding loss of velocity head, and if there is a flow there will
be a corresponding loss of velocity head in impressing this velocity
upon the stream and in maintaining it.
If the velocity of the flowing current is v} then

v2
•«-,
and    /& = •«-

in which h represents the velocity head expressed in terms of the
liquid in motion (water, kerosene, liquid iron, mercury, etc.).
For example, when any liquid is impressed with a velocity of
flow of 4 m 43 per second, there will be required, according to
the formula, the expenditure of a velocity head h of 1 m. This
will be 1 meter in height of water, kerosene, liquid iron, mercury,
or of the particular liquid which is in motion.
If this meter of velocity head is expressed in kilograms per
square meter, it will be found that, for each of these different
liquids, a different pressure is required to produce the same
velocity of 4 m 43 per second, according to their density, as follows:

Liquid 	Kilograms
per square
meter 	Atmospheres 	Millimeters
of water 	
Kerosene 	800 	0 08 	800 	
Water 	 	1000 	0 10 	1,000 	
Liquid iron.                                . . . 	6,900 	0 69 	6,900 	
Mercury. .   .                           . 	13,595 	1 . 3595 	13,595 	

RELATION  BETWEEN  THE HEAD  AND  PRESSURE       33
From this it may be seen that without regard to the kind or
density of the liquid which is in motion, any particular velocity
will correspond to a velocity head, which may be absolutely
determined and which will be obtained by the formula
But the pressure necessary to impress motion upon a liquid
will be different for each liquid and is proportional to its density.
In considering the movement of gases, the same fundamental
principles must be observed:
1.	Motion or velocity of flow cannot be initiated or maintained
without a corresponding loss of head or pressure, as the loss of
head and the velocity impressed have the relationship of a cause
and an effect.
2.	Any particular velocity of flow corresponds to a velocity
head expressed in terms of the gas which is in motion, which may
be determined by the formula
3. Equal velocities will be impressed upon gases of different
densities by equal velocity heads, but by different pressures.
These pressures are proportional to the specific weight of these
gases or to the weight of a unit volume.
As the gases appear to act as a form of liquid having the
particular property of considerable variation in its specific weight
according to changes in its temperature, the third principle is of
great importance in all computations relative to the circulation
of the flame or hot gases.
The following examples will illustrate this point:
A. In the heating chamber of an open-hearth furnace the hot
air emerges from the port with a velocity of 18 m per second at
a temperature of 1000°. What is the pressure required to impress
this velocity upon the air?
To impress a velocity of 18 m per second upon a fluid will
require a velocity head h—16 m 51.^
In this case it is air at 1000° which is in motion; the weight
of 1 cu m of this gas is
1 ^9
Aiooo = 1+Vy^ = 0 kg 277.
(1) Refer to Appendix III.

f

34

APPLICATION OF THE LAWS OF  HYDRAULICS

A column of air 16 m 51 in height at a temperature of 1000°
produces a pressure per square meter of

or

= 0.277X16.51=4 kg 57 per square meter
6 = 4 mm 57 of water.

Therefore, in order to impress upon the hot air emerging from
the port a velocity of 18 rn per second it is necessary to provide a
pressure acting upon that air of 4 mm 57 of water column. This
is the hydrostatic pressure created in the regenerator chamber
and the vertical uptakes, or flues leading to the port, which are
filled with hot air.
If it is assumed that during the passage of the air through
the regenerator checkerwork and through the uptake there is no
loss of pressure due to friction or other causes the vertical height
required to produce this pressure may be computed. The value
found in this manner will evidently be too small, since actually
the resistance and friction through the regenerator and uptake
cannot be neglected.
Assuming that the air at the bottom of the regenerator has a
temperature of 50° and the temperature at the heads is 1000°,
the average temperature will be 525°. The hydrostatic pressure
which this will give is
5=4.57 = 7^" -      1'29
from which the value of H = 5 m 37.
Therefore the vertical height of the regenerator and the gas
or air uptake should not be less than 5 m 50 or thereabouts, as
only a regenerator and uptake having a height greater than this
will be able to supply the hydrostatic pressure sufficient to impress
upon the air in the heads a velocity of 18 m per second.
The fundamental points of the mechanics of the circulation of
the gases in furnaces have now been stated. The following is a
brief summary of the principles involved:
The chambers of furnaces filled with hot gases create in their
upper parts a positive hydrostatic pressure which expends itself
or is absorbed in impressing upon the hot gases the velocity
necessary for their circulation in the furnace.
There are two causes which act to retard or absorb the velocity
of the hot gases:

RELATION  BETWEEN THE  HEAD  AND  PRESSURE       35
1.	The friction of the gaseous currents against the walls of the
chambers and  flues,  which has  not  been  considered  in these
computations, as sufficient data have not been available to estab-
lish the value of the coefficient.(1)
2.	The effect of changes in the direction of flow.
In the computations made for ventilating ducts it is considered
that a change in direction of 90° introduces a resistance equal to
the velocity head, or that all of the velocity of the flowing gases
will be lost or absorbed. If this is correct a change in direction
of 180° may be considered as equivalent to two changes in direction
of 90°, that is to say, it may be assumed that the resistance offered
will be equal to twice the velocity head. A change in direction
of 45° may be assumed as offering a resistance equivalent to 0.6
of the velocity head/2)
The following method is employed in approximating the resist-
ance occasioned by changes in the velocity of the gases by reason
of their passing from a larger to a smaller or a smaller to a larger
flue or passage.
If a gas flows from a small channel into a larger channel or
chamber there will be a change in velocity from Fmax to Ymin, and
there will be no loss of head; but, when the gas passes from a
larger channel into a smaller channel a sufficient velocity head will
be required to impress upon the gas the increase in velocity
required.
The computation of the resistance offered by the checkerwork
of a regenerator is given below as an example. This checkerwork
is composed of vertical channels, those in one tier being 120 mmX
60 mm and in the alternate tiers 60 mm X 60 mm.
The velocity of the gas in the smaller channels is" Fmax and
in the larger channels Vmm, so that
	  V max
mln	?)    *
C1) This lack has recently been supplied, in part by W. A. Mojarow, in a
paper on the "Friction of gases in brickwork flues" in the Rev. de la Societe
russe de Metallurgie, 1913, No. 3, pp. 325-370; Revue de Metallurgie, XI bis,
May, 1914, P> 820. Appendix IV.
(2) Considerable data covering the flow of air may be found in, Le Chauflage
Industrielle by H. Le Chatelier, p. 47? & seq. D. Murgue "On the loss of head
in Air Currents in Underground Workings. Trans. A.I.M.E., 1898, Vol.
XXIII. Appendix V. (Notes et Formules p. 1090 et seq.)

-' I
I     '   !

36

APPLICATION OF THE LAWS OF HYDRAULICS

I

When the gas passes from a larger channel into a smaller
channel the velocity changes from 7mm to Fmax- If the velocity
Fmm corresponds to a velocity head Amm and Fmax to a velocity
head hmaiK} then to produce the increase in velocity from Fmto to
Fmax a velocity head will be required equal to /tmax~^min.
This quantity represents the resistance, or the velocity head
required by one tier of the checkerwork.
If there are N tiers, their total resistance or velocity head
required will be
5=

in which At is the weight of 1 cu m of the gas in motion at the
temperature t.
B. What will be the velocity head required to overcome the
resistance offered by the changes of velocity of the air in passing
through a checkwork 6 m in height (52 tiers)? The average
temperature of the air is

50+1050

= 550°.

The velocities are Fmm = 0 m 50 per second, Fmax=l rn 00 per
second.
The weight of 1 cu m of air at a temperature of 550° is
Fmm =0 m 50 per second corresponding to hmln = 0.01274,
Fmax=l m 00 per second corresponding to Amax = 0.05097,
from which
ftrnax -fcmta = Om 03823 ; ;
&-egen = 0.03823X52X0. 43 = 0 mm 85 of water.
And therefore the resistance due to changes of velocity in the
checkerwork is equal to 0 mm 85 of water column, while the
regenerator 6 m in height produces a hydrostatic pressure of
A = 6(1. 29-0. 43) =5 mm 16 of water.

RELATION BETWEEN THE HEAD AND PRESSURE  37

So that, in the regenerator chamber, neglecting the resistance due
to surface friction, the pressure of the air will increase to
5.16-0.85 = 4 mm 31 of water.
The foregoing considerations being kept in mind, the working con-
ditions within the open-hearth furnace may be analyzed.

fig. 23.
Fig. 23 shows a model reproducing the longitudinal vertical
section of an open-hearth furnace. This model is placed between
two sheets of glass and
immersed in a glass
tank filled with water;
colored kerosene is cir-
culated through the
model. The mechanics
of the circulation of
the gases within this
type of furnace are
clearly shown: the re-
generators by heating
the air and the gas
produce a positive hy-
drostatic pressure. It
is this pressure which
impresses their veloci-
ties upon the gases in
motion; it is com-
pletely absorbed in
overcoming the friction
in the uptakes, etc.,
and in producing the
velocity with which the
gases enter the heating
chamber of the furnace.
In the heating cham-
ber, the gases have a
very small velocity, and their hydrostatic pressure is, on the
average, equal to the pressure of the atmosphere, which must
be the case, by reason of the number of working doors and
openings.
The descent of the light gas through the uptakes and regen-

•;

38	APPLICATION OF THE LAWS OF  HYDRAULICS
erators, and its passage through the flues and reversing valves
to the base of the chimney, commences at the heating chamber
where the hydrostatic pressure is equal to that of the atmosphere.
In order to draw the light gases downward to the bottom of the
regenerator chamber, it is necessary to establish a negative
hydrostatic pressure or draft depression at that level.
This is the function of the chimney, which, therefore, has a
double purpose:
1.	To draw the hot gases down to the bottom of the regenerator.
2.	To impress upon them the necessary velocity and to over-
come the losses of head due to changes in the direction of flow,
changes in velocity and the friction against the walls of the flues,
etc., in this portion of the furnace.
The computations for reverberatory furnaces, based upon the
laws of hydraulics, were included, some time ago, among the
obligatory exercises.for the students in the metallurgical section
of the Polytechnic Institute of Petrograd; as a result of this, a
very large number of these furnaces in the workshops of Russia
have been recalculated. Ordinarily the problem, as given,
involved the computation for furnaces actually in use within the
different plants, based upon the daily consumption of fuel. The
volume of producer gas being determined, the volume of the
products of combustion was calculated. This was usually based
upon a secondary air supply one and one-half times as great as the
theoretical air supply. The analysis of these furnaces actually
in service has shown the following:
1.	That open-hearth furnaces of defective construction were
subject to a rapid filling up of the regenerators, and for this reason
served only during comparatively short campaigns; the velocities
were too great, and the hydrostatic pressure of the hot air and
gases was barely sufficient to produce the necessary velocity.
Sometimes these computations showed negative results, that is to
say, the calculations showed that forced draft was necessary for
operation of the furnace.   But, nevertheless, the furnace worked
without forced draft, though in a defective manner which caused
trouble.    It follows, therefore, that these methods of computation
have in themselves a certain factor of safety.
2.	The gas regenerators and the air regenerators should receive
different volumes of the waste gases.    In computing these two
quantities of gas, it was found that the draft depressions necessary
1.	
RELATION  BETWEEN  THE HEAD' AND  PRESSURE      39
to cause these volumes of the gases to pass into their corresponding
regenerators were, in a great many furnaces, nearly of equal value.
On the contrary, for American furnaces, where the air passes
through the port with a velocity of about 8 m per second or a
little more, and the gas attains a velocity of about 58 to 60 m per
second, the chimney' drafts required for the regenerators for air
and for gas have very different values.
This, therefore, explains the necessity of having different dampers
or regulating valves for controlling the draft upon the regenerators
for gas and those for air.
In a general way all the computations made have confirmed
this conclusion.
3. Occasionally, but very rarely, there has been found an open-
hearth furnace in which the air and the gases had a hydrostatic
pressure which was greater than was necessary (Lysva Works,
Oural). This is due to the low velocities in the furnace and to the
large size of the reversing valves employed. M
When furnaces of this kind are new it is necessary to work with
the air and gas regulating valves partially closed. After the
furnace has been in use for some time the cinders and dust com-
mence to obstruct the checkerwork, and the supplementary resist-
ance due to the regulating valves may be decreased. This per-
mits the furnace to be operated with the regenerators badly
obstructed.
This also explains why, in certain works, the checkerwork has
to be renewed after one hundred to five hundred heats, while in
other plants, the regenerators last six months or more. When
there is an excess of hydrostatic pressure of the gases, there is the
possibility of controlling the operation of the furnace, and of
utilizing the air and gas valves as rheostats, which permits the
prolonging of the campaign of the furnace. Therefore, the
computation of the hydraulics of the gas in the open-hearth furnace
supplies the criteria for their construction. These calculations
make it unnecessary to have extensive tabulations of the dimen-
sions and proportions of actual furnaces, with which so many
metallurgists burden their memories and notebooks.
(1) Strangulation of the furnace due to the small size of the reversing
valves is one of the principal defects in reversing furnaces.

40

APPLICATION OF THE LAWS OF HYDRAULICS

VII. THE   APPLICATION   TO   HOT   GASES   OF   THE   THEORY   OF
HYDRAULIC  FLOW   OVER  THICK-CRESTED   WEIRS.
In a large reservoir from which there is a flow over a weir of
Q cu m of water per second there will be established at a constant
height H above the sill of the weir, a water surface which supplies
the hydraulic gradient necessary for the flow (Fig. 24). The

i i

fig. 24.
depth of the water flowing over the weir will be determined by the
formula:
There is also the formula
Q = 0.356 V2gH*,
from which

CD)

\

in which b signifies the length of the weir.
This formula makes possible the determination of the depth
of the channel connecting two basins of water, and applies equally

to  the   depth   of  all  streams
whose  bed   presents  a  grade
sufficient to compensate for the
inevitable friction losses of flow.
Each reverberatory furnace
having a horizontal roof forms
the bed of an inverted stream,
fig. 25.	in which there flows, not water,
but hot gases (Fig. 25). Re-
verberatory furnaces, in order that they may function properly,
must be so designed as to take account of the following facts:
All of the material which is to be reheated in the furnace is
placed upon its hearth. Much heat will be lost in the reheating
of this material, as well as by radiation from the walls. The

INVERTED   WEIR	41
furnace must, therefore, be strongly heated by the hot gases;
and this is not possible unless the nappe or free lower surface of
the current of hot gases is in contact with the hearth of the furnace,
or, as it is expressed in the shop, unless the flame licks the hearth.
This fact supplies the method by which reverberatory furnaces
may be proportioned by computation. It is evident that, in
furnaces working in the most satisfactory manner, the depth of the
inverted gaseous stream must be equal to the height of the roof
of the furnace above the hearth. Referring Lo Fig. 25, h repre-
sents this height.
The formula giving the depth of the gaseous stream has been
established in a brilliant manner by J. C. Yesmann/1) to whom we
are indebted for the mathematical study of this case. In his
work/2> it is shown that the formula (Z>) cited for water, becomes
for gases
in which ht represents the depth or thickness of the layer of gas
in motion; Qt, the volume of gas flowing in cubic meters at the
temperature t; B, the length of the weir over which the gas flows,
the inverted weir (the width of the furnace).
The coefficient A is different for each value of ht and the length
B of the inverted weir. The values of these coefficients are given
in the following table: (4)
ht=         0.30	0.50	0.75	1.00
5 = 1.00 2.00 5.00 1.00 2.00 5.00 1.00 2.00 5.00 1.00 2.00 5.00
A=3.42 3.54 3.62 3.29 3.46 3.57 3.13 3.37 3.54 2.97 3.28 3.53
According to this, in making the computation for a reverbera-
tory furnace it is considered as an inverted weir of which the depth
above the crest is determined by Yesmann's formula.
For the motion of the gases flowing through horizontal flues
and under the straight horizontal roofs of continuous ingot heating
furnaces, this formula will give results which very closely approach
those obtained in practice. For ascending roofs, the actual
thickness of the layer of gas will be less than the value obtained
C1) Eevue de la Societ& russe de Metallurgie, 1910, pp. 819-348, and Ann.
de I'Inst. Polyt. de Petrograd, 1910,
(2)	Refer to Appendix I.
(3)	For this formula in English units refer to p. 193.
<4) For coefficients in English units refer to p . 257.

42'         APPLICATION OF THE LAWS  OF HYDRAULICS
by the Yesmann formula. For descending roofs, it will be greater.
In his work, Professor Yesmann has given the mathematical
expression for the first case, but he has introduced certain coeffi-
cients of friction for which no accurate data exist at present.
In what measure is actual usage found to accord with this
formula. For verifying Yesmann's formula, a test furnace has
been built at the Polytechnic Institute of Petrograd; but during
the time that it has been in service it has been impossible to
obtain a gaseous current with a lower free surface or nappe which

2.8

Scale A =
3.0      S.I

3.3

3.5        3.6

in
meters
0.5
0.75
1.0
Y
fig. 26.—Values of Coefficient A.
was free from eddies. In this current of gases the surface is mixing
with air. For this reason the measurement of the thickness of the
gaseous stream is difficult. It is hoped that this difficulty may be
overcome, and that it will be possible to effect the verification of the
formula for the flow of gases under inverted weirs by accurate
methods. In the meantime, Yesmann's formula has been tested
by application to furnaces which were in use. The tests have been
based upon the assumption that since the furnace works well and
the shop is satisfied, the hot gases which flow in the inverted chan-
nel must lick the hearth of the furnace in a satisfactory manner.
The reverberatory furnace itself forms a true inverted channel

INVERTED  WEIR

43

for the flow of the gases. In analyzing each of these furnaces,
the research has been concerned with the principal dimensions.
It has been found in the course of this work that, in many furnaces,
the dimensions which seemed to be the least important have the
most important effect, and conversely, that those to which great
importance had been attached were of no significance.

}

fig. 27.—Furnace N.
It is also clearly apparent that these methods make it possible to
regulate accurately the quantity of fuel consumed and diminish
it accordingly, in many cases, by slight corrections applied to the
furnace.
As an example of the method of computation and of its impor-

fig. 28.—Lyswa Furnace.
tance, the calculations are presented for a continuous heating fur-
nace in the N M works, using a very good grade of English coal,
and a similar furnace at the Lyswa works (Oural), using a coal
from the Kis61ow mines, having 25 per cent of cinders or ash and
3 per cent of sulphur. The defects in these furnaces and the
methods used in improving them were plainly shown by these
computations. (Refer to Fz^s. 27 and 28.) Computations tabulated
on page 45.)
It may be seen, from the  computations for "the furnace N
(1) A large Russian Works.

44         APPLICATION OF THE LAWS OF  HYDRAULICS

il
h

I

(Fig. 27) that the flame follows the hearth of the furnace, if the
furnace does not hold any ingots, and this is very nearly what may
be actually seen in this furnace.
In the furnace at the Lyswa works (Fig. 28) there has been
found to be a complete identity between the actual and calculated
heights of the strangulating ridges in the roof above the hearth of
the furnace (calculated value 539 mm; actual dimension 525 mm),
but the dimension computed for the height at waste gas ports was
considerably less than that in the furnace. When these conclu-
sion had been reached, A. J. Onoufrowitch, managing director of
the works in the Lyswa district, was asked the following questions
regarding the details of the work of this furnace :
1.	Have the strangulations in the roof any effect in forcing the
hot gases down on the hearth of the furnace?
2.	Do the gases seem to remain at a short distance above the
hearth of the furnace at the waste gas end?
A reply was received giving the following facts concerning the
record of this furnace:
The furnace had been originally constructed without strangula-
tions and worked very badly. The managing director had then
dropped portions of the roof a sufficient distance to bring the hot
gases down to the hearth. He stated that he had been led by
trial to give this lowered section a height of 525 mm (Fig. 28),
the thickness of the layer of hot gases in the furnace chamber.
To the second question he replied that the furnace had not
worked well at the end connected with the chimney (the rear end
of the furnace), the hot gases seeking the roof. He proposed to
correct this condition later by the removal of the present roof,
replacing it by a horizontal roof 150 mm lower; Ayoo would then
be equal to 500 mm.
This shows that Yesmann's formula has received a complete
confirmation in the computations verifying these two furnaces.
It is accordingly permissible to make some other comparisons.
QQAfi
The "N" furnace heated £=1.31 times the weight of
2 16
times the volume
ingots, but it consumed per second
of fuel burned at Lyswa; that is to say, per unit weight of ingots,
2 77
the consumption of fuel was -^-^=2.11 times greater in the
i. ol

i

INVERTED  WEIR

45

	N Furnace.
Fig. 27 	Lyswa Furnace.
Fig. 28 	
Dimensions of Hearth 	 	16X2. 1 =33 m2 6 	13X2 =26 rn2 	
Production per 24 hours . .       	 	f         3,800 pouds 	2,900 pouds 	
Per sous/re meter 	I       62,300 kg
1,860 kg 	47,400 kg
1 850 kg 	
Coal consumed per 24 hours 	f           800 pouds 	409 pouds -J 	
Coal consumed per second .       ... 	I       13,000 kg
0 kg 154 	6,700 kg
0 kg 079 	
Ratio between weight of coal and
weight of ingots  	 	21.1 per cent 	16 8 per cent 	
Gas volume per kilogram of coal
burned with 50 per cent excess
air supply                      	 	14 m3 04 	9 m3 89 	
Gas,  volume burned per  second
reduced to 0° 	Qo = 2m3 16 	Qo — 0 m3 78 	
Gas, volume burned per second at
/ = 1200°             .           	 		Q1200 = 4 m3 2 	
Height of roof above hearth at the
right of the strangulation, com-
puted by Yesmann's formula for
a temperature of 1200° 	 		hizooo ~ 0 m 530 	
Effective height 	 	 	 		0 m ffgff 	
Gas, volume per second at t = 700° .
Height of roof at chimney or waste
gas    opening    by    Yesmann's
formula £ = 700° 	Q7oo = 7m3697
/J,7QO   = ()    ft).    01 	Q700 = 2m3780
&7oo — Om 479 	
Effective heieht 	 	tnm-0 m,90 	h™ — 0 m 850 	
" N " works. To what may this greater fuel consumption be
attributed. Evidently to the greater height between the roof
and the hearth of these furnaces.
Why was it found necessary at the " N " works to raise the
roof to a certain height above the hearth, while at the Lyswa works
it was found necessary to lower the roof to accomplish the same
result? An examination of the design of the " N" furnace
(Fig. 27) leads to a negative conclusion. Indeed, according to
Yesmann's formula a furnace will require less combustible wb^n
the roof is closest to the hearth. Accordingly the roof should be
brought down as low as possible.
The hot gases consist of a mixture of air, combustible gases and
the products of their reaction upon each other. The combustion
takes place while the hot gafces are passing through the furnace;
C1) The quality of the coal is not considered in this computation.

46	APPLICATION  OF  THE  LAWS  OF  HYDRAULICS
the heat released, therefore, serves to heat the ingots and to
maintain the hot gases at a high temperature. If the flames, that
is to say, the mixture of combustible gases and air, in which the
reaction is taking place, impinge against the cold ingots, a deposit
of soot will be formed, and carbon, carbon monoxide and hydrogen
will pass off unburned through the waste gas port. It is evident
that such a method is not advantageous, as it is necessary for
combustion to occur in the heating chamber in order that the heat
may be utilized. From this effect it is evident that the flaming
gases should not be cooled while the reaction of combustion is
taking place or until it has been completed. On the contrary,
if the reactions of combustion are very nearly completed, the hot
gases produced may be cooled very rapidly.
The Lyswa furnace has a large firebox, allowing the producer
gas to mix perfectly with the secondary air.    On the other hand,
1 0 |	in the " N " furnace there is a very small firebox with very poor
| I	mixing of the producer gas and the secondary air.    The flaming
; '	gases from this firebox are forced directly down upon the ingots
I ;	without any precautions;   the production of soot is inevitable.
If	It is for this reason that these gases sweep along under the roof,
I f'	from the strangulation which is located immediately over the
bridge wall, to obtain a better mixture; and from this point on the
velocity of the gases is increased, thus diminishing the thickness
of the layer of gases below the arch. As a result of these condi-
tions, the furnace works very poorly.(1)
A furnace at the Zavertse works, where the height from the
hearth to the roof is only 350 mm, will serve as an example of a
continuous reheating furnace with a very low roof. This furnace
gives off enormous quantities of smoke when coal is placed in the
firebox. There is no flame in the heating chamber and the heat
there is not sufficient to ignite the gaseous products which are
given off in great volume by the fresh charge of coal as it is distilled
on the fire.
Continuous reheating furnaces, therefore, will not work well
with low roofs; on the other hand, the fuel consumption increases
very rapidly as the roof is raised. From Yesmann's formula it
can be deduced that
(1) The formation of soot by the cooling down of the flaming gases is partic-
I	ularly noticeable in open-hearth furnaces working with a charge of cold pig.

o
fa

o
CO ,

iil
48	APPLICATION  OF  THE  LAWS OF HYDRAULICS
I     [j	Moreover, according to this principle, the use of a roof sloping
i   I' ^ 1	upward tends to increase the velocity of flow of the hot gases and
'   (? > |	in this manner to decrease the thickness or depth of their stream.
1   . I,	They are thus kept away from the hearth, and the fuel consump-
I   ' ['	tion is increased, as it is necessary to increase the quantity of gases
flowing in order to force them to lick the hearth. At the same
time, these statements should not lead to the conclusion that con-
temporary continuous reheating furnaces cannot be reconstructed
so that they will work in a satisfactory manner.
Figs. 29 and 30 show a model of the " N " furnace immersed
in water; a stream of colored kerosene flows into the heating
chamber from the firebox. The two half-tones show the outflow
of the waste gases through openings pierced in the hearth of the
furnace. Fig. 29 shows that with this method of outflow of the
waste gases there remains upon the sole or hearth of the furnace
a layer of cold air. The rise of the hearth forms a pocket from
which the colder and heavier gases cannot flow by gravity. This is
a very serious defect of continuous reheating furnaces having the
roof and the hearth rising from the firebox end toward the charging
end. The ingots or billets heating on the hearth of the furnace
chill the gases, and these chilled gases cannot by any possibility
reach the chimney, since they are heavier than the hot gases.
In Fig. 30 the current of colored kerosene has been increased,
but it has not been possible to force out the water from the pocket
on the hearth, as the pressure has not yet become higher than the
water pressure, that is to say, the atmospheric pressure. When
this point is reached a portion of the kerosene escapes through the
interstice or small opening between the sheets of.glass forming the
sides of the model. It is evident that this is not a desirable
manner of working as the outflow of the chilled gases from the
hearth will take place through the working doors, instead of
through the waste gas opening to the chimney.
In practice, therefore, a furnace of this design will work under
the conditions shown in Fig. 29, and the ingots or billets will not
be well heated - except on their upper portion, since their lower
portion will rest in the layer of chilled gas on the hearth of the
furnace and the cold air drawn in through the working doors.
This prolongs the time required to heat the ingots, increases the
defects in the metal, etc.
The problem of the rational construction of the continuous

•18 '

50	APPLICATION OF THE LAWS OF HYDRAULICS
reheating furnace for ingots and billets was solved in a very
'	satisfactory manner by the designer of the American Morgan
furnace, which has a descending roof (Fig. 31, 32 and 33).    It is
rather interesting to know that Morgan was not led to construct
his furnace in this manner by consideration of the circulation of
'	the heated gases, but simply because it was found more convenient
to push the ingots up a sloping skid.    The ingots remained in
;	contact with one another when heated on skids with an upward
slope, a condition which was difficult to maintain when the skids
were level or sloped downward. It has been found that this
\,	construction with a roof sloping downward from the firebox end
I	of the furnace to the end at which the waste gases are taken off
\,	and where the cold ingots enter the furnace is the very best solution
; ,                           of the continuous reheating furnace problem.
< ;	It may be seen in Fig. 33 that producer gas at a high tempera-
I1	ture (1000° or thereabouts) and secondary air heated in recupera-
!!	tors enter the combustion chamber.    Here the mixture is burned,
| !	and the products of combustion, as they give up their heat, pass
* j	under the descending roof between the ingots resting on the
I *	water-cooled pipe skids, and descend into the recuperator tubes.
I j	In this furnace, the ingots are literally plunged into the hot
i
gases. The model which has been made shows, when immersed
in water and traversed by the stream of colored kerosene, that
there will be no drawing in of cold air at the working doors, and
that there will be no pockets of chilled and stagnant gases. On
j j	the contrary, the chilled gases fall upon a hearth a sufficient dis-
"l j	tance below the skids to insure the immersion of the ingots in a
| *	layer of hot gases, and from, this hearth the colder gases drain
I }	into the recuperator.    The photograph, Fig. 31, was taken while
] \	the model was being filled with- kerosene.    It shows extremely
^'	well how the hot incandescent gases from the flame fill the upper
portion of the heating chamber in a horizontal layer which increases
in thickness, and how these gases, as they cool, drop lower by
reason of their increase in weight. The cool gases fall away from
the ingots as they give up their heat to them.
The idea of the descending roof for continuous reheating furnaces
has come into general use in many plants.- In central Russia
there may still be found a number of older furnaces which have
roofs ascending from the firebox end, and some of which also have
a downward inclination of the roof at the opposite end.

52

APPLICATION OF THE LAWS OF   HYDRAULICS

The type of roof which should be chosen—ascending, descend-
ing or horizontal—will depend upon the result which is desired
from the furnace.
1.	A horizontal roof will give a high temperature at the firebox
end of the hearth and a low temperature at the rear end of the
furnace.
2.	If a higher temperature is desired near the firebox end of the
furnace,  and a diminishing temperature toward the rear end,
the descending roof should be used.    The firebox end will form a
high chamber, in which the flaming gases will remain for a short
period of time and where they will complete their combustion.
The hot products of combustion will drop below the hotter flame,
and as they gradually give off their heat and become cooler, will
descend in horizontal layers.    The coolest gases will pass from the
heating chamber by means of the waste gas port in the hearth of
the furnace.
3.	In certain cases it is necessary to maintain a uniform tempera-
ture throughout the length of the furnace; it is then necessary to
use an ascending roof.
In the author's personal practice the following case came up
for analysis: two steel boxes for the annealing of steel sheets were
heated upon the hearth of a furnace. The first box heated much
more rapidly than the second box, and the annealing of the sheets
was accomplished at a temperature which was much too high.
This peculiarity of the furnace caused considerable trouble to the
plant, and it was impossible to hold back the annealing of the
first box so that the annealing of the second box would be com-
pleted at the same time. The furnace was changed so that the
annealing of both boxes was completed at the same time and tem-
perature, by replacing the descending roof of the furnace by a
horizontal roof. This was done because the author had a ground-
less fear, at this time, of making an ascending roof, which would
have carried the total mass of the hot gases to the rear end where
they would have distributed themselves very effectively and
uniformly throughout the full length of the furnace.
Vm. VELOCITY IN INVERTED WEIRS.   RATIONAL CONSTRUCTION
OF FURNACES OF THIS TYPE
Yesrnann's formula provides a method of computing the
normal velocity of the current of hot gases in an inverted

VELOCITY IN INVERTED WEIRS

53

weir according  to the depth of the layer or stream of gases,
It is

or    Q = j

A3

in which o;=the area of the cross-section;
B = the length of the weir or width of the furnace;
ht=the depth or thickness of the stream of gases under
the inverted weir or the head at the crest;
t — the temperature of the hot gases;
Q = the volume of gases flowing;
A = a coefficient.
From which
h >i	;	n~~,
and    v==s \I~JT3
normal velocity of gas flow under inverted weir
B = 1 m 00 = width of furnace, corresponding to length of weir.

Al-
A =
t 	1 mOO
2.97 	Om 75
3.13 	0 m 50
3.29 	0 m 30
3.42 	

	Velocity, Meters per Second =?; 	
500° 	4.368 	3.497 	2.650 	1.936 	
600° 	4.785 	3.830 	2.913 	2.121 	
700° 	5.168 	4.138 	3.135 	2.291 	
800° 	5.526 	4.423 	3.352 	2.450 	
900° 	5.861 	4.691 	3.555 	2.598 	
1000° 	6.178 	4.945 	3.747 	2 . 739 	
1100° 	6.479 	5.186 	3.930 	2.872 	
1200° 	6.768 	5.417 	4.105 	. 3.000 	
1300° 	7.046 	5. 638 	4.272 	3.122 	
1400° 	7.310 	5.852 	4.434 	3.240 	
1500° 	7.566 	6.056 	4.589 	3.354 	
1600° 	7.814 	6.256 	4.739 	3.464 	
1700° 	8.055 	6.458 	4.885 	3.571 	
1800° 	8.288 	6.634 	5.044 	3.674 	
a- 	l.OOt; 	0.75/> 	0.50?; 	0.30?; 	
(For the values of A refer to page 41.)

54

APPLICATION OF THE  LAWS OF  HYDRAULICS

normal velocity of gas flow under inverted weir
B=2 m 00 = width of furnace, corresponding to length of weir.

ht = 	1 mOO 	Om 75 	Om 50 	0 m 30 	
A = 	3.28 	3.37 	3.46 	3.54 	
t 	Velocity", Meters per Second = v 	
500° 	3.764 	3.131 	2.462 	1.839 	
600° 	4.123 	3.428 	2.691 	2.014 	
700° 	4.454 	3.704 	2.823 	2.176 	
800° 	4.761 	3.959 	3.108 	2.326 	
900° 	5.050 	4.199 	3.296 	. 2.467 	
1000° 	5.323 	4.427 	3.474 	2.600 	
1100° 	5.584 	4.643 	3.677 	2.727 	
1200° 	5.832 	4.849 	3.806 	2.849 	
1300° 	6.069 	5.047 	3.961 	2.965 	
1400° 	6.299 	5.238 	4.140 	3.077 	
1500° 	6.520 	5.422 	4.255 	3.185 	
1600° 	6.736 	5.599 	4.394 	3.289 	
1700° 	6.941 	5.772 	4.530 	3.390 	
1800° 	7.142 	5.939 	4.661 	3.489 	
Qt = 	2.00/> 	1.50* 	l.OOw 	0.600 	
These tables shows that, for a horizontal roof, the velocity of
the hot gases ordinarily varies from 1 m 94 to 8 m 29 per second.
And, as in reverberatory furnaces, it is necessary that the hot gases
should remain in the furnace a sufficient time to give up heat to
the material being heated, in certain industrial heating applications
there will be found to be a relationship between the circulation
velocity of the hot gases and the application. But it is evident,
on the other hand, that there should be no necessity for accelerat-
ing the velocity of the hot gases, because this would lead to the
construction of extremely long furnaces.
A number of attempts have been made to determine the time
which is required for the transmission of the heat in the hot gases to
the materials being heated and to the walls of the furnace. Observa-
tions and computations have led to the establishment of two limits

VELOCITY IN  INVERTED WEIRS

55

normal velocity of gas flow under inverted wier
B = 5 m 00 = width of furnace, corresponding to length of weir.

fc.= 	1 mOO 	0 m 75 	0 m 50 	0 m 30 	
A = 	3 . 53 	3 . 54 	3 . 57 	3.62 	
t 	Velocity, Meters per Second —v 	
500° 	3.386 	2.908 	2.344 	1.778 	
600° 	3.709 	3.185 	2.568 	1.948 	
700° 	4.006 	3.440 	2.774 	2.104 	
800° 	4.283 	3.678 	2.965 	2.249 	
900° 	4.543 	3.901 	3.145 	2.386 	
1000° 	4.788 	4.112 	3.315 	2.515 	
1100° 	5.022 	4.312 	3.477 	2.638 	
1200° 	5.246 	4.504 	3.631 	2.755 	
1300° 	5.460 	4.688 	3.779 	2.86 	
1400° 	5.666 	4.865 	3.923 	2.976 	
1500° 	5.864 	5.036 	4.060 	3.080 	
1600° 	6.057 	5.201 	4.193 	3.181 	
1700° 	6.243 	5.361 	4.322 	3.279 	
1800° 	6.424 	5.516 	4.448 	3.374 	
Qt= 	5.00?; 	3.75?; 	2.50v 	1.50v 	
for the drop in temperature of the gases per second. The method
of determining the rate of the drop in temperature is as follows:
The difference between the theoretical calorific intensity, or
temperature, of the combustible and the temperature of the
products of combustion leaving the heated zone is divided by the
time in seconds which the products of combustion remain in
the heated zone. This gives the average drop in temperature of
the gases per second.
For open-hearth furnaces this drop in temperature has been
found to be from 200° to 250° and for large brick kilns with a
spherical roof—down draft—from 70° to 80° per second.
Therefore, taking 1500° as the temperature produced by the
combustion of a coal with an air supply 1.50 times the theoretical
requirements, and 600° as the temperature of the products of com-

56

APPLICATION OF THE LAWS OF HYDRAULICS

I I
I I
I	}

bustion leaving the heating chamber, there is a temperature drop,
or cooling of the gases in the heating chamber, of 9()()°7 that is to
say, the gases remain in the* chamber only four or five seconds.
If these data are considered in connection with an ordinary type
of continuous heating furnace for ingots, in which the lower free
surface of the gases is in contact with the hearth of the furnace,
and the height from the hearth to the* roof is 0 m 75, the velocity
of the gases entering the heating chamber will be 5 m 41 per
second and of those leaving the chamber 3 m 42 per second.
The average velocity will be
5.41+3.42    ,       .t	T
___^™_-==4 ni 41 por second;
Z
from this it may be determined that the length of such a furnace
will be from 17 m 00 to 22 m 50.
Therefore, when the velocity of the current of hot gases must
be limited to very small values the result will be a long heating
chamber.
One of the many defects in the olden* types of roverboratory
furnaces was the constriction of the opening over the bridge wall
where the hot gases entered the furnace. This resulted in an
impinging current of burning gases arid the rapid cutting away of
the brickwork owing to the high velocity of the gases. This high
velocity was considered necessary in order to effect an intimate
mixture of the combustibles and the eornburent. This method of
mixing is now considered undesirable4 and ineffective. In the
later types of reverberatory furnaces it has been completely
abandoned. An intimate mixture of the* producer gas from the
jfirebox and the secondary air is essential, but this mixture should
not be made at the bridge wall.
The height of the opening over the bridge wall may be com-
puted by Yesmann's formula

IX. REVERBERATORY FURNACES CONSIDERED AS INVERTED
WEIRS WITH A CISTERN OR .RESERVOIR. DIMENSIONS
UPON WHICH THEIR CORRECT OPERATION DEPENDS
As a general proposition, very long furnaces are not common
and in many cases are undesirable. Nevertheless, it is sometimes
necessary to retain the hot gases in the heating chamber as long

REVERBERATORY FURNACES

57

as possible, by reducing their velocity. This effect is obtained
under the crest of an inverted weir for gases, in the same manner
in which it would be done on a weir carrying water, by providing

fig. 34.
a cistern or cutting a deeper reservoir in the weir, making an
upstream and a downstream crest.

 

fig. 35.
When a weir having a thick crest (Fig. 34) is transformed into
a weir with a cistern or reservoir (Fig. 35), the velocity of flow of
\

n   n   n
ssa%S$s$$^^
v\S	^...-^	_..-.^-	^—*^_

fig. 36.
the water in the reservoir is reduced, while the level of its free
surface remains the same.
In securing this result with an inverted weir for gases, all of the

58	APPLICATION OF THE LAWS OF HYDRAULICS
dimensions of the furnace heating chamber are affected (Fig. 36),
but the level of the lower free surface of the stream of gases remains
at the hearth of the furnace, and the furnace continues to work
well. The gases, however, remain in the heating chamber a
longer time and a better transfer of their heat to the material
being heated is obtained. The temperature of the gases leaving
the furnace and, accordingly, the temperature of the material
being heated, are different.
In this manner it is not difficult to pass from the consideration
of the continuous or gradual reheating furnace to that of the
chamber type of furnace. Fig. 37 shows a type of furnace inter-
mediate between the ordinary reheating furnace and the chamber

fig. 37.
type of furnace. This is a reheating furnace at the Pouliloff
works; it is very short and has a high roof permitting very large
ingots to be placed upon its hearth.
Figs. 38 and 39 show the arrangement of a kiln for the burning
of silica brick, designed by the author. This is a multiple-chamber
furnace (Siemens system); the gas and the air enter and the prod-
ucts of combustion leave the heating chamber at the hearth level.
The hot products of combustion rise to the roof of the chamber,
and, as they gradually lose their heat, descend towards the hearth
and then pass through the flues leading to the regenerators. The
furnace chamber is constantly filled with flame, and the hearth
is always in contact with the hot gases. The design may be

REVERBERATORY FURNACES

59

modified in reconstruct-
ing existing brick kilns
to suit this method of
firing.
As the reader may
see, the transition from
the consideration of the
gradual or continuous
heating furnace, the
simple inverted weir, to
the consideration of the
chamber furnace with
down-draft is readily
made. The chambers of
these furnaces are com-
puted upon the basic
idea of the time during
which it is necessary for
the hot gases to remain
in the chamber, and this
in turn is fixed by the
drop in temperature of
the heated gases per
second. But, in design-
ing and constructing
these furnaces, it is
necessary to depend
upon Yesmann's for-
mula in all those cases
where the flow of the
gases in motion takes
place under an inverted
weir.
For example, in a
furnace with working
openings closed by doors,
the height of the door
openings should not ex-
ceed hi. If the waste
gas flues leave the fur-

X
figs. 38, 39.

1?"'"
I   r
f

60

APPLICATION  OF THE LAWS OF  HYDRAULICS

naces laterally, the ports in the wall should have; their sills at the
hearth level, and their height should not exceed /?,/. If, on the
contrary, the waste gases are taken off from a chamber furnace

Fio. 40.
by ports having a sill at a higher level than that of the hearth of
the furnace, the hearth can never be brought up to a high tem-
perature.
As an example of the experiments made to obtain satisfactory

Fiu. 41.
operation, without any realization of the necessary conditions, a
kiln designed for the burning of silica bricks and using regenerative
firing methods is shown (Fig. 40). In order to force the hot
gases to act on the silica brick set on the hearth of the furnace,

REVERBERATORY FURNACES	61
the designer placed a wall in the center of the heating chamber and
connected the two halves of the chamber by ports in the lower
portion of this wall. Nevertheless the bricks on the hearth were
not sufficiently well burned. It therefore became necessary to add
a supplementary waste gas flue with ports in the hearth of the
heating chamber.
A very interesting type of chamber reverberatory furnace has
been installed at the Lyswa works for the remelting of scrap and
large broken castings. It was built by M. Onoufrowitch after an
American design (Fig. 41). The rear portion of an ordinary
reverberatory furnace has been replaced by a large chamber,
the waste gas flue having been left in its former place.
Computations for this furnace may be made in the following
manner: the consumption of coal is 0 kg 31 per second. Assum-
ing that the air supply is 1.40 times the theoretical requirements of
combustion, and that the temperature t is equal to 1300°, the
volume of gas Qo = l m3 82 per second and Qi3oo = 10 ni3 48 per
second. For a furnace width of 1 m 60, therefore, hi3QQ= 1 m 05.
That is, the normal thickness of the layer of gas below the
inverted weir for this furnace is equal to 1050 mm and, for this
furnace to work, the distance from the hearth to the top of the
waste gas port should not exceed 1050 mm. Otherwise the hot
gases would not touch the hearth of the furnace and it would not
heat well. The vertical distance from the tapping hole to the
top of the waste gas port actually is 1100 mm, which agrees very
"well with the calculated distance. The charging door of this
furnace is very large and high, but it. is hermetically closed when
the furnace is in operation, and on this account it occasions no
loss of the hot gases.
The volume of the heating chamber of the Onoufrowitch furnace
is llm3 00, of which 8 rn3 70 are comprised in the chamber. By
reason of this, the gases remain in the heating chamber slightly
longer than one second, and therefore the furnace gives good
results.
A very interesting type of furnace is that used in the heating
of steel plates. In this case the necessity of having the hot gases
at the level of the hearth is still more absolute than in ordinary
furnaces. In effect, the presence of air upon the hearth of the
furnace causes considerable damage, as it oxidizes the iron and in
this manner produces a quantity of surface defects. It is for this

62	APPLICATION OF THE LAWS  OF  HYDRAULICS
reason that these furnaces must be so constructed as to prevent the
least possibility of free air getting in on the hearth.
These are chamber furnaces, and the height from the hearth to
the roof may be great. The best furnaces are constructed with a
high arch; the space immediately below it serves as a combustion
chamber, and is very effective in promoting an intimate mixture
of the combustible gases and the air; the combustion of the gas,
therefore, takes place with very nearly the theoretical air supply.
These furnaces are operated with the doors constantly or very
frequently opened. Therefore the height of the charging opening
is the most important dimension and fixes the working quality of
the furnace. This height must be less than the height ht as
indicated by Yesmann's formula.
The Sud-Kama works show an example of a plate-heating
furnace upon the hearth of which there is no inflow of air and
with which, accordingly, they have succeeded in solving the
difficulty of utilizing the waste heat from the furnace in a boiler.
The data for its computation are as follows: the coal consump-
tion per second for one chamber is 0 kg 023. The quantity of gas
per second for theoretical combustion is
Q0 = 4.01X0.023 = 0 m3 092 per second,
Qiooo = 0 m3 429 per second.
The width of the charging opening is 0 m 85.
The height calculated for this opening (according to Yesmann)
ht = hiQQQ, is 0 m 216 and the effective value is 225 mm.
It may be seen by this that the working opening, which is
closed by a door, has a height very well proportioned to the volume
of the gases circulating in the heating chamber. It is for this
reason that the opening of this door, which is operated by a pedal,
does not cause an inrush of cold air into the furnace, as occurs
in furnaces of other systems, for example, in the gas-fired furnace
of the type used at the Alapayewsky works.
The following are the data for these furnaces: the quantity of
wood consumed per compartment or heating chamber per second
is 0 kg 0185. The volume of gas per furnace at 0°, Q0 = 0 m3 082;
at 1000°, Qiooo^O m3 382.
The height of the working door, computed according to the
theory of the inverted weir feiooo = 0 m 164. Nevertheless, the
charging opening is 400 mm in height. This explains why the

THE THEORY OF JETS

63

hearth of this furnace is constantly covered with a layer of air,
and why the waste gases, as analyzed by M. Asseyew, showed
3.85 per cent of CCb and 16.65 per cent of 62- This was the
cause of the abandonment of these furnaces at the Alapayewsky
works.
The conclusion that the good or bad working qualities of plate-
heating furnaces depended upon the height of the working opening
was entirely unlocked for at this time. Since then this conclusion
has been completely verified. There is no doubt whatever that
this is only one of the numerous surprises which will be revealed
by the application of the hydraulic theory to furnaces,
X. THE APPLICATION TO HOT GASES OF THE THEORY OF JETS
OF WATER
If the resistance due to friction in the pipes and in the air is
neglected the vertical height to which a vertical jet of water will
rise will be equal to the head and will be

The jet from an
inclined fountain de-
scribes a parabola
whose middle ordi-
nate (Fig. 42) will be
Tr   v2 sin2 5

fig. 42.

In applying these formulas to hot gases, that is to say, to a
light liquid in motion within a heavy liquid, it is necessary to
turn the diagram upside down, as the particles in motion are acted
upon, not by their weight and gravity in a downward direction,
but by the difference between the weight of the particles in motion
and a corresponding volume of the medium within which their
motion takes place. The resultant force will act in an upward
direction, thus inverting the diagram, as is indicated in Fig. 43.
Yesmann has developed the following expression for an infin-
itely thin jet of hot gases, projected from the port of an open-
hearth furnace:

64	APPLICATION OF THE LAWS OF  HYDRAULICS
Let "y = the initial velocity of the fluid in motion;
Am=the specific weight of the fluid in motion;
Ai = ihe specific weight of the fluid at rest.
The weight of each unit of volume of the fluid in motion is less
than A*. The upward force which acts upon each unit volume of
the fluid in motion is, therefore, equal to A* — Aw. The upward
acceleration due to this force is

^//////////A

fig. 43.
2g
A°
The depth to which the jet will descend for this case is
ry   v2 sin2 5       Am
A°
For hot gases
Am =

from

H=-

2g

Ao
Ao         Ac
1+att    l+atm

sn
2g

2

l+at,

R_v2 sin2 B    a+ti =v2 sin2 d   273+t,
2g        tm-ti        2g     X tm-tf
For vertical jets, when 5 = 90°, this formula becomes
H^X~l^k

(F)

THE THEORY OF JETS	65
When ^ = 0°, that is to say, when the jet enters cold air, the
formula becomes
77-V
H~2g
V2
and as y designates the head h the formula becomes
# = 273
h     tm
a proportion which has already been given on page 31.
The application of the theory of gaseous jets to the open-
hearth furnace is illustrated in Fig. 23, which shows a model of an
open-hearth furnace, within the heating chamber of which a cur-
rent of colored kerosene is circulated. As may be seen in the cut,
all of the heating chamber, except that portion occupied by the
bath, is filled with the kerosene. Here, or more exactly, in all
that portion of the heating chamber which is below the sills of the
gas ports, water remains, and there is no means by which it can
be forced out of the heating chamber.
The presence of the water clearly demonstrates the most
important defect of the open-hearth furnace and many other
similar furnaces. The hot gases enter and leave the furnace
immediately below the roof, and all that portion of the heating
chamber below the level of the sill of the ports and above the steel
notch or tapping hole, a distance which varies in actual furnaces
from 0 m 50 to 1 m 50, is outside of and below the direct current
of the gases.
In the model it is clearly shown that the bath of the open-
hearth furnace is in a pocket, from which the cooled gases cannot
flow naturally and where they remain, accordingly, practically
immobile. In order to expel these cooled gases from the hearth,
as well as to mix the heated gases forming the flame, the gas and
the air are directed downward upon the hearth, and as they enter
the heating chamber at a high velocity, the phenomenon of the
gaseous jet is utilized in forcing their current downward to a depth
equal to that of the furnace below the port sills, or down to the
level of the tapping hole. In European furnaces the entry velocity
of the gas and air varies between 12 and 18 meters per second,
while the gas velocity in some American furnaces is as high as 50
meters per second.
If the theory of the gaseous jet is correct, all open-hearth

66	APPLICATION OF THE LAWS  OF HYDRAULICS
furnaces which operate satisfactorily should conform to it.    This
may be determined as follows:
The air enters the heating chamber of the open-hearth furnace
!;	preheated to a temperature of 1000° to 1100°, as does the producer
gas.    Their combination forms a flaming jet which, according to
the Wanner pyrometer, has a temperature of from 1800° to 1850°
!	instead of the theoretical temperature or calorific intensity of a
flame in an athermal chamber of 2100° or more.^
Knowing the quantity of fuel which is transformed into gas in
the producer per second and its composition, it is not difficult to
compute the volume per second of the producer gas and the air
required for its combustion. Consequently it is not difficult to
compute the velocity with which the preheated gas and air enter
the heating chamber.
I	For example, a furnace which has a nominal capacity of 30
tonnes, and is operated to make four melts per day, consumes
0 kg 347 of coal per second, and this at 0° corresponds to 1 m3 81 of
gas and 2 m3 52 of air per second. & Assuming 1000° as the tem-
perature of the gas and the air, the volumes entering the heating
chamber each second will be 8 m3 44 of gas and 11 m3 77 of air.
The gas and the air combine in the heating chamber of the furnace
!	and give a current of flaming gases at a temperature of 1850°.
!!	To what depth will this jet of flame drop within the heating
chamber, if the gas and the air are flowing into the chamber with
;	velocities equal to Fair and VgBa, making angles of a and /? with
the horizontal?
The operation of an open-hearth furnace is impossible unless
the bottom is well sintered in place.    If the bottom is not well
made, it will be dug up or float up on the molten metal, and in a
furnace in which the bottom cannot be thoroughly sintered the
i      !	metal will not be sufficiently heated.
The depth H of the gaseous jet must absolutely be greater than
the distance from the sill of the gas port to the tapping hole.
(1} The method of computing the Calorific Intensity Curves of various com-
bustibles, as developed by the translator from the methods of Mallard
and Le Chatelier, and as used by Damour, are given in an appendix to this
volume.
C2) One kilogram of coal gives approximately 5 m3 22 of producer gas; this
requires about 6 m3 54 of secondary air, this being 1.25 times the theoretical
air supply, plus 0 m3125 of air for the oxidization of certain elements of the
metallic bath.

THE THEORY OF JETS	67
This height, which has been given by Professor M. A. Pavlow
for thirty-six of the best American and European open-hearth
furnaces, varies in his table from 500 to 1875
Returning to the formula upon page 64,
?;2sin2 B    273+*i
~     2g	tm+t<
it may be seen that the depth to which the gaseous jet descends
increases with the increase in it, that is to say, with the temperature
in the heating chamber of the furnace. It is clear that when the
chamber is cold, that is, when £* = 0°, H has its minimum value.
When tt = tm, H becomes infinite. This shows that if a certain
velocity is impressed upon some of the particles in the midst of a
fluid, and if no account is taken of internal friction, the displace-
ment and the duration of the motion of these particles will be
infinite.
If the temperature within the chamber of the open-hearth
furnace U is not equal to 0° nor to the temperature of the hot gases
tm of the jet of flame, the depth H to which the jet descends will
become greater and greater as the difference between tm — tt
becomes less, that is to say, it will be greatest when the gases
filling the chamber are lightest. Thus, for example, a jet of
kerosene directed downward into water will penetrate it to a
greater depth than it will if directed into mercury. In a furnace
chamber filled with hot gases the jet of hot gases will descend to a
greater distance than it will into a chamber filled with atmospheric
air, cold and heavy.
All those who have assisted at the starting up of an open-hearth
furnace know that at first the flame in the cold furnace clings to the
roof and drops further and further toward the hearth, as the tem-
perature of the furnace gradually increases. In heating up a new
furnace, it is necessary to make the bottom, by burning it on in
place, that is to say, to form it of its different elements, incorporat-
ing a small quantity of refractory clay with a silica sand, or a
small quantity of basic slag or of dolomite containing from 3 to 7
per cent of magnesium silicate. This bottom cannot be made
except at a temperature of from 1600° to 1700°, and it is impossible

(i)

Rev. de la Sod etc russe de Mttallurgic, 1910, pp. 169-183.

68

APPLICATION OF THE LAWS OF HYDRAULICS

i

to sinter it in place unless the flame or hot gases lick the hearth of the
furnace.
As the depth H of the gaseous jet is a function of the tempera-
ture of the immobile gases filling the heating chamber of the open-
hearth furnace, the dimensions have been calculated in the follow-,
ing manner: all of the data from existing furnaces as given in
the table by Professor Pavlow have been used to determine the
' temperature t within the heating chamber at which a jet of flame
or hot gases at 1800° would touch the bottom of the furnace; that
is to say, at which H exactly designates the distance from the sill
of the gas port to the tapping hole.
For the 30-tonne furnaces Nos. 20, 21, 23, 24, 25, for which the
inflow of gas and secondary air at 1000° will be 8 m3 44 of gas and
11 m3 77 of air per second, the dimensions and the results of the
computation are given in the following table:

							Distance 	
Number
of
Furnace 	Area
of
Gas
Port 	Veloc-
ity of
Gas at
1000° 	Area
of   •
Air
Port 	Veloc-
ity of
Air at
1000° 	Inclina-
tion of
Gas
Port 	Inclina-
tion of
Air
Port 	from the
Bottom of
Gas Port
Vertically
to Tapping 	
							Hole 	
	m2 	m/sec 	m2 	m/sec 	Degrees 	Degrees 	Millimeters 	
20 	0.275 	29.6 	0.54 	21.8 	15 	38 	1150 	
21 	0.358 	23.5 	0.57 	20.6 	13 	40 	980 	
23 	0.440 	18.9 	0.72 	16.3 	33 	33 	980 	
24 	0.260 	32.4 	0.56 	21.0 	10 	38 	1020 	
25 	0.320 	26.3 	0.64 	18.4 	15 	41 	1370 	

Except in Furnace No. 23, the streams of air and gas have
different velocities and different inclinations; the masses of the gas
and of the air are also different.
The jets of air and gas at different inclinations combine in the
flame with the same velocity and inclination. This can be resolved
by the parallelogram of velocities, taking into account the different
densities of the air and the gases.
The average velocity and inclination of the flame may be
obtained graphically by the parallelogram of the velocities of the

THE THEORY OF JETS

69

gas and of the air multiplied by coefficients proportional to their
weight.    Now the ratio of the weights (1) in this case is equal to
1.81  X1.069^1.9349 = 37.26 per cent
2.525X1.29      3.2575    62.74 per cent
Therefore for Furnace No. 20, for example, the result is
For the air:   21.8X0.6274 = 13.6773
.For the gas:  29.6X0.3726=11.0290
The diagonal of the parallelogram for these two values is equal
to 24 m 50 per second at an inclination of 27°. The results, which
will be obtained for the other furnaces by similar computations,
are given in the following table:

Number 	Average 	Average 	
of 	Angle 	Velocity 	
Furnace 	ex.. 	V. 	
	Degrees 	Meters per
Second 	
20 	27 	24.00 	
21 	29 	21.20 	
23 	33 	17.30 	
24 	25 	24.50 	
25 	29 	21.00 	
Inserting the above values in the formula
?;2 sin2 a    273+*,
// 	 ~~       pj	~ /N ™~       *
with the values of v and a. given in the table and assuming that
kn=1850° and that H equals the difference in level between the
sill of the gas port and the tapping hole, the temperature U at
which the stream of flame drops to the level of the hearth at the
tapping hole may be computed as follows, in order to determine
the temperature to which the gases filling the furnace must be
raised before it becomes possible to start making the bottom:
(1) It should be remembered that at 0° the volume per second of the gas is
1.81, and its specific weight is 1.069. The volume of the air is 2.525 and its
specific weight 1.29.

70

APPLICATION OF THE  LAWS OF HYDRAULICS
Furnace No. 20 ....... fc>  74°
21 ....... tt> 58°
23	....... tt> 22°
24	....... k>  70°
25

The following example shows the influence of the density of the
medium which the jet of gas penetrates. For Furnace No. 20
the depth H = 1 150 mm at 74°.
Determining the depth of the jet at a temperature ti = Q°,
there will be obtained

273+0
•- = 864 mm.
=— sin2aX
-1850-0
Therefore the flame or stream of hot gases does not touch the
hearth, and the distance by which it falls short of so doing is
1150-864 = 286 mm.
Therefore, in these five furnaces, each of 30 tonnes capacity,
selected at random, such a velocity and an inclination have been
given to the gas and the air in the heads that the flame settles to
the hearth when the other portions of the furnace are at a com-
paratively low temperature.
It is evident that perfect repairing of the hearth is assured in
this manner, but that it is not an advantageous arrangement in
the regular working of the furnace. A similar investigation deals
with the circulation of the hot gases in the long furnaces used in
American plants, where the flues in the heads have a very slight
slope and where the velocities are very low for the air and very
high for the gas.
This data has been taken from Professor Pavlow's table for
two 60-tonne furnaces, Nos. 35 and 36.
Making the same assumptions as in the case of the 30-tonne
furnaces, the volume of air at 1000° will be 23 m3 54.per second
and the gas at the same temperature will be 16 m3 88 per
second.
Making the calculations for the temperature U at which it
becomes possible to make bottom in these furnaces, the results
are as follows:

THE THEORY OF JETS

71

	Furnace No. 35 	Furnace No. 36 	
Area of ffas ports 	0 m2 7300 	0 m2 3935 	
Velocity of cas at port 	 	23 m   11 per sec 	4!2 m  90 per sec 	
Area of air ports     	     	 • . 	2 rn2 70 	3 m2 75 	
Velocity of air at port 	 	8 rn  72 per sec 	6 m  28 per sec 	
Slope of gas port 	 	6° 	12° 	
Air port 	17° 	26° 	
H = depth  of  jet = difference  in  level
between sill  of  gas  port  and  the
tapping hole    	 	0 m  92 	1 m  00 	
Average velocity  of  the mixture  by
parallelogram    ... 	llm 80 per ,sec. 	20 m 50 per sp * 	
Average slope of mixture by parallelo-
gram             	 	9° 30' 	14° 30' 	
ti at which the mixture commences to
lick hearth           	 	1531° 	646° 	

These computations would show that the making of the bottom
in Furnace No. 35 would be difficult, and it is hard to believe that
the design published is correct. (1>
As regards Furnace No. 36, it will be comparatively easy to
make the bottom, and the flame will not be deflected from the
surface of the bath. In the operation of this furnace (No. 36) its
ports will be burned and worn away, their area will be increased
and the velocity of the gas will be accordingly reduced. How
much may the port bo worn away without interfering to an
appreciable extent with the repairing of the bottom?
The formula (F), on page 64, provides the solution of this
problem.
The bottom may be made in a satisfactory manner wheiv
^=1400°; the corresponding value of v may be deduced:
X
,'         v2 sin2 14.5°     273 + 1400
2X9.81
1850-1400
from which v = Q m 20 per second.
(1) A great deal of empiricism exists in the arrangement of the heads of
these furnaces, and in many cases the furnaces as they go into operation
differ widely from the drawings. In some plants no two furnaces have
identical heads.

Tfr-

72	APPLICATION OF THE LAWS OF HYDRAULICS
The velocity for the original section was 20 m 50 per second;
the ratio of these velocities is
20.50
9.20	'
which shows that the furnace will continue to function with a gas
port area 2.2 times its original area.
This analysis is riecesssary to enable the designer to plan the
lines of the furnace in such a manner that a long campaign will be
assured.(1)
XI. METHODS OF COMPUTING FOR FURNACES OF VARIOUS TYPES
In this chapter it is proposed to supply a computation scheme
which will be of service to engineers and technicians whose duties
make it necessary for them to follow closely the working of rever-
beratory furnaces. All the data which are available at this time
are based upon a small number of furnaces. For this reason it is
impossible to confirm the absolute exactness of the coefficients
which are presented.
The verification of these numerical constants is necessary in
order to fix their limitations. Research should be undertaken by
others, and the author will be glad to give the fullest recognition
to those co-workers who desire to contribute to the improvement
of furnace work and who will aid him in attaining that end.
The following order of procedure is suggested for use in making
the computations and sketches for a furnace.
In designing a furnace, the first thing to do is to roughly outline
the heating chamber. Within this outline should be indicated
the direction of the gaseous currents and, consequently, the sys-
tem upon which the furnace works.
For example, in the case of a brick kiln, the height will be
fixed by the consistency of the unburned bricks, which will limit
the height to which they may be set, and the length and width
(or diameter) will be fixed by the capacity of the kiln, or the
number of bricks to be burned at one setting.
In the case of a furnace for the gradual or continuous heating
of ingots, the dimensions of the hearth of the furnace will be
(1) An analysis of this character might show that expensive cooling device
were neither desirable or necessary.

METHODS OF  COMPUTING FOR FURNACES	73
determined from data including its production, that is, the number
of ingots to be heated per hour, the time required for their reheat-
ing and their arrangement upon the hearth of the furnace.
The distance from the hearth to the roof of the furnace will
be established by keeping the following fa'cts in mind: sufficient
space must be provided to obtain complete combustion of the hot
gases, and constant contact of the hot gases with walls or material
at a high temperature is an essential condition. A very serious
fault of many furnace designs is the premature cooling of the
flame or burning gases by directing them in such a manner that
they impinge upon cold ingots or other cold material. On the
other hand, it would serve no useful purpose to make the chamber
too large, but it is desirable to make the roof of sufficient height
to give the hot gases of the flame a sufficient time to complete their
reaction before they come in contact with bodies sufficiently cold
to impede or prevent the completion of the reaction of combustion.
When the lines and working method for the heating chamber
have been determined, its volume may be computed.
The same method of procedure is used for tempering furnaces,
annealing furnaces, iron-melting furnaces, puddling furnaces, etc. ;
the very first thing that is necessary is to determine the dimensions
of the heating chamber and its volume. When the foregoing have
been fixed, the composition of the furnace gases, or, more exactly,
the volume of air required with reference to that theoretically
required to burn the fuel, is assumed.
Calculations show that a good coal from central Russia,
burned with the theoretical volume of air required, gives a theoret-
ical calorific intensity of 2082°. With 70 per cent excess air
supply this coal will give a calorific intensity of 1400°; and with
double the theoretical air supply (100 per cent excess air) the
calorific intensity will be 1250°.
Now, it is evident that these temperatures can only be obtained
with instantaneous combustion in an athcrmal chamber, the total
amount of heat released being absorbed in raising the temperature
of the gases of combustion. In reality the best means of lowering
the temperature of the jet of burning gases is to operate the furnace
so that combustion takes place with only the theoretical air supply.
Such combustion requires a certain length of time; the combustion
of the last traces of combustible gas requires a considerable amount
of time in its combination with the small amount of oxygen

»».
74	APPLICATION  OF THE LAWS OF HYDRAULICS
present, and it will not be effected in the presence of objects Haich
tend to cool the gases.
»	This flame has a soft and languishing character, and an average
,      •	temperature in the neighborhood of 1100°, and is employed exclu-
|	sively  in  chamber  brick kilns,  tempering  furnaces,   annealing
><	furnaces and furnaces used in the manufacture of plates and sheets.
11	It is only in the very large chamber brick kilns, where the radiation
'f	losses are insignificant, that it is possible to obtain a temperature
'''	in the neighborhood of 1400° with this kind of combustion.
ij	If, on the other hand, it is necessary that the reaction of
[•	combustion should be completed rapidly, the actual temperature
jj	realized will be a little lower than the computed temperature.
| (	In this case it will be necessary to have an excess of air and an
t\	intimate mixture of the air and gases forming the flame.    The
f j	greater the excess of air, the greater will be the proportion of the
f |	high temperature core in the flame.
| i  '	A flame with a great excess of air is sharp and penetrating and
is frequently more detrimental than useful in the uniform heating
of material. It can be used in the puddling furnace or in the
melting of iron, where the temperature in the furnace, as required
by the process, very closely approaches the temperature of the
hot flaming gases, or where the operation to be performed some-
what resembles that required of the gas welding or cutting torch.
1'	The slowness and diffusion of the energy in the reaction of
,	theoretical combustion is a phenomenon which is utilized in a
number of ways, when it is desired to have a temperature which
is not very high, but which is uniform (for tempering, annealing,
the reheating of plates, etc.).    In these cases, the reaction of
'	combustion is slowed down by using cold air and gas which are not
*	well mixed, in a very large combustion chamber out of contact
I   , c   ,	with cold material.   An ideal combustion chamber for a furnace
of this character would be a high free space under a roof or dome,
from which the currents of hot gases produced by combustion
would fall, and in which the hot flaming gases would always be in
contact with incandescent brickwork.
In practical work the composition of the furnace gases may
be assumed, according to the character of the product. Five
cases are presented here.
1st Case.—Small furnaces, within which the hot gases remain
only a fraction of a second and are directed immediately upon a.

METHODS OF COMPUTING FOR FURNACES	75
cold body. Combustion occurs with cold air and solid fuel
burned in a thin layer upon a simple bar grate. As an example of
such a construction, the firebox of a tubular boiler may be taken.
Combustion is effected rapidly under very unfavorable conditions
—the air supply is usually double that theoretically required.
2d Case.—A simple firebox, with a grate, but with a simple
brick arch over the fuel bed. Combustion occurs in a thick bed
of coal. In the case of the furnace working with chimney or
natural draft, it is necessary to have sufficient air pressure to
overcome the resistance of the fuel bed to the passage of the air
and gases.W Combustion is rapid, as in the preceding case, but is
effected under more favorable conditions. A thick bed of coal is
an excellent medium of combustion; the firebox covered with an
arch makes a satisfactory combustion chamber. Practice has
shown that, under these conditions, when the fire is well operated,
the combustion of coal may be effected with an air supply of about
1.50 times that theoretically required.
A furnace fired in this manner in the Lougansk works, using
a blower, burns 200 kg of coal per hour per square meter of grate
surface. When fireboxes of this type are used with natural or
chimney draft only, such a high rate of firing cannot be used; the
fuel consumption for such cases should not exceed 70 kg per hour.
For the ordinary types of furnaces with a firebox of this kind,
such as puddling furnaces, roverberatory furnaces for the melting
of iron, copper, etc., and for reheating furnaces, the computation
should be based on an air supply 1.50 times that theoretically
required, and with very good coal 1.70 times.
3d Case.—Producer-gas-fircd furnaces. These should be
figured as having a secondary air supply 1.50 times that theoretic-
ally required.
4th Case.—Regenerative or Siemens furnaces. These should
be computed for a secondary air supply of 1.25 to 1.50 times the
theoretical requirements.
5th Case.—Annealing furnaces, tempering furnaces, chamber
brick kilns, etc., should be computed for the theoretical air supply.
(1) This was mentioned in an earlier chapter. This pressure varies with the
height between the grate and the hearth of the furnace. The simplest method
of providing this pressure is by lowering the grate until it is sufficiently far
below the hearth to provide the pressure required to overcome the resistance
of the fuel bed.

T
76	APPLICATION OF THE  LAWS  OF  HYDRAULICS
|    f f	According to the composition of the gas and the amount of
I    * 11	excess air, there will be obtained different quantities of the products
f,   ] I '	of combustion, per kilogram of coal.
Ill	By computation it can be shown that one of the best grades of
coal mined in the Donietz basin (central Russia) W requires for the
combustion of 1 kg of coal an air supply of 8 m3 71, and the volume
of the products of combustion is 9 m3 04, theoretical or neutral
combustion.
According to the above, the volume of gases given off by the
combustion of 1 kg of this coal will be
Theoretical air supply		9 m3	04
1.25 times theoretical air supply		11	22
1.50			13	39
1.75			15	59
2.00			17	75
!!?   :
For producer-gas-fired furnaces, 1 kg of coal gives about
5 m3 22 of producer gas. With a blower combining the air and
I{   f i	the steam, this requires 3 m3   16 of air for the primary supply
j\   \ j	and 5 m3 54 for the secondary air supply.    The volume of the
products of combustion with the theoretical air supply arc 9 m3 71;
and with an air supply of 1.50 times the theoretical volume the
volume of the products of combustion will be 12 m3 54.
Knowing the quantity of combustible which will be used in a
unit of time and the resulting volume of the products of combus-
tion, there is another factor which must be determined: the time
that the products of combustion or hot gases remain in the heating
chamber of the furnace.
f
i}     *     \	(i) The average composition of this coal is:
Per cent
C		84.75
H2		4.80
02.;		4.83
N2.°.		1.44
S		1.48
Moisture		0.90
Ash		1.80
For larger quantities of moisture and ash, it would be necessary to correct the
air supply and the products of combustion volumes accordingly.

METHODS OF COMPUTING FOR FURNACES	77
According to calculations based upon various furnaces in
service, it was found that the time during which the waste gases
remained in the furnace varies from a fraction of a second to 3, 5,
7, and up to 10 seconds. The determination of the length of time
which the gases must remain in the furnace chamber is based
upon the following considerations :
Computations may be made which will give the theoretical
calorific intensity obtained by the combustion of a coal with an
assumed excess of air—for example, the combustion of the best
grade of Donietz basin coal, with an excess of 73.3 per cent of air
over that theoretically required will give a calorific intensity of
1400°. If, for the designing of a continuous ingot heating furnace,
it is assumed that there will be a temperature of 700° for the gases
at the exit port, the total drop of temperature in the heating
chamber will be 700°. If the drop in temperature of these gases
per second is known, it is comparatively simple to determine the
time the gases should remain in the heating chamber of the
furnace.
According to those computations which have already been
made—computations which at the best are only approximate—
the following values have been found for the drop in temperature
per second:
Open-hearth furnaces		200° per second
Continuous reheating furnaces. ..	150°-200°
Annealing furnaces		100°—150°
Chamber brick kilns		80°
It should not be considered that these values are perfectly
established. Exact data covering the drop in temperature of the
gases per second can only be obtained by a series of observa-
tions for each of the varieties of furnaces, using for this purpose
furnaces which are correctly designed and constructed. This
last point presents the principal difficulty which exists at
present.
It is evident that the drop in temperature per second of the
gases in a furnace heating chamber is a function of:
(a) The losses by radiation, which are a function of the
exposed surface of the furnace, the conductivity of the walls and
the temperature of the hot gases on the inside of the chamber;

78	APPLICATION  OF THE LAWS  OF HYDRAULICS
that is to say, the losses by radiation are peculiar to each type
and size of furnace.(1)
(6) The ability of the body being heated to absorb heat from
the hot gases and by radiation. This may be generalized in the
following statement:
Assuming that one reheating furnace is charged with cold
ingots and another with hot ingots, it is very evident that these
two furnaces will work in different fashions. The drop in tempera-
ture of the hot gases in the first of these furnaces will be much
greater than it will be in the second furnace. Accordingly, in the
first furnace the time during which the hot gases remain in the
heating chamber should be diminished and the volume of the gases
per second should be increased. It is therefore necessary that the
dimensions of the heating chamber and the size of the ports should
be designed and constructed to conform to these conditions.
Similar differences will exist in furnaces designed for the
production of different outputs. Consider, for example, a rolling
mill and a reheating furnace to serve the mill. It is evident that
the operation of the furnace must be regulated to suit the output
|| \	of the rolling mill, that is, when the mill is working fast and
*   I	without interruptions of output, it will be necessary to heat fast
•) -	and,  accordingly,  to decrease the time  during which the hot
.?•'!;	gases remain in the furnace.    On the contrary, if the work of the
»|j||:	mill is subject to interruptions, the time during which the hot
[ j	gases remain in the heating chamber will be increased and the out-
, i! !!	put of the furnace will accordingly be decreased.
i ;j	The foregoing shows the importance of some of the factors
I f	which have to be established, and it is desirable that the value
j! !|	of these factors should be based upon furnaces actually in service,
I;	by accurate determinations of the drop in temperature of the
i\i	gases in the heating chamber per second.    These values are of
!,i	primary importance in the design computations for furnaces.
'I	Therefore, according to the operating conditions of the furnace
whose design is to be established, the following order of procedure
is observed:
1.	The necessary volume of the heating chamber is computed.
2.	The volume of gases obtained per kilogram of combustible
(1) Note by translator.—The exposure of the furnace to air currents and the
convection currents arising from the hot walls must be taken into considera-

METHODS OF COMPUTING FOR FURNACES	79
burned is assumed, according to the operating condition of the
furnaces to be designed.
3.	The theoretical calorific intensity of the combustible, with
the assumed excess air supply over that theoretically required, ls
computed. W
4.	The following temperatures have been established for the
gases leaving the heating chambers of furnaces:
Open-hearth furnaces		1600°
Puddling and reverberatory furnaces		1250°
Tempering or heat treating furnaces		850°
Annealing furnaces, etc		1000°
5.	The difference between the computed temperature, or the
theoretical calorific intensity, and the temperature of the gases
leaving the heating chamber is divided by the number of degrees
of temperature drop of the gases per second.    This determines the
length of time during which the hot gases remain in the heating
chamber.
6.	Dividing the volume of the heating chamber by the time
during which the hot gases remain in it gives Qt, the volume of the
gas at the temperature £, which passes through the heating chamber
each second.    This value divided by 1+al, gives the volume of
the gases at 0°, and, according to the volume of gases required
at 0°, the quantity of fuel required per second, per hour or per
twenty-four hours will be fixed.
7.	Knowing Qh according to formulas previously given, the
principal dimensions of the furnace may be determined.    This is
done by fixing the velocity of flow of the gases in the different
parts of the furnace, and then computing, according to the condi-
tions, the hydrostatic pressure of the gases and the vertical dis-
^Note by translator.—This maybe done by the use of the methods of Mallard
and Le Chatelier. The theoretical calorific intensity, however, assumes that
combustion occurs instantaneously in an athermal chamber, the total amount
ot heat released being absorbed in increasing the temperature of the products
of combustion. In practice the velocity of combustion is not instantaneous
but requires an appreciable time interval; the chamber in which combustion
occurs is more or less dithermal and for this reason the practical or actually
obtained calorific intensity is less than the theoretical. A further difference
is due to the fact that the fuel usually contains more or less moisture, gases
being frequently saturated to the dew-point temperature, and in addition the
air supply contains some moisture. The design and construction of the
furnace affect the result.

80	APPLICATION OF THE LAWS OF HYDRAULICS
tance which must exist between the level of the grate and the
hearth of the furnace, if this last operates with natural or chimney
draft, or the draft pressure which is necessary if the air is forced
in by a blower. After this, the required height of the chimney
may be computed.
It is not desired, in this work, to present the complete com-
putations for the design of all of the many different types of
furnaces. The following, however, gives an example of the
application of these methods of computation, as they have been
used by the author.
Problem.—The design required is that of a small furnace for
the reheating of small pieces of iron (billets or fagots) to be
installed in connection with a waste heat boiler. The height
between the hearth and the arch of the furnace cannot be less than
0 m 41; the width of the heating chamber is to be 2 m. The
temperature of the gases at the outlet port is to be 1200°.
Computing the volume of the gases,

Q2

120Q

from which $1200 = 2 m3 77 per second,
k'qq= 0 m3 514 per second
One kilogram of coal burned with an air supply 60 per cent
in excess of the theoretical requirements produces
9.04+(8.72X0.60) = 14 m3 27 of gases.
From this the quantity of coal required per second may be
deduced
x : 1 =0.514 : 14.27,       x = 0 kg 036,
which will be 129 kg per hour or 3 tonnes 110 for twenty-four hours.
Fixing the dimensions of the furnace:
(a)  Height at Bridge Wall.—This height will be determined as
an inverted weir with the hot gas temperature £ = 1400°.
Quoo = 0.514(1+-—T) =0.514X6.12=3 m3 15 per second,
V      -*/o/
= 0m423.

METHODS OF  COMPUTING  FOR FURNACES

81

(6) Height of Bridge Wall.—Considered with reference to the
velocity of the gases over the bridge wall, it is theoretically possible
to decrease this velocity over the hearth by increasing the thickness
of the stream of flowing gases by one-half their thickness over
the bridge wall.(1) As it is necessary that the velocity should not
be too great over the hearth, the roof will be given a downward
slope and the height of the bridge wall will be fixed at not more than
one-half the height of the opening over the bridge wall. In the
construction of the bridge wall this proportion will be reduced to
one-third (140 mm), and the roof will be given a downward slope
of the same amount toward the exit port for the gases; a general
longitudinal outline of the furnace will, therefore, appear as in
Fig. 44.
The working chamber will be supplied with two working doors,

 

fig. 44.
each having a clear opening 400 mm in height. The hearth will be
given a slight grade or slope toward the gas-exit port, in order to
permit the cinder deposited upon the bottom to drain off into the
cinder pocket in the flue. The waste gas flue will be dropped
below the level of the hearth, giving any cold air or gases which
may enter the working chamber a chance to drain out of the
chamber. With the usual construction, it is impossible to prevent
small amounts of cold air from entering the furnace below the
doors.
(c) Dimensions of Grate.—These will be based upon the
assumption that 75 kg of coal can be burned per square meter
per hour (p. 75) (chimney draft):
= 1 m2 72 or approximately 2 m 0X0 m 90.
^ According to Yesmann h =•§//.

82

APPLICATION OF THE LAWS OF HYDRAULICS

;i

(d) Vertical Distance of Grate Bars below the Hearth of the
Furnace.—This distance must be sufficient to impress the desired
velocities upon the gases in the different portions of the furnace
and firebox.
Starting with the passage of the air through the ash pit, the
volume of air required is
8.71X1.60X0.036 = 0 in3 501 per second.
In order to secure a velocity of 0 m 50 per second in the ash pit
this pit must be given an area of 1 m2 00 = 2mOXOm 50.
To impress a velocity Vi = 0 m 50 per second upon the air, a
velocity head hi=Q m 0127 is required, neglecting friction,M
from which
5i = 1.29X0.0127 = 0 mm 016 of water.
The total free area between the grate bars is equal to
1 m2 80    n    2 _.
—r— = 0 m2 60.
o
The velocity ¥2 of the air passing through the grate will be
0.501 : 0.60 = 0 m 835 per second,
from which fe = 0.036 and
B2= 1.29X0.36 = 0 mm 046 of water column.
Resistance of the Fuel Bed.—It is assumed that the depth of the
bed of burning coal upon the grate has a thickness of 150 mm and
that it is formed of three layers or tiers of coal in small pieces,
each layer having a thickness of 50 mm; therefore in passing
through the fuel bed the air will lose its velocity three times.
The velocity head required to impress upon the air the velocity
with which it passes through each layer or tier of the fuel will
be the resistance offered by that tier to the passage of the air,
and the total resistance of the bed of fuel upon the grate will be
the sum of the resistances of the number of tiers into which it is
assumed that the bed of fuel is divided.
The volume of air which will be contained in the spaces or
interstices between the pieces of coal forming the fuel bed may
be calculated as follows: the specific weight of coal is about 1.20,
^ Velocity heads required, refer to Appendix III.

METHODS   OF COMPUTING FOR FURNACES	83
that is, a cubic meter of solid coal will weigh about 1200 k<r;
a cubic meter of coal in small pieces will weigh about 700 kg.
It follows that the volume of the spaces filled with air will be
^200 _ 700
equal to — J9QQ~ — ^ 0 m3 42 and that the total cross-sectional
area of these interstices will be equal to 0 in2 42 per square meter.
As the total area of the grate is 1 m2 80; the area of the air spaces
will be
0.4X2X1. 80 = 0 m2 750
and the velocity of the air passing through them will be
y3 =   '       = 0 m 68 per second,
from which A3 = 0 m 0235 W and 83 = 1.29X0.0235 = 0 mm 03 of
water; and as the velocity is lost three times, once for each layer
of the fuel bed :
$3 = 0.03X3 = 0 mm 09 of water column. (2>
The velocity of the gaseous products of combustion above the
fuel bed may be determined in the following manner:

y4 =     '       = 1 m 54 per second,
from which
l     n      iir       i   *     0.115X1.326(3)     A         Aor7r   r
A4~0 m 115 and 54 = - p-t^ - = 0 mm °275 of water.
O . O«7
= 3 m
The velocity of the hot gases over the bridge wall
3 45
423x2
(1)	Refer to Appendix III for heads required for various velocities.
(2)	Note by English translator. — The foregoing is not exactly correct, but it
illustrates the method to be followed.   The lower layer of the fuel bed will be
composed mostly of ashes and a small amount of burning fuel.    The second
layer will be burning fuel and the third layer will be composed of burning coal
and partially burning or fresh fuel.   Another factor that has not been con-
sidered above is the increase in temperature of the air and its change into the
gases of combustion.    A considerable volumetric expansion will result in
increased resistance to the passage of the air.
(3)	This is the weight of 1 cubic meter of the products of combustion.

84	APPLICATION OF THE LAWS OF HYDRAULICS
from which
/*5 = 0 m 716 cd and fc JL™^?§6 = o mm 155.
The total of these pressures and losses will be
1.	In the ash pit		<5i =0 mm 016
2.	In the grate openings		62 = 0         046
3.	In the fuel bed		<53 = 0        090
4.	In the upper part of the firebox....	54 = 0         027
5.	Over the bridge wall		85 = 0         155
8 =0 mm 334
Therefore, the hydrostatic pressure required at the level of
the grate will be, as a minimum, + 0 mm 334 of water column.
At the temperature £=1200°, the weight of 1 cu m of gas in
the furnace will be
Therefore a column of this gas 1 m in height will give a hydro-
static pressure of
1.29-0.246 = 1 mm 044 of water.
Then, using x to express the height in millimeters of the column
of gases corresponding to the 'pressure of a water column of
0 mm 334 in height, the following proportion can be written :
x   ^0.334
. 1000~~1.0447
from which : x = 3 19 mm, which is the minimum vertical distance
of the grate bars below the hearth of the furnace.
(e) Waste Gas or Smoke Flue.— As the hot gases from the
furnace are to be passed under a boiler, there is no necessity for
increasing their velocity of flow. Increasing their velocity would
necessitate a decrease in the gas pressure below the boiler by
means of the draft supplied by the chimney. But such a decrease
in the pressure is always accompanied by the sucking in of the
cold outside air, which reduces the temperature of the gases and
decreases the production of steam; it is therefore desirable to
(1) Refer to Appendix III.

METHODS OF COMPUTING FOR FURNACES	85
give the waste gas flue sufficient area to reduce its frictional
resistance to the passage of the gases to a minimum.
Assuming for the waste gas flue, considered as an inverted
weir, a width of 1 m, its height will be determined by YesmamVs
formula :
V
___
12X120Q==Q inm 636>
In order to insure the contact of the hot gases with the hearth
of the furnace, the waste gas flue is inclined downward from the
hearth level. This provides, at the same time, a pocket into
which the cinders from the hearth may drain.
It is now necessary to check the time period of the hot gases
in the heating chamber of the furnace and to determine the drop
in the temperature of these gases per second.
The average temperature of the hot gases will be
1400+1200
from which      t	Qiaoo = 2 m3 96.
The volume of the heating chamber of the furnace is equal,
according to the dimensions given, to 2 m3 80. The time during
which the hot gases remain in this chamber is therefore in the
neighborhood of one second, and the drop in temperature of the
gases is in the neighborhood of 200° per second, which may be
considered normal for this type of furnace.

i'

part II
PRINCIPLES FOR THE RATIONAL CONSTRUCTION OF
FURNACES
the problems of furnace construction will be solved when it is
possible to regulate the temperature within the enclosure of their
£'	heating chambers according to the requirements of the material
t	to be heated.    The gas passes from the firebox into the heating
(	chamber   without   having   completed   combustion.    The   first
*'	problem to be solved, therefore, is to afford space in the heating
chamber within which combustion may be completed.    With a
short concentrated core of burning gases the highest temperatures
are obtained.   At other times, according to the material and the
method by which it must be heated, it is necessary to prevent the
formation of a jet of burning gases and to provide a general
combustion of the gases throughout the heating chamber (a long,
t	soft flame).
*	The second problem is in the heating, by means of the hot gases
obtained, of those objects which have been placed in the heating
!	chamber of the furnace for this purpose.
f	For the time being, the first of these problems will be neglected,
and this portion of the present work will be devoted exclusively
to the solution of the second problem, which may be more definitely
stated as follows: In what manner may the hot gases be circulated
so that they will, in the most perfect manner, surround the objects
being heated and be carried out of the heating chamber, in order
|	that their place may be taken by hotter gases?    In what manner
1	may the heating chamber be adapted to obtain such a circulation
I	of the hot gases?
*	The solution of this second problem is very simple, but in
I                     spite of its simplicity it is very poorly understood by practicing
I                     furnace  designers.    Upon the following  pages  are  collected a
I                     number of designs of furnaces which have been operated or are

88

RATIONAL CONSTRUCTION   OF FURNACES

if

still. in operation, and which infringe the most simple natural
laws, that is to say, a veritable collection of the monstrosities of
furnace design.
The Subdivision of a Current of Hot Gas. — Assume that the
current of hot flowing gas Q, which is giving off heat or cooling,
is to be divided between two vertical ascending channels, gi and #2,
this division to be effected in the manner shown in Fig. 45. The
veins of gas q\ and q% are at temperatures ti and fe and gi = <?2
and £i = fe. Assume that during the operation of this system the
amount of heat lost from the branch q\ is a little greater than the
amount of heat lost from the branch q% and that, accordingly,
the temperature ti becomes slightly less than fe- When fe> ti, the

fig. 46.
weight of the column of gas q\ becomes greater than that of the
column of gas #2, and accordingly the velocity of the current qi
will become less than that of the current #2- The decrease of the
velocity of the current of gas qi results in a further lowering of
its temperature t\; in other words, the velocity of the current of
gas qi will continue to diminish, and its temperature t\ will con-
tinue to decrease. During this time the velocity of the current
of gas #2 will, on the contrary, be increased, and its temperature
will become higher. The current of gas q\ will finally cease to
flow and the entire volume of the current of gas Q will then pass
through the branch q%. But there will still be a loss of heat from
the channel qi and after the velocity of this current has decreased
to zero it will reverse and travel in the opposite direction, as is

THE SUBDIVISION OF A CURRENT OF HOT GAS

89

indicated in Fig. 47.    From the preceding, it may be readily seen
that a current of hot gas which i$ giving off heat or cooling cannot be
subdivided into equal ascending currents.
When,   however,   the   attempt  is
made to subdivide the current of gas
Q into two   equal descending currents
(Fig. 46), it will  be completely suc-
cessful.
fig. 47.
Assuming, for example, that the
temperature of one of these currents,
q\, should become less than the tem-
perature of the current q%. In this
case the weight of the column of gas
qi will be increased, and the velocity
of its descending motion will be in-
creased. The current of gas qi will
become stronger than #2, its tempera-
ture will gradually increase and it will
finally become equal to #2. It can be concluded from this that
the problem of subdividing a current of gas which is cooling or
giving off heat into equal descending channels may be solved
in a very simple manner, owing to the fact that there is always
a tendency for the temperatures of these descending streams to

remain uniform.
Therefore, if it is desired to sub-
divide a current of hot gas which is
cooling or giving off heat, into equal
streams, it is necessary to give these
streams a downward or descending direc-
tion of flow] or, in other words, a cur-
rent which is cooling may be subdivided
into uniform descending streams.^
fig. 48a.
(1) Accordingly, it is possible to approxi-
mate the fractional resistance in the two chan-
nels between which the current is divided,
when one branch has a higher resistance or
a higher heat loss than the other, because
the stream of gas divides itself accordingly.
In Fig. 43a, such a case is shown.   The
stream of gas Q is divided into two descending streams q\ and #2, the average
temperatures of which are different, being denoted by t\ and /2. The average

79T
90	RATIONAL CONSTRUCTION OF FURNACES
It is frequently necessary to subdivide a current of cold air or
gas which is being heated, as in the hot-blast stove or in furnace
regenerators. This problem may be solved as follows : Figs. 48 and
49 show a current of .a cold gas circulating through a channel,
having walls heated to incandescence. Assume that the stream
of cold gas being heated has been equally divided between two
velocities of these two streams are denoted by ui and u>> and the friction in
the two branches in millimeters of water is & and &.
The condition necessary for the maintenance of equilibrium, in this case,
is that the increase of the hydrostatic pressure in the two branches q\ and r/2
shall be equal. If there were no loss of hydrostatic pressure in impressing
the velocities ?/i and u? upon the two branches and in overcoming the fric-
tional resistance & and & of the two channels to the passage of the gas, the
hydrostatic pressure in millimeters of water in the channel q\ of a height h
would be, taking 1.29 kg as the weight of a cubic meter of the furnace gas
at°°
J1.
I	1.29A
<>
f }\	For the branch qz, the hydrostatic pressure would be
*°
A part of these increases in the hydrostatic pressure will be expended in
overcoming the frictional resistances & and £>, and in impressing the velocities
hi and uz upon the columns of gas. These last losses, in millimeters of water,
may be expressed in the following manner :
wi2     1.29         ,    uS     1.29
—X: -    and   —
and the condition for the equality of the increases in hydrostatic pressure
in the two branches is given by the following equation:
In this equation there are six variables; five of these must be known in
order to fix the value of the sixth.
For example, the checker openings around the outside of the checker-
work of a Cowper hot-blast stove lose a great deal more heat by radiation
and by the cooling effect of the outside of the stove than the central passes.
By reason of this they have a much greater cooling effect upon the current
,	of hot gases, and therefore the current of gases flowing downward through
|l	these openings is reinforced, since if fe<*i, ii2>%.   By measuring fe and th
it is not difficult to find —.
Us

THE SUBDIVISION OF A CURRENT OF HOT GAS

91

descending channels q\ and #2 having equal temperatures t\ and fe,
that one of these streams takes up the heat a little faster than the
other and that, for example, ti becomes slightly less than fe-
The column of gas q\ becomes, therefore, slightly heavier than the
column #2, the current qi commences to flow with greater energy,
and its velocity increases; .ti commences to become sensibly less
than fe, the current q\ has a greater cooling effect than the current
g2 which continues, on the contrary, to take up more heat; and,
in the end, the entire stream of gases passes through the branch gi,
while in the branch q2 there will be established at the same time a
reverse current which circulates as indicated by the clotted arrows
(Fig. 48).

Q
S-^
vb
fig. 48.

Q

\
tf1 		\
72 	I 		
			y 		
			1 		
			//• 		
			1 		
			'/ 		
			^
x 		
tl 		t<> 	s 		
V 		V 		;^; 	

	«"—» 	
	*"— Q 	
^^;,,,.	,;,/^
fig. 49.

Therefore, a current of cold gases which are being heated cannot
be subdivided equally between descending channels.
When the subdivision of a stream of cold gases is made through
ascending channels, the results will be as desired. Assuming that
the currents flowing as indicated in Fig. 49 were not equal, q\>q%
and, consequently, fe>£i- If fo>£i, the weight of the column
<72 will be less than the weight of the column gi, the current #2 will
become stronger; this will cause the temperature fe to become
lower; at the same time t\ will increase in this manner and the
two temperatures will be equalized; the two currents q\ and #2
will therefore be maintained equal.
• It therefore follows that when a current of cold gas is to be
heated it should be subdivided into a number of ascending streams.

wr
\ I i i

92	RATIONAL CONSTRUCTION  OF  FURNACES
These rules regarding the subdivision of gaseous currents,
while extremely simple and elementary in character, have received
very little attention from metallurgists. The experienced chimney
builder, who installs hot-air-heating apparatus in residences, is
well acquainted with these laws, which are absolutely ignored by
a number of very eminent engineers.
A number of examples of incorrect furnace construction are
shown below. These furnaces are designed to work in complete or
partial opposition to the foregoing rules; they accordingly work
very poorly, and many of them have had fco be completely
abandoned.
In industrial practice, so many of these defectively designed
furnaces are encountered that it is absolutely impossible to enumer-
ate all of them. It is therefore thought that the best method
of illustrating these defects will be a systematic description of the
various types of furnaces and heating apparatus, with a brief
description of the correct and incorrect constructions.
They will be taken up in the following order:
I. Vertical Regenerators;
II. Horizontal Regenerators;
III.	Hot-blast Stoves;
IV.	Hot-blast Temperature Equalizers;
V. Iron Tube Hot Blast or Air Heaters;
VI. Steam Boilers;
VII. Chamber Furnaces, Brick and Pottery Kilns;
VIII. Cementation Furnaces;
IX. Annealing Furnaces for Malleable Iron ;
X. Continuous or Multiple-chamber Kilns;
XL Muffle Furnaces;
XIL Vertical Furnaces for Tempering, Annealing and Heat
Treating;
XIII.	Horizontal Tempering Furnaces;
XIV.	Annealing and Heating Furnaces for Boiler Plates;
XV. Coal-fired Reverberatory Furnaces;
XVI. Siemens or Regenerative Heating Furnaces;
XVII. Pit Furnaces, Heating and Soaking Pit;
XVIII. Continuous-heating Furnaces;
XIX. Tunnel Furnaces.

VERTICAL  REGENERATORS

93

f

I. VERTICAL REGENERATORS
The ordinary vertical regenerator is so constructed that it
should work in a rational manner; that is, the high-temperature
gases descend regularly and subdivide among the vertical passes
according to their temperature, while the air and gas which is
being heated subdivides into the ascending passes in the same
manner. This is why the idea of Schenwelder, of dividing each
of the checker chambers into two compartments, in order to secure
uniform working, is fundamentally wrong. He introduced into
regenerator construction a superfluous complication, and for this
reason his design has been abandoned.
Nevertheless, it should not be concluded from the above that
any sort of a vertical regenerator will always work in a regular
manner. Vertical regenerators have an inherent tendency to
work uniformly, but poor design may cause them to work in a
very irregular fashion.
t Cf^jJ.K^pJ^nju^|jj>ijj^^	\^^^^^y^\^^-^^yr\\^^
fig. 50.
For example, Fig. 50 shows a very common form of regenerator,
in which the current of
gas from the vertical flues
leading to the ports is
jetted upon the top of the
checkerwork. It is very
evident that in this case
it will be impossible to
secure uniform operation.
The checkerwork can only
work in a uniform man-
ner when sufficient space
is provided below the
arch over the chamber for

the velocity of the gases to become zero or very close to zero.
The eddies, which are formed under too low an arch, disturb the
gas distribution and prevent the furnace from working uniformly.
In order to secure uniform results it is necessary to provide suf-
ficient space to absorb these eddy currents, in order that the
gases may enter the checkerwork with a very low velocity below
the arch over the chamber. As an example of a very good type
of regenerator we have shown the chamber of a 40-ton open-hearth
furnace at tho, plant of the Pennsylvania Steel Co., Fig. 51.

94

RATIONAL CONSTRUCTION OF FURNACES

From time to time vertical regenerators are designed without
regard to the fundamental principles that a current of hot gases
in cooling should pass downward, and a current of air or gas which

fig. 51.
is being heated should pass upward.   Figs. 52 and 53 show such
construction.
In each of these cases the current of gases changes its direction
of flow from upward to downward, or vice versa. Thus in Fig. 52
the gases which are giving off heat enter at the top and flow to the

 

.... lm^id—L, ',.,,. L,,, 1	'^...Iv.'
/•///^w^^^v^
fig. 52.

fig. 53.

bottom of the checkerwork (in the correct manner) and then turn
and flow from the bottom to the top of the second chamber (in an
incorrect manner); in Fig. 53 the gases which are giving off heat
enter at the bottom and rise to the top (in the incorrect way),
then they flow downward (in the correct manner).

HORIZONTAL REGENERATORS

95

II. HORIZONTAL REGENERATORS
Horizontal regenerators have a bad reputation. There is
nothing surprising in this, because in the design of this type
of regenerator there is displayed a gross disregard of the rules
governing the subdivision of gaseous currents. Take, for example,

fig. 54.
the regenerators of the celebrated furnaces designed by H. H.
Campbell, which could not be forced to work well (Fig. 54).
In these regenerators the hot gases enter and pass out of the
upper part of the chamber. It is evident that in this checker
chamber the gases flow in an inverted channel and, if the depth
of the flowing stream is less than the distance from the arch to
the bottom of the chamber, they will not touch the latter.

fig. 55.
Note by English translator.—It may very readily happen that the con-
ductive area of the checkerwork will be sufficient to cause the lower portion
of the checker to reach a high temperature; but at the same time the
frictional resistance to the flow of the gases and air will usually be so great
that this design of checker will not work without forced draft. Horizontal
recuperators are subject to this same defect and it is difficult to secure good
results unless the passages are very short.

rr

i

96

RATIONAL CONSTRUCTION OF FURNACES

It is comparatively easy to correct these regenerators in a
manner which will cause them to work better.    Fig. 55 shows the
correction or change which
should be made. [This
change, however, does not
affect the frictional resist-
ance of this type of checker
work.] The hot gases enter
the top part of the cham-
ber and leave at the bot-
FIG. 56.	torn; the height of the cham-
ber h  may be   calculated

according to the formula of Professor Yesmann in the same manner
as the height of the flues leading to the reversing valves; in this
way it is possible to design
these chambers of such a
height that the lower free
surface of the current of
gases will be at the level
of the bottom of the
chamber.
fig. 57.
The checkers designed
by Dalen (a well-known
German designer of fur-
naces) show a construction equally erroneous (Figs. 56 and
57). Here the hot gases are conducted into the checker cham-
ber, not at the top, but below the middle of the chamber.

fig. 58.
Such a regenerator heats
the gas nicely (Fig. 56),
but it works very in-
efficiently, because the
heated gases are very
light and the hottest
gases are trapped in the
upper part of the cham-
ber and cannot pass out
to the flues, while the
upper portion of the checker does not do any work at all and
forms a pocket filled with immobile heated gas.
Fig. 58 shows a horizontal regenerator constructed in a rational

HOT-BLAST STOVES

97

manner. The wall act, indicated by dotted lines, may be removed,
as it is useless.
The construction shown by Fig. 51 is very good; in this there
are two vertical regenerators placed side by side in place of a
horizontal regenerator. The correct direction is given to the
flowing gas currents. The main defect of these regenerators is
due to the frictional resistance which they offer to the passage of
the gases.
Regenerators in which the built-up checkerwork is replaced
by vertical channels or cells, constructed in a manner similar to
that used in the hot-blast stove designed by Withwell, are
considered in the section upon " Hot-blast Stoves."

III. HOT-BLAST STOVES

The regenerative principles of Siemens were applied by Cowper
in 1860 to the heating of the air for blowing blast furnaces, w At
first, however, these hot-blast
stoves were not a success.
Percy Wedding, in his Manual
of Metallurgy, shows some of
the early designs of hot-blast
stoves, one of which is given in
Fig. 59. The first stoves were
heated with coal fires; the gas
from the blast furnace was not
utilized until later. The hot
products  of  combustion   from
the fire flowed directly upward
to the top of  the  stove and
passed out of the structure through a primitive chimney valve
in the dome.   The cold blast entered the apparatus at the top and
(1) Note by translator.—The early blast furnaces were simple open-topped
shafts with no bell or hopper. The gas was burned at the head of the furnace,
and the blast pressure was very low. The charging was very elementary;
in many cases the top of the furnace was reached by an inclined plane up which
the charge was carted in simple dump-carts which were backed up to the open
shaft and dumped the charge into it. Later, when the bell and hopper were
utilized to close the top of the furnace the gas became available for heating
the blast and making steam. (The name, Hot Blast Stove, is a survival from
the early coal-fired stove.)

98

RATIONAL CONSTRUCTION OF FURNACES

• f f

the hot-blast valve was connected to the lower part of the stove.
It may be readily seen that the currents of gas and air in this
apparatus were circulated in the wrong direction; that is, in the
opposite direction to the natural convection currents.
Cowper afterward perceived the error in the gas circulation
in his early design, and in later designs the currents of gas and air
were circulated in the correct direction (Fig. 70). Combustion
took place in a central or eccentrically placed chamber, the hot
gases rising to the dome where they were reversed and subdivided
among a number of parallel passes down through the checkerwork.
Uniting in a lower chamber, they, were then carried away through
the chimney valve. The cold blast entered the stove chamber
below the checkerwork, through which it passed upward in a
number of parallel streams to the dome of the stove. There it
changed its direction and passed downward through the combus-
tion chamber to the hot-blast valve. The Cowper hot-blast stove
retains this general arrangement to the present day.
It would be difficult to find any apparatus which has passed
through as many modifications of design as have these stoves;
however, very few of these modifications have come into extended
use, because practically all of them have been based upon an
entirely false idea in regard to the laws governing the circulation
of gases while heating and cooling.

Fig. 60.
The single weak point of the Cowper hot-blast stove lies in the
location of the combustion chamber, which, in
the form of a vertical tube, or chamber, occupies
a very large amount of space and is very poorly
adapted for the purpose for which it is employed.
The attempts to improve the design of these
stoves should be directed toward the elimination
of this tube for the combustion chamber. The
space located immediately below the dome of the
stove might be employed for a combustion cham-
ber, as is suggested below. Moore's patent (Fig.
60) shows a single-pass construction of this char-
acter, but is badly worked out. In Moore's
stove the hot gases of combustion pass upward,
in the opposite direction to their natural convection
currents.

The first modification of the Cowper stove was made by

HOT-BLAST STOVES

99

Withwell. The experiment shown in Fig. 61 illustrates the defect
of the Withwell stove. Stoves of two designs were photographed,
immersed in a glass tank filled with water, WithwelFs design on the
left and the Cowper design on the right. The period illustrated
is that during which they are upon gas, or heating. The uniform
level of the lower surface of the colored kerosene forced downward
through the checker passes of the Cowper stove illustrates the
regularity of the heating of its checkerwork. In the Withwell
stove, on the other hand, the chambers are filled with the colored
kerosene in a manner which is far from uniform. The chambers

fig. 61.
through which the kerosene descends are completely filled, while
those in which it rises are not filled at all, the kerosene rising in a
thread-like stream which comes into contact with a very small
portion of the wall area of the chamber. These chambers, there-
fore, will not be uniformly heated; and for this reason will impart
very little heat to the air. If water is introduced at the lower
part of the model to represent the cold blast which is being heated,
it will be seen that those chambers through which the water rises
are completely filled, while in those in which the water passes
downward it falls in small streams which have very little contact
with the walls of the chamber. A mere glance at these models is

100

RATIONAL CONSTRUCTION OF FURNACES

sufficient to show clearly the reasons which have led to the com-
plete abandonment of the Withwell stove. ^
The ideas of Withwell have found their realization in the
Massick and Crook stove, which had quite a name at one time,
and which was only distinguished from the Withwell stove by the
arrangement of the passes. This arrangement was such that the
gases traveled alternately up and down through the three
passes. The Massick and Crook hot-blast stove has now been
superseded for reasons which will be clearly evident to the
reader.
Many inventors have applied themselves to the problem of

 

fig. 62.

fig. 63.

securing uniformity in the operation of the checkerwork heating
surface and passes, apparently without the slightest suspicion
that the regular and uniform descent of the hot gases in cooling
is a natural property of the gases. For a time the design patented
by Becker (Fig. 63) was much favored. In this design the open-
ings in the checkerwork were given different dimensions, naturally
a> Withwell himself noted the defects in his design, and in a later design
(Fig. 62) he gave the hot gases a circulation in the proper direction, from top
to bottom. This design approximates the type of regenerator shown in
Fig. 51.

HOT-BLAST  STOVES

101

resulting in a less uniform heating than is secured in the ordinary
design of the Cowper stove. M
In the model (Fig. 61) of the Cowper stove the cross-section
was intentionally made with checker openings of several sizes,
in order to show, in a graphic manner, that such complications
of the checkerwork are useless.

The hot-blast stove patented by J. Z. Stephenson and J. Evans
(Fig. 64) has never come into any ex-
tended use. In order to insure a uni-
form distribution of the hot gases
through the checkerwork the inventors
resorted to a series of complicated walls
and dampers in the chamber below the
checkers.
fig. 64.
The discussion carried on in the
technical journals, between Luhrmann
and these inventors, is mentioned merely
for its historic interest. Luhrmann con-
tended that the largest portion of the
waste gases passed through the section
above A and the smallest portion
through the section above C. The in-
ventors claimed the contrary. This
discussion made it very clearly apparent
that the ideas of contemporary constructors, in regard to the cir-
culation of the gases, were confused to a most remarkable extent.
The quarrel was finally settled to the satisfaction of both parties.
In the Cowper stove the work of the checkerwork is inherently"
uniform, and all walls and dampers below the checkers, for the
purpose of distributing the gases, are superfluous. (2>
(1) This design will give less frictional resistance in the large openings than
in the small; accordingly, the waste gases from the large passes will be hotter
than the gases from the smaller passes.
<2) In the Revue de M6tallurgie, for February, 1913, p. 362, can be found the
designs of a Cowper stove built for the furnace at Caen, France, and provided
with five chimney valves connecting the chamber below the checkerwork
with a bustle pipe outside the stove. The idea was, of course, that this would
conduce to the uniform distribution of the gases heating the checkerwork.
This idea, in many ways, resembles that of Stephenson and Evans, men-
tioned above. The multiplication of the chimney valves is useless. It would
be sufficient to replace them by a single valve whose dimensions may be
computed by Yesmann's formula.

102

RATIONAL CONSTRUCTION OF FURNACES

In a very large number of designs for hot-blast stoves the
attempt is made to circulate the hot gases in cooling and the
cold gases in heating, in directions contrary to their natural con-
vection currents.
The accompanying sketches of hot-blast stoves—Hartmann
(Fig. 65), Hugh Kennedy (Fig. 66), Macco (Fig. 67), Frank
Roberts (Fig. 68), Harvey (Fig. 69)—show that the laws governing
the subdivision of currents of hot gases while cooling and cold
gases while heating are not very well understood at the present
time.
Construction of the Combustion Chamber for a Hot Blast Stove.
—In the statements which follow, the attempt has been made to

Combustion Chamber
Fig. 65
• '    >' Plow of Products Combustion
	^. u<]ow of Air

Fig. 66

k. 67

show the rational location of the combustion chamber for a hot-
blast stove. For this purpose it is necessary to digress slightly
at this point, in order to set forth the rational chamber conditions
which are necessary for combustion.
If a flame or jet of burning gases in which the reaction of
combustion has not been completed is directed into a cold chamber
or upon cold objects, combustion will not be completed, even in
the presence of an enormous excess of air. Theoretical combustion,
without an excess of air, can only be obtained when the reactions
of combustion are completed in a chamber where the flame is sur-
rounded by incandescent walls and within which it is held for
one or two seconds. The construction of the combustion chamber

HOT-BLAST STOVES

103

must be such that it is possible to hold the flaming gases in the
chamber for a predetermined length of time, and that the walls
of the chamber will be heated to the highest possible temperature.

Fig. 08

Flow of Products of Combustion
Plow of the Air
How should the flame of reacting gases be brought into the
combustion chamber?
In the Cowper stove (Fig. 70) the combustion chamber forms
a cylindrical or elliptical opening extending the full height of the

F
104	RATIONAL CONSTRUCTION" OF  FURNACES
stove and open to the space below the dome at its upper end.
The volume of the combustion chamber is very large, w Never-
theless, it does not function in a satisfactory manner, because the
streams of flaming gases have a very high temperature and,

 

fig. 70.

fig. 71.

accordingly, a very slight density.    For these reasons, the stream
of flaming gases rises very rapidly, leaves the combustion chamber
(1) Guilow, in an article (Revue de laSociete russe de M&tallurgie, 1911, p. 164)
gives the volume of the different portions of a Cowper hot hlast stove at the
Kouchwa works, and the time the gas remains in these portions, as follows:

	Volume
Cubic Meters 	Time,
Seconds 	
Combustion chamber 	14 53 	4 60 	
Dome of stove 	6 16 	1 77 	
Checkerwork openings 	42 40 	16 96 	
Chamber below the eheckerwork 	 	5 14 	5 14 	
			
Totals 	 	68 23 	28.47 	
			
Note by translator to English.—It is rather interesting to compare these
volumes with the volumes of hot blast stoves given in a paper by Arthur
J. Boynton, National Tube Co., Lorain, Ohio, before the October, 1916,
meeting of the American Iron and Steel Institute. The Russian furnace
is undoubtedly much smaller than the American furnaces.

HOT-BLAST STOVES

105

without encountering any obstruction to delay it and flows into
the space below the dome. Accordingly, the rising column of
flaming gases passes upward without filling the combustion
chamber and is surrounded by an atmosphere of unburned rela-
tively colder gases, through which it passes. Direct observation
of the combustion of blast furnace gas in the Cowper hot-blast
stove shows that, as the ratio between the gas and the air supply
approaches the theoretical requirements, combustion ceases to
be silent and becomes noisy. The flame commences to jet out
around the gas burner in bursts, indicating a temporary extinguish-
ment of the flame in the combustion chamber, which is immediately
filled with a comparatively cold explosive mixture.

Everything indicates that the correct location for the combus-
tion chamber of the Cowper stove is the dome or space above the
checkerwork. The streams of flame which are produced cannot
pass directly out of this chamber, but are held under the dome,
heating its walls from below. The dome forms a permanent
firebox for their combustion. Below the dome of the Cowper
stove, therefore, there is a stationary hot zone, which burns those
portions of the gases which have not been utilized in the combus-
tion chamber, as soon as they come into contact with the heated
chamber. For these reasons the construction of a Cowper stove
with the combustion chamber
located elsewhere than in
the dome is fundamentally
wrong.
However, if the gas and
the air are simply introduced
above the checkerwork of
the stove, as is shown in
Fig. 72, there is evidently
danger that a portion of the
cold gas and air, in place of
entering into the reaction of
combustion and forming a
flame, will drop down to the
bottom of the stove, through	fig. 72.
the checker openings, just as
a heavy liquid will sink downward through a light liquid. In
order to prevent this occurrence, which is undesirable and

106

RATIONAL CONSTRUCTION OF FURNACES

wasteful, it is useful to direct the currents of gas and the cold
air for their combustion upward toward the dome of the stove
and give the combustion chamber an arrangement similar to that
shown in Fig. 73. There are many advantages in constructing
a hot-blast stove in this manner. In the Cowper hot-blast stove

the combustion chamber actually
occupies nearly 35 per cent of the
space inside of the shell and causes
an unnecessary increase of nearly
50 per cent in the cost of the
stove.
The analysis of this particular

fig. 73.

fig. 74.

I!
i .
I

case of combustion-chamber construction permits the following
rules to be deduced:
1.	The jet of flame in the chamber should not be directed
horizontally.
2.	The streams or jets of gas and air entering the chamber
should be, where possible, directed upward toward the dome or
roof.
3.	The products of combustion should be carried away from
the combustion chamber at the hearth level, in either a vertical
or a horizontal direction, as shown in Fig. 74.
Nevertheless, it is sometimes necessary that a vertical combus-
tion chamber should be used. In this case, it is not necessary to
repeat the error made by Cowper and construct the chamber as an
open pit (Fig. 70). It can be covered by an arch pierced by one or
Note by English translator.—Although Professor Groume-Grjimailo an-
nounced his theories over ten years ago they have not become very widely
known. Confusion and lack of knowledge still prevail among the designers
of hot-blast stoves. The direction of the natural convection currents of hot
gases in cooling and of cold gases in heating are ignored by the constructors
of three- and four-pass stoves.

HOT-BLAST  TEMPERATURE  EQUALIZERS

107

more openings; the total area of these openings may be arrived
at by the use of the formula given in an earlier chapter of this
work, for furnaces having an orifice in the roof for the escape of
the waste gases.
If the area of these orifices and the volume of the combustion
chamber are correctly proportioned, the combustion pits of the
Cowper stove will be completely filled with the burning gases,
which will be held in the combustion chamber by reason of the
strangulated outlet, until the reaction of combustion is completed.
The free space below the dome of the stove will cease to play the
part of a combustion chamber, and it will become possible to carry
the checkerwork up higher into the dome of the stove.

IV. HOT-BLAST TEMPERATURE EQUALIZERS
It is not difficult to show that the construction of a rational
apparatus for the equalization of hot-blast temperatures is not
practicable.
Fig. 75 shows the general arrangement of such hot-blast
equalizers as have been constructed.
Assuming that the temperature of
the blast is higher than that of the
brickwork in the equalizer, the
branch A, in which the hot gases
rise, will work irregularly, whereas
the branch B, in which the hot gases
pass downward, will be heated uni-
formly. The branch A will not heat
in a satisfactory manner; the branch
B will heat in a satisfactory man-
ner.
fig. 75.
Assuming that the temperature
of the hot blast drops below the
temperature of the brickwork, the
branch A will commence to cool
uniformly and rapidly, whereas
the branch B will cool irregularly and slowly.
No one has been able to obtain satisfactory results from the
use of hot-blast temperature equalizers, and for this reason they
are very rarely used.

1:

108

RATIONAL CONSTRUCTION OF FURNACES

V. IRON TUBE HOT-BLAST OR AIR HEATERS
This type of apparatus is now practically unknown, except
for the description of it which may be found in various books.
In the Manual of Metallurgy, by Percy-Wedding, twelve types
of iron tube air heaters are described, some dozen or so of pages
being devoted to their construction and the causes which led to
their being abandoned. Of the many types of this apparatus, the
only ones which have survived are those of the Besseges works
and the Cleveland type; all of the others have passed out of use.

^l^o^.^^/o^^^'.i^^-^-i^r-^^^^'^/S^r^^^v/i^ro;
'"•'•#• £vi^
fig. 76.
The reason for their abandonment is very simple: all of the
iron tube air heaters described by Percy-Wedding had the outlet
for the waste gases at their highest point. The hottest gases of
combustion rose immediately to the top of the chamber, licking
the surface of the iron tubes, and heating them irregularly, the
top being much hotter than the bottom. The tubes, heated in
this manner, burned out, warped and broke.
In the Besseges type of air heater the products of combustion
pass from chamber to chamber through ports in the division walls.
These ports are located at the level of the hearth. In this appa-
ratus the reacting portion of the flaming gases rise and then drop
through zones of uniform heating, where combustion is completed.

HTKAM   BOILKRS

109

These local centers of combustion arc* due to the excess air supply.
In proportion as they cool, the gases drop lower and lower, uni-
formly heating all of the tubes, which for this reason work in a
satisfaetory manner.
The Cleveland iron tube air* heater, which is not so widely
known, likewise works upon the (Iwvndrnft principle, (Fig- 70).
The disappearance of the numerous typos of iron tube air
heaters and the survival of the Bcwege.x and Cleveland designs
supplies a very good example of the importance of giving the cor-
rect direction to the circulation of the gases in furnaces.
VI. STEAM BOILERS
The constructors of steam boilers very rarely consider the
rational distribution of the hot, gases. Those defects are particu-
larly frequent in the most recently designed types of water-tube
boilers, an well as in the older designs. The lack of knowledge
of the laws governing the flow of the heated, gases explains the

_c:u

(
t
d I 	f J 		

	idly11-
Fm. 77. 	jljlju 	

numerous and complicated forms of baffling of all. kinds, aB well
as the use of special dampers to force the hot gases to bathe the
heating surface of the boiler and its tubes regularly and com-
pletely.
(Note, by Englwh trantttatfir. -The* ahHolute neglect and dinregard of tho
most elementary laws of phynicn is not corifinod to tho circulation of the
heated gawK, hut, is gronnly violated in the water ctintulution an well.)
In reality it is not necessary to have any baffling nor walls.
The hot gases have a natural tendency to flow in such a way that
the entire heating surface of tho boiler will be bathed by thorn
in a very uniform and regular manner. Without going into details,

110

RATIONAL CONSTRUCTION OF FURNACES

some of the useless and erroneous forms of boiler setting and
baffling which are given as " good " construction in Hutte are
shown below. These will very clearly indicate the ideas which
the author is endeavoring to set forth.
Fig. 77 shows a single-drum cylindrical boiler as illustrated
upon page 865 of the first volume of the French translation of
Hutte (edition of 1911).
Fig. 78 shows the correct method of setting the same boiler.
All of the baffling which was supposed to force the hot gases to
travel in a zigzag path has been eliminated. The hot gases, being
light, have a tendency to rise and apply themselves to the shell
of the boiler. Any constrictions of their path have a detrimental
effect, as they tend to increase the velocity of flow. In order to

						
1 					1
/! 	
		^ 			s 	
^ 	O^vVvVVwJ 	1 			& 	

fig. 78.
increase the time during which the heated gases remain in contact
with the boiler after leaving the firebox, the waste gas outlet has
been dropped as far as possible by lowering the hearth of the gas
chamber behind the bridge wall.
(Note by English translator.—This setting would be greatly improved by
placing the grate and firebox in a separate setting where the mixing gases
would not be chilled below the ignition point.)
The circulation of the gases in a boiler set in this way is effected
in the following manner: The boiler will be constantly bathed
by the hottest gases which tend to rise to the highest part of the
setting. As these gases are cooled they will drop lower and lower
by reason of their increase in weight while cooling. They will
finally, at their lowest temperature, fall to and pass out through
the waste gas outlet.
In order to avoid detrimental eddy currents it is necessary to

STEAM  BOILERS

111

fix the height of the opening over the bridge wall by the formula
for the inverted weir and avoid high gas velocities.
Fig. 79 shows the setting of a four-drum cyclindrical boiler,

fig. 79.
having the drums arranged in pairs above each other, according to
Hutte. The cross-section of this setting shows that the heating
chamber is divided into four flues for the hot gases:

fig. 80.
1.	One passage under the lower drums;
2.	Two passages at the sides of the two upper drums;
3.	One passage between the two upper drums.

fig. 81.
A very large proportion of the heating surface of this boiler is
covered and insulated by the numerous arches and baffles, making
it useless. It is very simple and easy to change this setting by the
removal of the walls and arches, as is shown in Fig. 80, at the same

112

RATIONAL CONSTRUCTION OF FURNACES

time lowering the waste gas outlet to the level of the bottom of the
gas chamber where it will remove the coolest gases in the setting.
Fig. 81 shows a two-drum cylindrical boiler (Hutte). In this
setting, those baffles which are built up from the bottom of the
setting are entirely useless and may be removed. This setting
will be better if built as shown in Fig. 82.
These three examples will serve to show very clearly the man-
ner in which boiler settings may be greatly simplified. Never-
theless, it is well known that commercial boilers, particularly
those designed for use upon ships, such as the Belleville, Niclausse,

fig. 82.
Yarrow, etc, are designed to work upon the updraft principle.
This is a serious error, as it violates the law of gaseous flow, and
as a result there is poor vaporization and a reduction in the
efficiency of the application of the heat.
VH. CHAMBER FURNACES, BRICK AND POTTERY KILNS
Barely thirty years ago, direct or updraft kilns were practically
the only kind used in the brick and pottery plants. At present
their use is decreasing and there is a strong preference for the
downdraft kiln.
It may be said that the direct or updraft kilns which are still
in service are the last traces of these kilns in this industry. At
the same time it is very curious to note that the firm, of Ernest
Schmatolla, t1) which is engaged almost exclusively in the con-
struction of brick and pottery-kilns, in a book published by them,
devote almost the entire volume to a description of the old updraft
kilns, and make no mention of the downdraft kiln beyond the
brief statement that these kilns generally give better results than
the updraft kiln.
(1) Ernest Schmatolla, Die Brennofen, 1903.

CHAMBER FURNACES,  BRICK AND POTTERY  KILNS     113

In a preceding chapter the principles governing the computa-
tion for the updraft chamber furnace -have been stated. By
partially closing the smoke hole in the dome it is possible to
force the free lower surface of the hot gases in the kiln chamber
down to the hearth level, and thus force the heating of ware
placed upon the hearth. Nevertheless such a method of heating
is very imperfect and is not uniform. Its mechanics are as
follows:

fig. 83.
The incandescent and burning gases issuing from the firebox
(Fig. 83) rise immediately to the
highest point in the chamber;
therefore the central portion of
the heating chamber does not
receive any direct action from
these ascending currents, and is
accordingly filled by heavier and
colder gases than those coming
from the fireboxes. These heavy
gases gradually drop to the
hearth of the chamber as the
upper parts of the chamber fill
with the hotter gases. Portions
of these colder gases in the bot-
tom of the chamber become
mixed with the heated gases
flowing from the fireboxes and rise with them. Finally a circu-
lation of gases is established within the chamber, so that all
portions of the charge are gradually heated.
Moreover, only a small portion of the heated gases circulate in
this manner. The largest portion of the hottest gases escape
immediately to the chimney through the smoke holes in the roof
of the kiln. For these reasons, all the ware, which is set where it
comes into direct contact with the hot gases is hard burned,
whereas the burn of the ware which only comes in contact with the
colder currents of gases will be less hard and portions of the ware
will receive a very slight burn.
While updraft or direct-draft kilns continue to be used in many
of the clay products plants, the principles of the downdraft kiln
Note by English translator.—Considerable heat is carried down to the
hearth of the kiln by conduction through the charge and the walls.

114

RATIONAL CONSTRUCTION OF FURNACES

are so well known in this industry that it will not be necessary to
devote much space to them.
Fig. 84 shows the same kiln (Fig. 83) reconstructed to work on
the downdraft principle. The distribution of the current's of hot
gases is very good, as the hottest gases rise to the arch of the
furnace and then divide themselves into uniformly descending
currents. One of the results of this reconstruction was the
reduction of the amount of defective brick turned out from
30 per cent to 1 per cent.
Fig. 85 shows a two-story kiln used in the manufacture of

tf I!

fig. 84.

fig. 85.

fig. 86.

porcelain. Such kilns are still actually in use. The upper
chamber works in an unsatisfactory manner, the hot gases being
divided into ascending currents; it is practically impossible to
regulate the distribution of the heat by changing the size of the
waste-gas opening. The lower chamber of the kiln, which works
on the downdraft principle, has a regular heat distribution.
Fig. 86 shows a kiln of this type correctly constructed, both
the upper and the lower chamber working upon the downdraft
principle. The firebox has been changed from the lower to the
upper chamber.
Note ly English translator.—Downdraft "beehive" kilns are widely used
in the manufacture of refractory brick. In the silica brick plants it is well
known that only one-seventh of the kiln capacity can be used for coke oven
shapes, many of which require two burns. The prevailing tendency in

CEMENTATION FURNACES

115

building larger and larger kilns is merely to increase the height and diameter.
However, there are limits upon the height, due to the crushing of the lower
tiers and the difficulty of securing an even burn throughout the kiln. These
difficulties do not appear in the small kilns.)
VIII. CEMENTATION FURNACES

fig. 87.
Mg. 87 shows an old type of cementation furnace cited in the
lectures of Professor Ledebur.    The hot gases rising from the

pig. 88.
firebox are subdivided immediately into ascending currents, which
are supposed to envelop and surround the boxes containing the
iron bars packed in charcoal. Much better results would be

116

RATIONAL CONSTRUCTION OF FURNACES

obtained  by reconstructing  this  furnace  upon the  downdraft
principle, as shown, in Fig. 88.

li

IX. FURNACES FOR ANNEALING MALLEABLE IRON CASTINGS
Fig. 89 shows the old style of annealing furnace for malleable-
iron castings, according to Professor Ledebur. Fig. 90 is from the
patent of P. Schnie in 1898, for the same purpose, but upon the
downdraft principle. It is evident that it was practical experience

fig.

 

1
I

and not theory which led the inventor to apply the downdraft
principle to these furnaces.
X. CONTINUOUS OR MULTIPLE CHAMBER KILNS
RING FURNACES
Ring furnaces or kilns, notwithstanding the apparent perfec-
tion of their design, have never worked in a satisfactory manner.
Their main disadvantages are the following:
Too rapid cooling of the burned ware;
The resultant cracking and spawling of the ware, which in
turn results in a considerable loss of product;
An excess of air during combustion, resulting in a very sharp
flame;
The high temperature of the waste gases;
The large amount of fuel required for burning the ware.

CONTINUOUS  OR MULTIPLE  CHAMBER KILNS         117
All of these defects are due to a disregard of the principles which
govern the subdivision of currents of gases when heating or
cooling.
This may be clearly shown by the consideration of a simple case
(Fig. 91), where A is the portion of the tunnel chamber in which
the air is preheated, B the portion of the chamber in which the fuel
is introduced and where the ware is burned, C the portion of the
chamber in which the ware is preheated by the waste heat, E the
flue connection to the chimney and D the portion in which the
ware is being set.
The sections may be considered in order, starting with section
B of the tunnel, where combustion takes place and the ware is
burned. The gas circulation which is to be established in this
section must be such that the hot gases flow to all parts of the
tunnel chamber being heated. The hot gases, however, imme-

_A
t max.

	^ Flow of products of combustion	7j7
,>. Plow of air
fig. 91.
diately rise to the roof of the tunnel and then flow to where the
cooling gases are drawn down into the waste-gas flue. The
placing of the waste-gas flue under the hearth of the tunnel is,
in general, favorable to the circulation of the heated gases, as it
apparently works upon the downdraft principle. Nevertheless,
it is not possible to obtain a uniform burn to the ware at the
bottom and the top of the turanel chamber. The upper part of
the tunnel is filled with a stream of light gases, the superheated
products of combustion, having a high temperature tfmax, while the
hearth of the tunnel is traversed by a current of waste gases which
are heavier and at a lower temperature W. In order that the
difference between the temperatures £max and tmm shall be as small
as possible it is necessary to set the ware to be burned in a compact
checker which will increase the resistance to the flow of the gases
in the upper part of the setting and to decrease the resistance to

I:

118

RATIONAL CONSTRUCTION OF  FURNACES

r
I:!'
H>
\-.\--
11

the flow of the gases in the lower part of the setting by the use
of an open checker.
By this artificial means it is possible to pass the greatest
portion of the hot gases near the bottom of the setting and in this
manner the temperatures £max and W may be very nearly equalized.
Therefore, in the portion C of the tunnel chamber the checkerwork
of the ware set to burn should be set close at the top and open at
the bottom.
The portion A of the tunnel chamber will be considered next.
This portion is filled with hot ware cooling, and through it is
passed the current of cold air to be heated. This air is a cold
and heavy fluid which will flow in the lower portion of the setting
without any tendency to rise. The only way in which this stream
of air can be forced to flow in the upper portion of the tunnel
chamber is to increase the resistance to its flow by the checker
work built in setting the ware in the tunnel, which for this purpose
should be set close at the bottom and open at the top, where less
resistance is required. Upon comparing the conditions required
in section A with those required in section C of the tunnel chamber,
it will be noted that they are diametrically opposed to each other.
It is true that the contraction of the brick or lime, in burning,
favors the correct method of operation in these sections. Since,
in the section of the tunnel chamber A, an open space will be
formed below the roof of the tunnel, due to the skrinkage of the
charge, this open space will be quite large in those kilns used in
burning lime. But in general, the operation of ring tunnel kilns
presents a complicated problem, to which there are two possible
compromise solutions:
1.	One solution secures an even heating of the crude material,
but the incoming air is poorly preheated and the cooling ware is
subjected to a sharp drop in temperature which is very liable to
result in cracked and spawled ware;
2.	The other solution secures a uniform preheat of the incoming
air and results in the gradual cooling of the burned ware, but
at the same time results in a non-uniform heating of the unburned
ware.
The first of these methods of operation is the one ordinarily
employed. For example, at the Wachter works at Borovitch, a
kiln of this type is used for burning firebrick. The lower part of
the tunnel is charged with lumps of fire clay whose quality will not

CONTINUOUS  OF   MULTIPLE  CHAMBER  KILNS        119
be injured by sudden cooling. An open checker is built on the
hearth of the tunnel with these lumps of clay, and on top of this
the brick to be burned are set in a close checker in the upper part
of the chamber. In this way the current of hot gases, which
tends to seek the highest point of the tunnel chamber, is retarded
in its flow and forced downward; the gases cool and produce a
current of colder waste gases over the hearth of the tunnel. The
brick which fill the upper part of the chamber are uniformly

 

Chambers Cooling

Gas      Chambers Heating
fig. 92.

heated and burned, but the utilization of their heat for the pre-
heating of the air is very poor and the kiln operates with very
little preheat of the air supply.
The construction and design of ring tunnel kilns is therefore
defective, because the currents of air being heated and those of
gases being cooled have the same direction of flow, whereas it is
necessary that the current which is giving off heat should flow
downward and that the current which is being heated should flow
upward. A ring tunnel furnace is ordinarily unable to satisfy

tv \iY r fi^r
'Utei] Lfeii UppJO [.!— ^j)[ -it- j.J'il MHg-il ptfKfcSCf
utzfcyo!^^
Chambers Cooling	Chambers Heating
FlG. 93.
this  condition,  and  for this  reason  its work  will  always  be
unsatisfactory.
The existing systems of ring chamber furnaces or kilns of the
Mendheim and other similar types are but little more satisfactory
than the ordinary types of kilns. Figs. 92 and 93 show two types
of the Mendheim ring chamber kiln, the latter of these having a
high bridge wall. The outside air enters the system through the
chamber from which the burned ware is being removed, and
passes in succession through all of the chambers which are cooling.

120

RATIONAL CONSTRUCTION OF  FURNACES

The course of the air through these chambers is indicated by the
arrows; the colder air tends to settle upon the hearth of the
chamber. It causes sudden and irregular cooling of that portion
of the setting through which it tends to flow, and at the same
time is not preheated to a high temperature and assists very little

 

jjf
li

fig. 94.
in the cooling of the setting. On the other hand the heating of
the setting is effected by gases which traverse these chambers in
the correct manner.
Due to the influence of the author's work, a Russian engineer,
K.-K. Adametzky (Varsovie), has secured a patent for the improve-
ment of the continuous chamber kiln by introducing supple-

^fc§»$^^
fig. 95.—Section CDEJ, Fig. 94.
mentary channels which connect the lower part of each chamber
with the upper part of the adjoining chambers. In this way it is
possible to realize the flow principles governing the heating and
cooling of gases in the operation of these kilns. However, the
construction is slightly complicated, and the author has succeeded
in finding a simpler method of accomplishing this result.

MUFFLE FURNACES

121

Figs. 94 and 95 show sketches of this type of kiln. Combustion
occurs in chamber III; the air is being preheated in chambers I
and II, and the bricks are being preheated in chambers IV and V.
The gases which are cooling have a downward flow, while the air
which is being heated flows upward; the circulation of the gases
is therefore correct. The change in direction of the flow of the
gaseous currents is effected by a system of channels or flues in the
walls separating the chambers: channels 6161, 6262, &3&s ... for
the air and d\d\, d^dz, feds ... for the products of combustion.
When the products of combustion are passing into a chamber
(for example, IV), the flues dd are open and the flues bb are closed.
The opening and closing of the flues bb and dd is accomplished in a
very simple manner by the damper brick shown in dotted lines.
The kiln which is designed according to this method is very
simple in construction, and the author will enter into correspond-
ence with any reader who may be interested in it. From this
short description of the ring tunnel or chamber kiln it may be
seen that it is not difficult to construct a continuous kiln which
will operate in a satisfactory manner through the rational flow of
the air and the products of combustion.

XI. MUFFLE FURNACES

For tne annealing and tempering of steel, the annealing of
brass and bronze and for other purposes, muffle furnaces possess
many advantages. A uniform temperature, the absence of jets
of flame, the small amount of oxidization and the protection of the
surface of the material being heated (a con-
dition very important in the stamping of
metals) make these furnaces a type much
favored in these works, despite the fact that
the muffles deteriorate quite rapidly. If the
currents of hot gases are circulated in a
rational manner, muffles of steel castings
will give a service of several years. Un-
fortunately, the great importance which
attaches  to  the  correct circulation of the
hot gases is not well known.	j?IG 95
Fig. 96 shows a muffle furnace which is
widely used.    The flame and hot gases are produced in a firebox

i i
ft i
1
i

122

RATIONAL CONSTRUCTION  OF FURNACES

below the muffles arid have an upward direction of flow. The
heating of these muffles is therefore not uniform and they wear
out very rapidly.
Fig. 97 shows the method of reconstructing this furnace to
conform to the rational principles of the circulation of gases. For
this purpose the hot gases enter the chamber at the top and pass
downward, and the waste-gas flue at the bottom of the chamber in
which the muffles are set draws off the coolest gases and passes
them, to the chimney.
It is by reason of the incorrect direction of the flow of the hot
gases that the vertical muffles used for tho trmporing of shells

^£sll=±g3s
Y

fig. 97.	I'Vu.98.
for artillery rarely work well. Fig. 08 shows a rnarmor of sotting
these muffles which has given Rood results in the author's practice,
because it gives the correct circulation of the hot gases. The
muffle furnace shown has "worked perfectly.
Attention is also called to a horizontal muffle furnace in the
Petrograd Arsenal which -was at last reconstructed as directed by
the author and which worked perfectly thereafter. <l> Originally
this muffle furnace, which operated "with updraft, had four fire-
boxes furnished with clampers; the muffle was of cast iron,
3560 mm long, 1000 mm wide and 100 mm high. It did not
operate in a satisfactory mariner. By direction of the author it
was transformed into a downdraf t furnace without any alterations
(1) Revue de h ftociete rusae do M&tallurqw, No. 5,1913;
XI, bis, p. 322, mai 1V14; Appendix V.

VERTICAL FURNACES  FOR TEMPERING	123
to the muffle, and since then has operated in a satisfactory manner,
the following points being worthy of note:
1.	In spite of the large size of the muffler, its temperature was
absolutely uniform, and no differences of temperature could be
detected between the different portions of the furnace, by the use
of a Le Chatelier pyrometer;
2.	By the operation of a damper, this temperature could be
regulated   very  accurately  within   a   wide   temperature  range
(900° to 400°) ;
3.	The quantity of fuel consumed (55 kg 80 per hour) corre-
sponded exactly with the computed fuel consumption.
The only trouble with this furnace resulted from the inter-
mittent operation to which it was subjected. This caused bending
and warping of the muffle which failed completely after about
two months' service, necessitating replacement. That this warp-
ing was entirely due to the intermittent operation of the furnace
is borne out by the fact that a vertical muffle for practically the
same class of work, installed in a furnace in the Poutiloff works,
which is operated continuously, lasts about fourteen months.
In order to eliminate the trouble in the furnace at the Petrograd
Arsenal the muffle was removed and the openings in the hearth
for the removal of the waste gases were relocated. This furnace
works very nicely for tempering and annealing, but it is no longer
a muffle furnace. Finally the furnace was reconstructed with a
new muffle constructed of special thin bricks, and since that time
no operating troubles have developed.
XII. VERTICAL   FURNACES   FOR   TEMPERING,   ANNEALING   AND
HEAT TREATING
The application of the downdraft idea has nowhere given such
brilliant results as when applied to vertical furnaces, and there is
no other form of furnace which gives so little satisfaction and so
much trouble as a vertical tempering furnace. The reason for
this is very simple. In every works " the heat-treating depart-
ment " is the " forbidden ground " of the plant. Secrets, secrets
and secrets! As a matter of fact, the men who possess these secrets
always know less than those who do not possess them.
Nevertheless, tempering and annealing furnaces only require a
working temperature varying from 800° to 1000° and—good or
bad—they may be operated. With regard to the heat-treating

m  ,
I ' f

124	RATIONAL CONSTRUCTION OF FURNACES

' \	furnaces it may be said that few of them are good and that the
!i	process of heat-treating which is actually in use is less satisfactory
than the tempering process.
• i,	For heat-treating or temper-drawing furnaces, the temperature
11	must be maintained at less than 700°, that is to say, at a tempera-
'',	ture at which the reactions of combustion can scarcely take place,
I.	and for this reason the gas must be burned outside the furnace;
i	after this it is necessary to cool it in a special combustion chamber,
to the temperature required.    It is then passed into the heating
' I	chamber of the furnace and heats this last in a uniform manner
| i	to 400°, 500°, 600°, according to the requirements of the work.
i \	The furnaces for the tempering of the tubes and jackets for
large guns are built as pits with fireboxes at different levels, the
waste gases being taken off at the highest part of the pit.    The
cannon are rotated on their axis during this operation.    Reheating
jj	these gun parts is done in'the same manner in Russia as in the rest
f*	of Europe, except that in Russia wood fuel is used, as it is con-
li	sidered better than coal for this purpose.    Recently it has been
II	found that these furnaces could be heated with gas, combustion
ji     ,	being effected by a large number of burners arranged spirally
'	around the chamber.
Two errors are committed in the design of these furnaces:
1.	The high-temperature flaming gases of the burner are pro-
duced in the heating chamber;
2.	The waste gases are drawn off at the top of the furnace.
With this system the heating of pieces as long as 18 m is a
matter of considerable difficulty, and it is evident that in the
furnaces for the tempering of such gun tubes, it is necessary to
make use of the downdraft principle. Just what must be done to
obtain this result is shown more accurately by the drawing (Fig. 99)
of a furnace which is in use in one of the large works for tempering
heavy field artillery jackets. The flame is developed in a firebox
independent of the furnace, from which the hot gases rise into
the free spaces located on both sides of the heating chamber,
entering the latter through a number of small orifices or ports;
then, rising to the top of the chamber, they are carried off by the
waste-gas flue. Taking these gases off at the top spoils the
furnace. If its designer had located the waste-gas port at the
level of the hearth of the heating chamber he would certainly have
obtained a much more uniform operating condition.

VERTICAL   FURNACES FOR TEMPERING

125

It would be very simple to change this furnace in the manner
shown in Fig. 100. Here the hot gases from the independent
firebox are set free in the heating chamber of the furnace and
drawn off from the bottom of the chamber. The circulation of
the heated gas is indicated by the arrows.
Certainly, this construction is not suitable for heavy artillery

 

fig. 99.

fig. 100.

tubes and jackets. A pit jn the neighborhood of 20 m in depth,
as required for the large naval guns, cannot be heated in such a
simple manner; but, in general, the problem may be very easily
solved if the radiation losses from the heating chamber are avoided.
Another type of vertical annealing furnace is that used for the
annealing of iron wire before and after it has been passed through
the drawing blocks. Fig. 101 shows the design of a furnace for

MT f

126

RATIONAL CONSTRUCTION OF FURNACES

I
I

this purpose according to the Meyl system, as constructed in a
works in Russia. This furnace, in spite of its complexity and high
cost, was very unsatisfactory in operation. The annealing of the
material was very irregular, and ultimately it became necessary

to rebuild the furnace. The
drawing (Fig. 101) shows
clearly the cause of these poor
results; the hot gases in the
heating chamber rose from
the gas ports at the bottom of
the chamber to the waste-gas
ports at its top and for this
reason the iron pot in which
the coils of wire were placed
was not heated uniformly.
fig, 101.
Moreover, the small amount
of space in the chamber did
not afford the possibility for
the development of the flame,
a portion of the gases being chilled below their ignition temperature
by the comparatively cold pot.
It is very evident that a furnace of this kind should be recon-
structed to work upon the downdraffc principle and in addition
should be furnished with a combustion chamber.

HORIZONTAL TEM-
PERING FURNACES
Fig. 102 shows a fur-
nace constructed accord-
ing to the Krupp system
for use in the heat-treat-
ing or tempering of shells
at a plant in Russia.
The Krupp Company
have adhered to the
system of heating the
material in the furnace
by heat radiated from
the roof. It may be	fig. 102.
seen by  this  ridiculous  construction how  far from  the  true

II

HORIZONTAL TEMPERING FURNACES

127

principles of heating they have been led by this theory. In
the furnace here shown, the purpose of the design was that the
shell should be rolled upon the hearth of the furnace, being heated
at the same time by the heat reflected or " reverberated " from the
roof; accordingly the incandescent gases from the fireboxes, in
which coke was burned, were passed through the free space under
the arch of the furnace, to the working opening at the highest
point of the arch. But the shells were not surrounded by the
incandescent gases; instead they were placed in a pocket of

fig. 103.
colder and stagnant gases which quickly absorbed any heat they
might receive by " reverberation.73
The work of this furnace was very unsatisfactory. In addition,
it was found desirable to substitute wood for the coke, as the
latter fuel is costly in Russia. This furnace was reconstructed
according to the author's design (Fig. 103). No change was made
in the general arrangement of the furnace, but the direction of
flow of the hot gases was reversed and the hearth was changed so
that the shell rested on a number of parallel ribs of brick, a grid-
iron hearth, arranged so that the colder gases were drawn off from
the hearth by ports below the level of the shell into waste-gas
flues. The furnace then worked perfectly.

f -	7^

128

RATIONAL CONSTRUCTION  OF FURNACES

XIV. ANNEALING AND HEATING FURNACES FOR BOILER PLATES
Fig. 104 shows an annealing or heating furnace for boiler plates.
The downdraft principle is widely used in these furnaces. They
work in a very satisfactory manner, but have the great disad-

fig. 104.
vantage that only one plate can be heated at a time, if it covers
the entire hearth of the furnace. Accordingly the output of these
furnaces is very small and the consumption of fuel is excessively
high. If an attempt is made to heat several plates at a time in
this furnace by placing one on top of the other in a pile, the heating
is irregular and not uniform, as the waste gases cannot be drained

fig. 105.
away from the heating chamber as they are cooled in giving up
their heat to the charge. In order to secure a rapid and uniform
heating of several plates at a time, provision must be made for the
cooled gases to flow out of the heating chamber as rapidly as they
give up their heat. Fig. 105 shows a plate heating furnace con-
structed for the purpose of heating several plates at a time.
These plates are piled upon iron skids. The waste-gas outlet is

ORDINARY REVERBERATORY FURNACES

129

located at the center of the hearth and the colder gases are drained
to it by sloping channels passing in this way underneath the plates
being heated. As the lower surface of the plates is exposed to the
hot gases, their heating is rapid and uniform.
Reiner, an engineer, conceived the plan of annealing or heating
plates by placing them in the furnace on their edges, and con-
structed the furnace shown in Fig. 106. This furnace did not
give satisfactory results because the hot gases circulated upon

 

fig. 106.
the updraft principle, and for this reason the annealing of the
plates was not uniform.    The idea was therefore abandoned.
The idea of Reiner may be conveniently utilized by reversing
the direction of flow of the gases to the downdraft method and
building the furnace with a solid roof, (*> placing the working doors
in the side wall.
XV. ORDINARY REVERBERATORY FURNACES FOR REHEATING
(With bar grates')
In coal-fired furnaces with the ordinary bar grate a temperature
of 1350° may be obtained in the firebox with a regulated air supply.
An air supply of 1.50 to 1.75 times the amount theoretically
required, according to the quality of the fuel used, will result in
such a drop of the temperature of the hot gases that it becomes
C1) Note by French translator.—In the plate annealing furnace, as designed
by Reiner, the plates were charged into the furnace through its roof and not
by doors in the side walls.

Iff I f
(	130	RATIONAL CONSTRUCTION  OF FURNACES
impossible to attain the necessary working temperature in the
furnace.
A furnace is a very delicate mechanism, which cannot be suc-
cessfully constructed unless the two following conditions are
successfully met:
1. The mixture of the air and the combustible gas must be
thorough;
,,•'•	2. The size of the combustion chamber must be such that the
-' -	jet of flame may form in the fore part- of the heating chamber.
In addition, as the working temperature of the furnace is very
! | '<	nearly equal to the instantaneous calorific intensity computed for
the fuel, the time during which the hot gases remain in the heating
chamber is less than one second; the supplying of flaming hot
! i |     }	gases to the heating chamber and the withdrawal of the waste
I	j	gases must be accomplished with uniformity.
I1	From the foregoing it is evident that the art of proportioning
^                                     these furnaces is, above all, a question of combustion, and that
this must be completed -before the gases reach the rear of the
heating chamber. It will be necessary to take up and analyze
I	this question in order that the direction to be given the current of
I	hot gases may be fixed.
I	In one of the preceding sections mention was made of the
§
;     i	conditions under which combustion may be best effected.    In
!   . '	postponing   the   examination   of   these   conditions   the   author
remarked that, for the better mixture of the combustible gases
with the eomburent, resource was had to a strangulation of the
opening over the bridge wall, just as a kerosene lamp is prevented
from smoking by the contraction of the chimney.
The only result of this contraction in the opening over the
bridge wall is that of increasing the velocity of the hot gases
passing that point. On account of this lowering of the roofs,
these gases, after passing into the heating chamber, are slowed
down and fill the chamber over the hearth, from which they are
drawn off through the waste-gas or chimney port. This shows
why it is necessary to place the waste-gas or chimney port at the
level of the hearth of the furnace, and exposes the error in the
construction of those furnaces which have an updraft and from
i |	which the waste gases pass away at the highest point.
Practice completely confirms these deductions; in all reheating
furnaces the waste gases should be carried away from the heating

SIEMENS TYPE EEHEATING  FURNACES

131

chamber at the level of the hearth; notwithstanding this fact, in
metallurgical plants for smelting copper, lead and some other
metals, a number of old furnaces are still in use which work on the
updraft principle.
Fig. 107 shows a reverberatory copper-refining furnace, the
waste gases from which are removed at the top. In this case
the metal in the bath is in contact with the coolest gases in the
heating chamber, and this very certainly lowers the working

fig. 107.
temperature of the furnace/1* or results in the expenditure of a
larger amount of fuel than would otherwise be necessary.
XVI. SIEMENS TYPE REHEATING FURNACES
Furnaces of the Siemens type are symmetrical, and the flues
and ports through which the gases pass to the heating chamber
serve also for the removal of the products of combustion. When
reheating furnaces are constructed according to this system, the
head construction of the open-hearth melting furnace is frequently
copied, a procedure for which there is no necessity, owing to the
difference in the purpose for which the heating furnace is used.
This difference affects the operation of the furnace in two
important respects:
1. The temperature to which ingots must be reheated for
rolling or forging does not exceed 1300°, and, for this reason it is
not desirable to direct the jet of flame from the ports directly
upon them. For the open-hearth melting furnace, on the con-
(1) In regard to the method of computation for these furnaces, refer to
T%      21

132

RATIONAL CONSTRUCTION OF FURNACES

I:.'

traiy, it is not only desirable but necessary that the jet of burning
gases should be directed against the surface of the bath.
2. The surface of the bath in the open-hearth melting furnace
is heated to the boiling point and at the same time rises 500 to
600 mm. The surface of the hearth of the reheating furnace is
solid, except that the melted cinder lies there, slightly wetting
the hearth. For this reason, in the open-hearth melting furnace it
is necessary to elevate the sills of the ports so that they are at a
higher level than the surface of the bath during the boil. But
there is no reason for elevating the sill of the ports for a reheating
furnace above the hearth level.
In actual practice, if the port sills of a reheating furnace are
raised above the hearth to a height equal to the thickness of the
ingots to be heated, as is ordinarily done, this will make it impos-

3gg^	
o\—i>^x^vn-n\\\\\\\\\^^

fig. 108.
sible to get rid of the colder gases which rest on the hearth, and
the ingots to be heated will be surrounded by these chilled gases.
It is evident that the rapid heating of the ingots is not possible
unless these colder gases can be drained off from the hearth of the
furnace. The port sills for Siemens type reheating furnaces,
should, therefore, coincide with the hearth level.
Fig. 108 shows a curious design for a Siemens type reheating
furnace. The hearth is 8020 mm long, with a width of 2000 rnm.
The roof is 1000 mm above the hearth and the heads are of the
type used on melting furnaces.
Originally, the roof was straight from one end to the other;
later it was dropped, just beyond the heads, as shown by the
dotted lines, to a height of 680 mm from the hearth. It is evident
that with a hearth length of 8020 mm, the jet of flaming gases did
not touch the hearth, and did not heat the ingots which were

SIEMENS TYPE REHEATING FURNACES

133

placed near ports through which the waste gases were passing.
The same phenomenon occurs in the open-hearth melting furnace
when, by reason of the wear of the ports, the velocity of the air
and gas is reduced, and the jet of flame has a tendency to seek
the roof of the furnace, its thickness being normally that of the
gaseous stream, as computed according to Yesmann's formula.
At the corners of the hearth, close to the ports, a pocket of colder
gases is formed, and the bath freezes. In the Goujon works, at
Moscow, a case of this kind occurred with a furnace having a
hearth 14 m long. In order to correct this condition two burners
for naphtha were installed, one behind the other.
In the case under consideration a different procedure was
followed. The roof of the furnace was dropped close to the
heads, to the height required for the inverted weir, thus forcing the

. 109.
fig. 110.

flame of burning gases to lick the hearth, not only where it issued
from the ports, but also farther on. While estimating at its true
value this method of reconstruction for the type of heads fre-
quently used upon these furnaces, the author believes much better
results can be attained in another way.
Figs. 109 and 110 are two sketches of constructions which may
be employed in such a case. They are based upon the following
considerations:
(a) The chilled gases are drawn off at the hearth level of the
reheating furnace; this method of removing the inactive gases
results in the uniform action of the hot gases upon the ingots and
favors their regular and uniform heating.
(6) The producer gas and the preheated air enter the heating
chamber of the furnace at a very low velocity, with the result that
combustion takes place throughout the entire chamber, and the
points of sharp combustion, close to the ports in the jet of flame,

134

RATIONAL CONSTRUCTION OF FURNACES

are eliminated. When the air and gas are heated to the tempera-
ture of the jet of flame, which may have a temperature of 1500°
to 1600°, the ingots being heated are liable to be burned if exposed
to the impinging action of the gases.
This assumes that the producer gas and the air are mixed
outside of the heating chamber of the furnace.
(c) In order to prevent the melted cinder from flowing into the
ports of the furnace the hearth is given a slight drainage slope from
both ends to the center of the hearth. The port sills are cooled by
inverted troughs immediately below the bridge wall, through

fig. ill.
which a forced circulation of cold air is obtained by chimney
suction.
A very interesting example of the complete neglect of all the
fundamental principles of rational furnace construction is found
in a Siemens type furnace for carbonizing and tempering armor
plate, according to the KruppW system. This furnace is a back-
ward step in design and construction.
It may be seen in Fig. Ill that the vertical heads of the
Siemens furnace are elevated 800 mm above the hearth of the
furnace. The armor plate to be heated was placed upon a car
supported above its deck by short brick columns, and then run
into the furnace. It was found, nevertheless, to be within a
pocket of chilled gases, which could nob be drained away from the
(1) This refers to the Russian works using the Krupp system.

PIT  FURNACES

135

armor plate. Moreover, this furnace \vas intended to work with a
negative pressure in the heating' chamber, with the result that the
reheating of the armor plate had to be accomplished while it was
surrounded by a current of colder air drawn in through the door
of the furnace. The effects of such a method of operation are
obvious.
It had been planned to carbonize and heat two armor plates at
a time, placing one above the other and separating them by a layer
of charcoal. It may be stated that the lower plate was car-
bonized much more slowly than the upper; and it was necessary
to give up the idea of carbonizing two plates at a time. Actually,
the carbonizing was done one plate at a time, double the number
of furnaces were required with twice the expense for installation.
Moreover, the men in charge of the Russian works were so
thoroughly impressed with the prestige of the Krupp Company
that they would not consent to the cutting down of these heads
to the level of the hearth of the furnace.
XVII. PIT FURNACES
In   pit-reheating   furnaces   the   defect   which   is   commonly
encountered consists in the incorrect location of the waste-gas

fig. 112.
ports. In these furnaces, by reason of the considerable height
of the heating chamber, it is very necessary that attention should
be paid to the locating of the waste-gas port at the level of the
hearth of the pits. Unless this is done, the lower parts of the

136

RATIONAL CONSTRUCTION OF FURNACES

ingots will be plunged into a pocket of cold and stagnant gas and
therefore will not be heated uniformly, the top of the ingots being
hotter than the bottom.
A number of designs for pit furnaces have been seen by the
author, but none of them were perfectly satisfactory, and in many
of them there were gross violations of the physical laws in regard
to the carrying off of the waste gases. Fig. 112 shows a pit
furnace of the " new Siemens system " of a very costly design.
These pits are only supplied with regenerators for the air supply,
regenerators for the gas being omitted. Therefore, the products
of combustion cannot pass out of the heating chamber without
passing through the air regenerators, which have a port sill or
bridge wall extending to a height of 600 mm above the hearth
of the pit (refer to the dotted line A}. It is very clear that the
hearth of these pits forms a pocket which will be filled with colder

fig. 113.
gases. Nothing can be done to save this furnace and make it heat
properly. The walls were lowered between the pits until the
height h was equal to the thickness of the stream under the in-
verted weir, as calculated by Yesmann's formula. After the
furnace was reconstructed in this manner the pits worked, but
the velocity of the gas in the heating chamber was equal to the
velocity under a normal inverted weir, that is to say, one under
which the height h equals 1 m, the velocity v being 6 m per second
(refer to page 52). A velocity as high as this is unsatisfactory.
The hot gases did not remain in the heating chamber a sufficient
length of time to give up their heat to the ingots. For this reason
the fuel consumption of these pits was very large. The best means
of reconstructing this furnace consists in removing the bridge wall
in front of the regenerator for air, so that the bottom of this port
will be as nearly as possible at the level of the hearth of the pits.
Fig. 113 shows Siemens type pit furnace at the Salda (Oural)

PIT FURNACES

137

works, constructed according to the designs of Dalen. The gases
are carried away near the top of these pits. For this reason, only
a small portion of the top of the ingots is exposed to the hot gases.
In the pits the lower portion of the ingots was heated much less
than their top. This made it necessary to obstruct the ends of
the furnace by charging ingots against the walls (thick end down).
In order to improve the work of the furnace it was necessary to cut
out the sloping portion of the bottom of the port, lowering it to the
level of the hearth of the pit.
As the Siemens fired type of soaking pit is the most desirable
furnace for the heating of ingots and is widely used, the principles
governing its rational construction are given:

\\^N>N'v'S\^
D_
n n

fig. 114.

fig. 115.

1.	It is desirable that the heating chamber of these pits should
be operated with a slightly negative pressure, in order that the
operatives will not be burned when the covers are taken off;
2.	The arches over the regenerators should be at the same level
as the covers, so that the entire furnace can be covered with cast-
iron plates forming a working platform;
3.	It is more convenient to make the regenerators horizontal
and construct them in such a manner that the gases enter at their
top and pass out at their lowest portion to enter the flues leading
to the reversing valves;
4.	The port sills should be placed as close as possible to the
level of the hearth of the pits.    If this construction is employed
1.	
138	RATIONAL CONSTRUCTION OF FURNACES
it will not be necessary to continue the walls between the pits
close to hearth, and the hot gases will have a low velocity;
5.	The dimensions of the ports should be computed by the
formula for the inverted weir.    This will make it possible to obtain
a slow velocity of flow for the hot gases and the air in these ports,
and a slow gas current through the heating chamber of the pits;
6.	In order to effect the mixture of the gas and the air, the
heads shown in Figs. 114 and 115 may be used.    The differences
i	between these two constructions are clearly shown by the figures.
\   :
\    '	XVHI. CONTINUOUS HEATING FURNACES	i
I-	In a previous chapter (page 49) it was stated that the only	\
I	continuous heating furnace which was correctly constructed was	*
the Morgan design. All the other designs for this type of furnace
contain many defects, which will be analyzed in the present
chapter.	I
The hearth of the furnace may be flat.    Of late, however, the	f
name of continuous furnace has been limited to that type of	>
furnace in which the material to be heated is pushed or carried	i
through the furnace upon water-cooled skids supported above the	i
masonry hearth of the furnace, or in lower temperature work by	I
conveyor chains.    This method is logical.    Like all other median-	I
isms in which work is placed alnd from which it is withdrawn,	f
a furnace should be:	;
Correctly fed by the hot gases coming from the firebox.   At	j
the same time the products of combustion must be carried away.
The stagnation of partially cooled gases within the furnace will
result in considerable damage; the hot gases from the firebox can-
not get into the heating chamber and this reduces the amount
of contact between the hot gases and the material being heated,
and in addition reduces the temperature differential between the
gases and the material.
When the ingots or billets are carried upon tubes there is
below them a canal or flue of a sufficient height to carry the chilled
gas dropping below the material being heated, and to carry this
cool gas to the chimney port in its flaw along the hearth. As it
passes off from the heating chamber its place is taken by hotter
gases. This arrangement results in a uniform circulation of the
gases. The flame of the reacting gases is in the highest and

CONTINUOUS HEATING  FURNACES

139

hottest portion of the chamber where complete combustion can
take place before the gases cool below their ignition temperature.

fig. 116.

The hot gases drop down toward the ingots or billets and lose
their heat by coming in contact with them, and the colder gases
then descend fur-
ther to the lower
level from which
they flow to the
chimney port.
fig. 117.
Compare this
type of construc-
tion with the
working system
of many contin-
uous heating fur-
naces of widely
known and used
designs. Fig. 116
is a photographic
demonstration of
the circulation of
the hot gases (colored kerosene) in a Morgan continuous heat-
ing furnace. Fig. 117 is a similar demonstration of the pocket

140

RATIONAL CONSTRUCTION OF FURNACES

of chilled gas (water) which forms in those continuous heating
furnaces having an ascending roof and hearth. It is readily seen
that in this last case the forcing out of the cold gases by the hot
gases flowing into the heating chamber is obstructed to the highest
degree.
The performance of these furnaces, when constructed with a
horizontal hearth, is slightly better. This type of hearth does not
form a pocket for the cold gases, but the flow of the colder gases
to the waste-gas port is very nearly cut off by the ingots which
are being heated.
In computing the width of the hearth of the furnace it is necessary
to give thorough consideration to the fact that the cold gases must
be removed from the heating chamber. In practice the hearth is
sometimes given a width equal to twice the length of the ingot to

/////m/

fig. 118.
be heated, so that at each end of the ingots a wide channel will be
formed for the cold gases.
What reason can be assigned for making the hearth so wide?
Would it not be better to proportion the width of the furnace
more closely to the length of the ingots or billets to be heated?
The author has been unable to find any other reply to the fore-
going questions than the following: In order that the furnace may
operate well and heat uniformly, it is absolutely necessaiy that
the burned gases be rapidly and completely carried away from the
heating chamber. The side channels, at the two ends of the file
or tier of ingots which are being reheated, form the only path by
which these gases may pass from the furnace. If a low temperature
at the charging end of the furnace is desired, it is necessary that
these channels" should have sufficient width.
In the case shown (Fig. 118), the continuous furnace has the
roof and hearth horizontal, and the height of the gas port above
the bridge wall is h; the height of the working doors is less than
this dimension; the waste gases are carried away from the heating

CONTINUOUS HEATING FURNACES

141

chamber by a port in the hearth of the furnace. The velocity
of the current of gases in the chamber is retarded because the
chamber is formed as an inverted weir having a reservoir (the
height of the roof above the hearth being hi>h); the ingots are
carried upon the hearth. Two currents of gases are possible:
aa immediately below the roof and bb over the hearth. In order
to reach the waste-gas outlet the hot gases aa must descend a
distance hi and expend in doing this a certain hydrostatic pressure,
which will be designated as 8 mm of water. The current bb has
to overcome the friction of the ingots. It is evident that the hot
gases cannot escape immediately through the waste-gas opening,
except in a case where the resistance to the passage of the current
of cooler gases bb, equal to <5i mm of water, is greater than 5,
that is to say, in a case where <5i is greater than 5.
The greater the width of the furnace in proportion to the

 

fig. 119.

fig. 120.

length of the ingots, the less will be the value of <5i; and therefore
there will be no reason to fear that the hot gases will pass imme-
diately to the waste-gas flue.
When the ingots are placed upon pipe skids (Figs. 119 and 120)
a channel pp will be formed below them through which the cooler
waste gases will flow to the waste-gas port q. The heating chamber
having a descending roof, a free space mm, a well-defined com-
bustion chamber, will be formed under this roof, providing a
rationally constructed heating chamber for continuous ingot
reheating furnaces. W
Figs. 119 and 120 show two methods by which the flow of the
reacting gases may be slowed down sufficiently to permit combus-
tion to be completed in the front portion of the heating chamber.
In Fig. 119 this is done by a sharp drop in the roof, dividing the
heating chamber into two sections, one much higher than the
(1) This arrangement, moreover, facilitates the operation of the furnace by
making it easier to roll the ingots over while they are heating.

142
RATIONAL CONSTRUCTION OF  FURNACES
other. This drop in the roof acts as a dam to arrest the -flow of
the gases for a sufficient length of time for the completion of
combustion. Fig. 120 shows the Morgan type of roof. The drop
in the roof simply checks the flow of the hot reacting gases; the
port through which the gases enter the heating chamber is located
some distance above the hearth. The author believes that these

^s^ss^^s^^ss^
d      n      n      n      o       n
fig. 121.
two methods of retarding the flow of the combining gases and
promoting combustion are equally good.
However, it is here necessary to call attention to an error often
made in the design of these furnaces. The working doors, A, B,
and C must not be located at different heights. If these doors are
placed at different heights, the highest door acts as a chimney in
conjunction with the lowest door. Cold air will be drawn into
the heating chamber at the lowest opening while a jet of flame

fig. 122.
and smoke will escape from the highest opening. The sills for all
of the working openings should be placed at the same level.
The last three illustrations in this chapter show the recon-
struction, according to the direction of the author, of two very
costly furnaces of a Swedish type. These furnaces were installed
in a plant located in the Oural district.
Fig. 121 shows the longitudinal section of the furnace as
originally built. During its operation it became very apparent

CONTINUOUS HEATING FURNACES

143

that the wall ab resulted in the formation of a pocket of stagnant
gases. As a remedy for this condition, the author suggested the
removal of the wall and the reconstruction of the furnace according
to the sketch (Fig. 122).
note.—Furnaces with descending skids give a great deal of trouble with
billets sagging due to improper heating conditions.
Another small furnace, of a similar design, is shown in Fig. 123,
in which the reconstruction recommended is shown in dotted lines.
These changes were made, and the output of the furnace was
thereby increased from 11.2 tonnes to 14.7 tonnes a day, that is
to say, an increase in output of 30 per cent, with the same coal
consumption.
As to the profile which should be given to the roof of a con-

fig. 123.
tinuous heating furnace, the following suggestions may be of
service:
If the mixture of the air and the combustible gases is not
sufficiently intimate in the firebox, it will be necessary to use some
method of restricting and retarding the flow of the reacting gases
within the port. The device frequently used is a strangulation or
restriction of the port or passage through which the reacting gases
enter the heating chamber. A serious disadvantage of this
method is that it gives the jet of flame an exaggerated velocity.
In order to absorb and reduce this velocity, two special forms of
roof construction are used, which are shown in Figs. 122 and 123.
If the mixing in the firebox is well accomplished, or if the gases
flow into a large free space under the roof of the heating chamber
at a low velocity, these spaces will act as a combustion chamber,
and there will be no necessity for the strangling of the flow through
the port.
If the rear end of the roof ascends, recourse is frequently had to

144

RATIONAL CONSTRUCTION  OF  FURNACES

11
|r

strangulations or dropping of ridges in the roof of the furnace.
The free height below such a strangulation should be

For an ascending roof, when a currrent of cold gases spreads
over the hearth, all of these strangulations are useless.
As a general conclusion, it must be remembered that a descend-
ing roof results in a concentration of the hot gases in the front
part of the heating chamber. An ascending roof causes the hot
gases to flow to the rear of the furnace, and for this reason con-
tinuous reheating furnaces .are built with descending roofs.
Furnaces for the uniform heating of long pieces of material W
should be given ascending roofs.
XIX. TUNNEL FURNACES OR KILNS
Notwithstanding the fact that tunnel furnaces or kilns present
attractive possibilities, they are used comparatively little, because,

fig. 124.
owing to the irrational construction of those already in use, they
rarely work in a satisfactory manner.
Figure 124 is a longitudinal section of the Groendal furnace
for curing briquets. The central portion of this kiln has a high
roof which forms a combustion chamber within which the com-
bustion of the producer gas occurs. This gas is brought to the
chamber by the gas flue 0 across the roof of the kiln. The gas
producer is operated with a blower. Air is supplied by a fan
blower and flows to the kiln through the flue P, entering the
kiln through ports in the roof, in the same manner as the gas.
The hot gases in this kiln flow directly under the roof. In order
C1) For example, tube- or pipe-welding furnaces.

TUNNEL FURNACES OR KILNS	145
to force these gases down to the hearth of the kiln the dampers si
and 52 are opened more or less.C1)
By forcing the hot gases to circulate through piles of briquets,
the frictional resistance to the flow of the gases is increased; it
becomes necessary, accordingly, to increase the pressure of the
blower, forcing the primary air in below the grate of the gas
producer and the gas into the furnace, and to increase the height
of the chimney. At the same time, the clay-filled joints, which
are not air-tight, tend to prevent any such increase in the pressure
from the blower.
In order to overcome this difficulty, Groendal forces a stream
of air under the cars in the kiln for the purpose of cooling them.
It is probable that supplementary air from this source enters the
chamber of the kiln and has a tendency to turn the *hot gases
back to the roof. As a consequence of this, these kilns must be .
made very long (from 50 to 70 m).
In his design of a tunnel kiln, Groendal commits the obvious
error of carrying away the waste gases by ports in the roof of the
tunnel. By reason of this location of the waste-gas outlet, the
train of cars carrying the briquets is plunged into a pocket of cold
gases. The second fault which he commits consists of seeking to
force the hot gases to pass through the pile of briquets for the
entire length of the tunnel. This is very difficult and in order to
accomplish it the inventor limits the charge of brick upon the
cars to two tiers.
The author believes that, in the design of the tunnel kiln, it is
necessary to place one feature of the problem above all the others.
It is not possible to force the stream of hot gases to pass through
the piles of briquets, which are 50 m long. It is more advan-
tageous to heat the briquets by a descending current of hot
gases.
The difference between these two methods—that of Groendal
and that proposed by the author—may be studied by comparing
the cross-sections of the tunnel kiln designed by Groendal (Fig. 125)
and the cross-section as corrected by the author (Fig. 126).
Groendal placed a flat roof at a distance of 150 mm above the
(1> It is claimed that the manipulation of the dampers ss and s4 improves
the preheating of the air by forcing it down on the hearth of the kiln. These
dampers are evidently useless for this purpose, as the cold air will naturally
seek the lowest portion of the chamber.

146

RATIONAL CONSTRUCTION OF FURNACES

fig. 125.

briquets, which are loaded on the cars in two tiers;  in squeezing
the hot gases against the briquets, and forcing them to traverse
fig. 126.
their checkerwork, he forces a part of the hot gases through the
orifices in the roof of the kiln.

TUNNEL FURNACES OR KILNS

147

The author thinks that there should be charged upon the cars
as many tiers of briquets as it is convenient to place, according to
the conditions of manufacture. He has shown three tiers in
Fig. 126. The tunnel is likewise made considerably larger than
the cars. The roof is raised so that there will be a space above the
top tier of briquets, sufficient for the current of hot gases to
follow the roof. By reason of the increase in width of the tunnel,
forming a free space on each side between the wall and the pile

fig. 127.
of briquets, two currents cf gases will be formed,* which will
follow the hearth of the tunnel and flow into the waste-gas ports.
The descending movement of the gases which causes them to pass
through the tiers of briquets is indicated by the arrows.
Moreover, in order to obtain, through the length of the kiln,
the descending circulation of the hot gases giving up their heat to
the briquets and the ascending circulation of the air being heated,
the author, instead of using the straight tunnel of Groendal, would
form the tunnel on the arc of a vertical circle, raising the central

fig. 128.
portion so that it will be higher than the ends, as is shown in
Fig. 127.
A tunnel kiln constructed upon this principle would not require
blowers, because the raising of the central portion (the combustion
chamber) above the end at which the cold air enters the tunnel,
would produce a hydrostatic pressure sufficient to overcome the
resistance to the air current offered by the tunnel through which
the cars pass, carrying the cooling briquets. On the other hand,
the hot gases which are produced in the combustion chamber

148

RATIONAL CONSTRUCTION  OF FURNACES

descend toward the low end of the tunnel, imparting their heat to
the incoming briquets, and acted upon by the draft from the
chimney, since the resistance offered by the tunnel, which has
been increased in size, is not very large.
The author believes that a tunnel kiln corrected as he has
indicated will work in a satisfactory manner. M
(1) While the author was writing these lines he did not know that, in Sweden,
the principle of the tunnel kiln built on the arc of a vertical circle, had been
applied with considerable success in the Aminoff furnace (Fig. 128) for the
continuous carbonization of wood (Revue de la Societe russe de Metallurgie,
No. 1, pp. 48-64,1912; extract, Revue de Metallurgie, decembre, 1913, pp. 678-9).
These results completely confirm the author's view.

CONCLUSION
it is clearly shown, by the large number of examples which
have been given, that only tho.se furnaces in which the circulation
of the gases corresponds to the natural laws will work in a satis-
factory manner; that is, the hot gases which are giving off heat
and cooling should flow downward; the cold gas which is being
heated should flow upward.
This simple truth was demonstrated at a very early date.
The first form of reverberatory furnace, working with natural
draft and furnished with a chimney, the so-called cupola, was
invented in 1698. In Fig. 129 are reproduced some designs and a
portion of the description taken from the Manual of Metallurgy
of Schltiter, edition of 1738. This furnace, from which the waste
gases pass off through the roof of the chamber, is the ancestor of
the updraft furnace.
In the same work there is also described another German
furnace, the inventor of which is unknown, but which was probably
built about 1730, for the purification of copper from lead (Fig. 130).
The disks of copper-lead are set on edge on a hearth shaped with a
gutter or flue which slopes downward and drains into the waste-
gas flue.
The flame or hot gas comes from a fire upon a grate of bricks.
In filling the heating chamber, these gases surround the disks of
metal, melting the lead, and descend between the disks and flow
toward the port and the chimney. Into the same flue the melted
lead flows, and-accumulates there, until it is drawn off, by means
of the sloping of the bottom of the flue, into a small pit in front
of the furnace (a fore hearth).
This shows that downdraft furnaces were invented a great
many years ago. Many thousands of furnaces have been con-
structed since that time; nevertheless it is only in this late day
that any clear conception has been arrived at concerning the
mechanics of the circulation of the hot gases within the furnace.

150

CONCLUSION

tpfer Gcbmeltj * Off ,toorm btc Q3lei}s (£rtje in (£ngellan& '
mit Gtein"-$ol)len gefdjmolijen ttwbm, if in bem
^urAentfjum Q3}allte obcr QBaleS ju ^lintadjirp obfer-
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ftoll, tt)ortn^upfec5(£rlje tjcratbtitet hjerben. ©ofcber ifl
ein 2Btn&»pfe un& ^at tetn ©fbliife, bflrtn bte^purung mtt
tauter Stein* jtofjten untetljalten wirb, foil ohngefeljr Anno
1693. won bretj curtcufcn £euten m»eniirt toorben fcijn, rto*
tjoncincr.yiomenjS 5Bl)rtat,ein Doctor Meclirmaunb Chymlcusf,
ber anbetc cm (bol&fdijmiot; unb ber bctttc ein cumufer SJlann
gehsefen, ine% baran ttelOJelb unb 3cit gert>anbt: btefcr
Off tfltnflflrlem 9Jlaupr»2Btt(i angcleflet, unb umljcr mtt
C	ftatv

fig. 129.

CONCLUSION

151

fig. 130.

APPENDIX I
FORMULA FOR THE INVERTED WEIR ACCORDING TO
THE COMPUTATION OF PROF. J.-C. YESMANN («
A current of hot gas of indefinite width is moving downward
at a very low velocity v (Fig. 25). After it has reached the level
of a horizontal sill DD having a length B (this dimension being
taken at right angles to the section shown) which is fixed, the
current commences to flow in a stream of a certain depth below
the sill, which confines it upon its upper surface. The dimensions
and arrangement of the orifice through which the gas flows are
assumed to permit it to flow freely without any increase in pres-
sure. The flow of the gas under these conditions is analogous
to the flow of a stream of water over the crest of a weir or dam.
As the gas reaches the level of the sill it changes its direction
of flow; the very slight vertical velocity becomes horizontal and
is increased by reason of differences in pressure and level. The
layer of gas, as it commences to flow horizontally, will be very
thin. If the width of the inverted weir or sill from D to D is
sufficient, as the flow is established, it will in time traverse some
given section as a current composed of a number of parallel stream
lines.
Take two cross-sections of the flowing stream, ab, where the gas
has not yet acquired the horizontal velocity component, and cd,
where it may be considered that the motion takes place in parallel
streams with a velocity V. The current at this point being
established, the small vertical velocity v, which is very slight as
compared with the horizontal velocity V, may be neglected. It
may therefore be concluded that the horizontal flow is effected
by reason of a difference in head or level, this last being composed
of the sum of the piezo and isometric heads.
(1) Extract from an article appearing in 1910 in the Annales de VInstitut
Poly technique de Petrograd.
1/53

154	APPENDIX I
This difference in head may be determined for the two extreme
flow lines, bd, the flow line following the horizontal surface of the
crest of the weir, and ac, which flows as the free surface of the
stream.
Assume that p« designates the hydrostatic pressure of the gas,
which is at rest at the point a, and pa is the hydrostatic pressure
of the gas which is in motion at the same point/1)
These two pressures are evidently equal:
pa=pi	(a)
The pressure at the point b which is located at a distance H
above the point a will be
(b)
||j I	Am being the specific weight of the gas which is in motion.
(1)	It should be carefully noted that there are two gaseous mediums present
at this point, the one in a state of motion, of which the flow is being studied
and the other assumed to be at rest, constituting an atmosphere within
which the flowing gas moves.
(2)	Knowing the pressure p$ at the point 6 of a gas, the pressure at any
other point a at any vertical distance designated
j	(^0)   as h (Fig. 131) may be deduced very easily.    The
i	differential equation for the hydrostatic head in
^ j	the case of all heavy liquids is as follows:
J	dp = Pgdz,
p designating the density of the liquid.
Now, according to Mariotte's law, the rela-
tion for gas will be
P	Po
- = constant = k = —,
P	Po
from which — = -dz, and by integrating, h being the difference in level and
p       K
A0 the specific weight of the gas at the point 6,
r P       ff /	\       gh      PO(77       A),
L— — -(z—zq) =— =—ti = —h.
Po    *"	fa      Po       Po
Passing to the exponential function and taking only the first two terms
of the developed series, which give an approximation sufficiently exact for
the purpose, by reason of the small value of h with regard to the piezometric
height —, the following expression is obtained,
ac

FORMULA  K)ll  THE INVERTED  WEIll	155
In the same manner it will be found that
p«=pi-A.,(H-/i),	(c)
pi^pt-^H-fy-AnJi,	(d)
At being the specific weight of the gas which is at rest and h being
the thickness of the layer of gas flowing through the section cd.
The difference in head or pressure which acts to cause the
flow of the gaseous vein Id is
S
The difference in pressure or head for the vein ac which rises,
as it flows a to c, the distance cci=//— A, will be
This difference in pressure or head being the same for the two
extreme veins or flow lines bd and cd, it is not difficult to see that
it will be the same for all of the intermediate veins or lines of flow.
Therefore, the velocity of all of the elementary veins or flow
lines may be determined, as they are based upon the difference
in level and they will be the same; that is, the velocities of all the
particles flowing through the section cd are equal.
It is possible to determine the theoretical velocity of the gas
in motion by the equation
from which
A)= ......    (1)
The theoretical volume of gas Qt which will flow under the sill
or weir in a layer whose thickness is h and whose width is B will
be equal to
h)A-^     ....    (2)
If it is possible, in the case of flowing gases which is being
analyzed, to adopt the hypothesis assumed by Boussinesq, for
the flow of water over a weir, the head at the crest h is established
in such a fashion that qt attains its maximum value for any given

156

APPENDIX I

value of H.    It is evident that the following expression will then
be obtained:
from which, according to Eq. (2),

»i *
ii
1

'H-h-
= 0,
h
2VH-h
.   (3)
-    (4)
from which
and
In taking into account this last relationship, Eq. (2) will take
the form

^-A,
and
The actual quantity of gas Q flowing under the inverted weir
will be less than the theoretical volume by reason of the frictional
and other resistance; therefore these equations will become:

2gH
<2=?\5

•A,-A,

(5)

«-\3

2gh^

-A,,

(6)

in which the coefficients p, and « may not be equal, as, in passing
from equations (3) and (4) to the actual flow of the gas, it will be
found that the relation between H and h is different from that
given in these equations.
According to the researches of Bazin, the coefficient m for the
flow of water is given by the formula

|^|m= [0.70+0. 185|] [0.

,     (7)

in which p is the depth of the channel and E& must not be less
than |ff .
« E being the distance DD (Fig. 25).

FORMULA  POR THE INVERTED  WEIR	157
In order to determine approximately the limits of variation
of the coefficients which enter into the preceding formula they
have been computed for two particular cases.
Assuming 0 m 30 as the depth of the layer of gas flowing under
the crest of the weir, this will correspond approximately to
# = 0 m 45, for which the minimum length of the sill or width of
crest E is 0 m 30 (-§•/?) and the maximum width of crest will be
in the neighborhood of 1 m (about 2/f); from which, applying
formula (7), for the first case ju= 1.045 and for the second case
ai=0.838. It may be assumed that these values will be the same
for a gas flowing under an inverted weir.
Actually, whatever the value of this friction for a gas, it will be
less than the friction of water, but it can be assumed, as a first
approximation, that this difference will be compensated for by
the greater friction of the free surface of the gas against the
medium which is at rest.
Therefore, the value of H being very nearly 0 m 45 and that of
E being 1 m, the following expression is obtained:
Q = Q.322BPlJ2glI^~^	(8)
Then, assuming that m = mi> for the case in which h is Om 30
and E is 1 meter, the expression will be
= ^—°-838B^2(7^	.    (9)
Q
If the current of gas which is flowing under the weir and the
gas medium through which it flows have the same chemical
composition it can be admitted that
A^r,
Am    T
t representing the temperature.
By taking Ao = 1 kg 29, the weight of a cubic meter of air when
it is at the temperature of 0°, that is to say when 2^ = 273°, it will
be found by Formula (9) that

„	158	APPENDIX I
I'i '
from which
If the thickness of the crest of the inverted weir exceeds 1 m,
the resistance to the flow of the gas will be increased and it will
£	be necessary to increase the value of h.    On the contrary, if the
thickness of the crest and the roughness of the wall surface are
p	diminished, the coefficient in the last formula will become less,
ij J'	and its minimum value corresponding to m = 1 will, as it is easy to
t<;	see, be equal to or very close to 3.05.
|! I	The preceding formulas have been established upon the sup-
11 |	position that the gas arriving at the bridge wall has a horizontal
\\	velocity equal to zero.    But it follows from these considerations
11 \	that, in the case where the horizontal velocity is not a negligible
'" *	factor (Fig. 132) the form of the formula does not change.

\
it
1    i
i	1
fig. 122.
In these cases it is evidently necessary to increase the value of
£72
the coefficient H to H-0.55—, conforming to^Bazin's formula,
p being the depth or thickness of the flowing current of gas before it
reaches the sill or weir, and being equal to the height of the stream
over the weir plus the value of H. When this last value is known,
it becomes possible to introduce into the formula a correction for
each particular case, as well as in the preceding computations.
It will be seen in the numerical examples examined that -the
relation between the thickness or depth of the gaseous stream which
flows through the opening over the bridge or its depth below the
inverted weir, the volume of gas per second Q and the length of
the crest of the weir at right angles to the direction of flow B, is
finally given by the equation:

FORMULA FOR THE INVERTED WEIR	159
A being a coefficient determined experimentally and depending
upon the depth of the gaseous stream, h, the thickness of the crest
of the weir in the direction of flow, Ey the velocity with which the
gases arrive at the weir or sill, the temperature and specific weight
of the gas composing the stream, and the roughness of the walls
at the sides and top of the flowing stream.

APPENDIX II
VOLUME OF GASES <«
Values of 1+0.00367*
The quantity 1+0.00367/ gives for a gas the volume at t° when the pressure
is kept constant, or the pressure at t° when the volume is kept constant,
in terms of the volume or the pressure at 0°.
(a) This part of the table gives the values of 1+0.00367* for values of /
between 0° and 10° C. by tenths of a degree.
(6) This part gives the values of 1+0.00367Z for values of i between —90°
and +1990° C. by 10° steps.
These two parts serve to give any intermediate value to one tenth of a degree
by a simple computation as follows: In the (b) table find the number
corresponding to the nearest lower temperature, and to this number add
the decimal part of the number in the (a) table which corresponds to the
difference between the nearest temperature in the (b) table and the
actual temperature. For example, let the temperature be 682°.2:
We have for 680 in table (6) the number	 3.49560
And for 2.2 m table (a) the decimal	  0.00807
Hence the number for 682.2 is	 3.50367
(a) values of 1+0.00367^ for values of t between 0° and 10° C. by
tenths of a degree

t 	0.0 	0.1 	0.2 	0.3 	0.4 	
0 	1.00000 	1.00037 	1.00073 	1.00110 	1.00147 	
1 	.00367 	.00404 	.00440 	.00477 	.00514 	
2 	.00734 	.00771 	.00807 	.00844 	.00881 	
3 	.01101 	.01138 	.01174 	.01211 	.01248 	
4 	.01468 	.01505 	.01541 	.01578 	.01615 	
5 	1.01835 	1.01872 	1.01908 	1.01945 	1.01982 	
6 	.02202 	.02239 	.02275 	.02312 	.02349 	
7 	.02569 	.02606 	.02642 	.02679 	.02716 	
8 	.02936 	.02973 	.03009 	.03046 	.03083 	
9 	.03303 	.03340 	.03376 	.03413 	.03450 	
t 	0.5 	0.6 	0.7 	0.8 	0.9 	
0 	1.00184 	1.00220 	1.00257 	1.00294 	1.00330 	
1 	. 00550 	.00587 	.00624 	.00661 	.00697 	
2 	.00918 	.00954 	.00991 	.01028 	.01064 	
3 	.01284 	.01321 	.01358 	.01395 	.01431 	
4 	.01652 	.01688 	.01725 	.01762 	.01798 	
5 	1.02018 	1.02055 	1.02092 	1.02129 	1.02165 	
6 	.02386 	.02422 	.02459 	.02496 	.02532 	
7 	. 02752 	.02789 	.02826 	.02863 	.02899 	
8 	.03120 	.03156 	.03193 	.03290 	.03266 	
9 	.03486 	.03523 	.03560 	.03597 	.03633 	
(1) Smithsonian Tables.

VOLUME OF  GASES

161

VOLUME OF GASES—Continued
(6) values of 1+0.00367* for values of t between -90° and -f 1990° C.
by 10° steps

t 	00 	10 	20 	30 	40 	
-000 	1.00000 	0.96330 	0.92660 	0.88990 	0.85320 	
+000 	1.00000 	1.03670 	1 . 07340 	1.11010 	1 . 14680 	
100 	1 . 36700 	1.40370 	1 . 44040 	1.47710 	1.51380 	
200 	1 . 73400 	1 . 77070 	1 . 80740 	1.84410 	1.88080 	
300 	2.10100 	2.13770 	2.17440 	2.21110 	2.24780 	
400 	2.46800 	2.50470 	2.54140 	2.57810 	2.614SO 	
500 	2.83500 	2.87170 	2.90840 	2.94510 	2.98180 	
600 	3.20200 	3.23870 	3 . 27540 	3.31210 	3.34880 	
700 	3 . 56900 	3.60570 	3.64240 	3.67910 	3.71580 	
800 	3.93600 	3.97270 	4.00940 	4.04610 	4.08280 	
900 	4.30300 	4.33970 	4.37640 	4.41310 	4.44980 	
1000 	4.67000 	4.70670 	4.74340 	4.78010 	4.81680 	
1100 	5.03700 	5.07370 	5.11040 	5.14710 	5 . 18380 	
1200 	5.40400 	5.44070 	5.47740 	5.51410 	5.55080 	
1300 	5.77100 	5.80770 	5.84440 	5.88110 	5.91780 	
1400 	6.13800 	6.17470 	6.21140 	6.24810 	6.28480 	
1500 	6.50500 	6.54170 	6.57840 	6.61510 	6.65180 	
1600 	6.87200 	6.90870 	6.94540 	6.98210 	7.01880 	
1700 	7.23900 	7.27570 	7.31240 	7.34910 	7.38580 	
1800 	7.60600 	7.64270 	7.67940 	7.71610 	7.75280 	
1900 	7.97300 	8.00970 	8.04640 	8.08310 	8.11980 	
2000 	8.34000 	8.37670 	8.41340 	8.45010 	8.48680 	
t 	50 	60 	70 	80 	90 	
-000 	0.81650 	0.77980 	0.74310 	0.70640 	0.66970 	
+000 	1.18350 	1.22020 	1.25690 	1.29360 	1.33030 	
100 	1.55050 	1.58720 	1.62390 	1.66060 	1.69730 	
200 	1.91750 	1.95420 	1.99090 	2.02760 	2.06430 	
300 	2.28450 	2.32120 	2.35790 	2.39460 	2.43130 	
400 	2.65150 	2.68820 	2.72490 	2.76160 	2.79830 	
500 	3.01850 	3.05520 	3.09190 	3.12860 	3.16530 	
600 	3.38550 	3.42220 	3.45890 	3.49560 	3.53230 	
700 	3.75250 	3.78920 	3.82590 	3.86260 	3.89930 	
800 	4.11950 	4.15620 	4.19290 	4.22960 	4.26630 	
900 	4.48650 	4.52320 	4.55990 	4.59660 	4.63330 	
1000 	4.85350 	4.89020 	4.92690 	4.96360 	5.00030 	
1100 	5.22050 	5.25720 	5.29390 	5.33060 	5.36730 	
1200 	5.58750 	5.62420 	5.66090 	5.69760 	5.73430 	
1300 	5.95450 	5.99120 	6.027 0 	6.06460 	6.10130 	
1400 	6.32150 	6.35820 	6.39490 	6.43160 	6.46830 	
1500 	6.68850 	6.72520 	6.76190 	6.79860 	6.83530 	
1600 	7.05550 	7.09220 	7.12890 	7.16560 	7.20230 	
1700 	7.42250 	7.45920 	7.49590 	7.53260 	7.56930 	
1800 	7.78950 	7.82620 	7.86290 	7.89960 	7.93630 	
1900 	8.15650 	8.19320 	8.22990 	8.26660 	8.30330 	
2000 	8.52350 	8.56020 	8.59690 	8.63~60 	8.67030 	

162

APPENDIX II

TABLE C
weight op gases
Values of 1-*-(!+0.00367*) for values of t between -90° and +2990° by
10° steps.

t 	00 	10 	20 	30 	40 	
-000 	1.0000 	1.0381 	1.0792 	1 . 1237 	1.1721 	
+000
100
200
300
400 	1.0000
0.7315
0.5767
0.4760
0.4052 	0.9643
0.7122
0.5646
0.4677
0.3992 	0.9319 ,
0.6944
0.5534
0.4600
0.3935 	0.9009
0.6770
0.5423
0.4523
0.3879 	0.8718
0.6605
0.5316
0.4450
0.3824 	
500
600
700
800
900 	0.3527
0.3123
0.2802
0.2541
0.2324 	0.3483
0.3087
0.2773
0.2517
0.2304 	0.3439
0.3053
0.2746
0.2494
0.2285 	0.3396
0.3019
0.2718
0.2472
0.2266 	0.3353
0.2986
0.2691
0.2449
0.2247 	
1000
1100
1200
1300
1400 	0.2141
0.1985
0.1850
0.1733
0.1629 	0.2124
0.1971
0.1838
0.1721
0.1619 	0.2108
0.1957
0.1826
0.1711
0.1610 	0.2092
0.1943
0.1814
0.1700
0.1600 	0.2076
0 . 1929
0.1801
0.1689
0.1591 	
1500
1600
1700
1800
1900 	0.1537
0.1455
0.1381
0.1315
0.1254 	0.1528
0.1447
0.1374
0 . 1308
0.1248 	0.1520
0 . 1439
0.1367
0.1302
0.1243 	0.1511
0.1432
0.1360
0.1296
0.1237 	0.1503
0.1425
0.1354
0.1290
0.1231 	
2000 	0.1199 	0.1194 	0.1188 	0.1183 	0.1178 	
t 	50 	60 	70 	80 	90 	
-000 	1.2247 	1.2824 	1.3457 	1.4156 	1.4932 	
+000
100
200
300
400 	0.8453
0.6447
0.5213
0.4378
0.3771 	0.8196
0.6301
0.5091
0.4308
0.3720 	0.7955
0.6157
0.5023
0.4241
0.3669 	0.7727
0.6020
0.4931
0.4175
0.3620 	0.7518
0.5892
0.4844
0.4113
0.3574 	
500
600
700
800
900 	0.3312
0.2953
0.2665
0.2427
0.2228 	0.3273
0.2922
0.2639
0.2406
0.2210 	0.3234
0.2891
0.2613
0.2385
0.2192 	0.3196
0.2860
0.2589
0.2364
0.2175 	0.3159
0.2831
0.2564
0 . 2344
0.2158 	
1000
1100
1200
1300
1400 	0.2060
0.1915
0.1789
0.1679
0.1581 	0.2045
0.1902
0.1778
0.1669
0.1572 	0.2030
0.1888
0.1766
0.1658
0.1563 	0.2014
0.1873
0.1755
0 . 1649
0.1554 	0.2000
0.1863
0.1743
0.1639
0.1546 	
1500
1600
1700
1800
1900 	0 . 1494
0.1417
0.1347
0.1283
0 . 1226 	0.1486
0.1410
0.1340
0.1277
0 . 1220 	0.1478
0.1402
0.1334
0.1271
0.1215 	0.1470
0.1395
0.1327
0.1265
0.1209 	0.1463
0.1388
0.1321
0.1260
0 . 1204 	
2000 	0.1173 	0.1168 	0.1163 	0.1158 	0.1153 	

APPENDIX III
TABLE 1
table of the  velocity heads or  pkessures required to  impress
velocities hanging from 0 to 30 m 90 per second

	0.0 	0.1 	0.2 	0.3 	0.4 	0.5 	0.6 	0.7 	0.8 	0.9 	
0 	0.00 	0.00 	0.00 	0.00 	0.01 	0.01 	0.02 	0.03 	0.03 	0.04 	
1 	0.05 	0.06 	0.07 	0.09 	0.10 	0.11 	0.13. 	0.15 	0.17 	0.18 	
2 	0.20 	0.22 	0.25 	0.27 	0.29 	0.32 	0.34 	0.37 	0.40 	0.43 	
3 	0.46 	0.49 	0.52 	0.56 	0.59 	0.62 	0.66 	0.70 	0.74 	0.78 	
4 	0.82 	0.86 	0.90 	0.94 	0.99 	1.03 	1.08 	1.13 	1.17 	1.22 	
5 	1.27 	1.33 	1.38 	1.43 	1.49 	1.54 	1.60 	1.66 	1.71 	1.77 	
6 	1.83 	1.90 	1.96 	2.02 	2.09 	2.15 	2.22 	2.29 	2.36 	2.43 	
7 	2.50 	2.57 	2.64 	2.72 	2.79 	2.87 	2.94 	3.02 	3.10 	3.18 	
8 	3.26 	3.34 	3.43 	3.51 	3.60 	3.68 	3.77 	3.86 	3.95 	4.04 	
9 	4.13 	4.22 	4.31 	4.41 	4.50 	4.60 	4.70 	4.80 	4.90 	5.00 	
10 	5.10 	5.20 	5.30 	5.41 	5.51 	5.62 	5.73 	5.84 	5.94 	6.06 	
11 	6.17 	6.30 	6.38 	6.50 	6.62 	6.74 	6.86 	6.98 	7.10 	7.22 	
12 	7.34 	7.46 	7.59 	7.71 	7.84 	7.96 	8.09 	8.22 	8.35 	8.48 	
13 	8.61 	8.75 	8.88 	9.02 	9.15 	9.29 	9.43 	9.57 	9.71 	9.85 	
14 	9.99 	10.15 	10.28 	10.43 	10.57 	10.72 	10.87 	11.02 	11.17 	11.32 	
15 	11.47 	11.63 	11.78 	11.94 	12.09 	12.25 	12.41 	12.57 	12.73 	12.89 	
16 	13.05 	13.22 	13.38 	13.55 	13.71 	13.88 	14.05 	14.22 	14.39 	14.56 	
17 	14.73 	14.91 	15.08 	15.26 	15.46 	15.61 	15.79 	15.97 	16.15 	16.33 	
18 	16.51 	16.70 	16.88 	17.07 	17.25 	17.44 	17.63 	17.82 	18.02 	18.21 	
19 	18.40 	18.60 	18.79 	18.99 	19.18 	19.38 	19.58 	19.78 	19.99 	20.19 	
20 	20.39 	20.60 	20.80 	21.01 	21.21 	21.42 	21.63 	21.84 	22.06 	22.27 	
21 	22.48 	22.70 	22.91 	23.13 	23.34 	23.56 	23.78 	24.00 	24.23 	24.49 	
22 	24.67 	24.88 	25.10 	25.31 	25.53 	25.74 	25.98 	26.23 	26.47 	26.72 	
23 	26.96 	27.20 	27.44 	27.67 	27.91 	28.15 	28.39 	28.63 	28.88 	29.12 	
24 	29.36 	29.61 	29.85 	30.10 	30.34 	30.59 	30.84 	31.10 	31.35 	31.61 	
25 	31.86 	32.12 	32.37 	32.63 	32.88 	33.14 	33.49 	33.66 	33.93 	34.19 	
26 	34.45 	34.72 	34.99 	35.25 	35.52 	35.79 	36.06 	36.34 	36.61 	36.89 	
27 	37.16 	37.44 	37.71 	37.99 	38.26 	38.54 	38.82 	39.11 	39.39 	39.68 	
28 	39.96 	40.25 	40.54 	40.82 	41.11 	41.40 	41.69 	41.98 	42.28 	42.57 	
29 	42.86 	43.16 	43.46 	43.76 	44.06 	44.36 	44.66 	44.96 	45.27 	45.57 	
30 	45.87 	46.18 	46.49 	46.79 	47.10 	47.41 	47.72 	48.04 	48.35 	48.67 	
163

164

APPENDIX III

TABLE 2
table op theoretical velocity v — \/2gh corresponding to different
velocity heads h

Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	
0.001
0.002
0.003 	0.140
0.198
0.243 	0.25
0.26
0.27 	2.215
2.259
2.301 	0.58
0.59
0.60 	3.373
3.402
3.431 	0.91
0.92
0.93 	4.225
4.248
4.271 	1.24
1.25
1.26 	4.933
4.953
4.972 	
0.004
0.005
0.006 	0.280
0.313
0.313 	0.28
0.29
0.30 	2.344
2.385
2.426 	0.61
0.62
0.63 	3.459
3.488
3.516 	0.94
0.95
0.96 	4.294
4.317
4.340 	1.27
1.28
1.29 	4.991
5.011
5.031 	
0.007
0.008
0.009 	O.a70
0.395
0.420 	0.31
0.32
0.33 	2.466
2.506
2.542 	0.64
0.65
0.66 	3.543
3.571
3.598 	0.97
0.98
0.99 	4.362
4.384
4.407 	1.30
1.31
1.32 	5.050
5.069
5.089 	
0.01
0.02
0.03 	0.443
0.626
0.767 	0.34
0.35
0.36 	2.584
2.620
2.658 	0.67
0.68
0.69 	3.625
3.652
3.679 	1.00
1.01
1.02 	4.429
4.451
4.473 	1.33
1.34
1.35 	5.108
5.127
5.146 	
0.04
0.05
0.06 	0.886
0.990
1.085 	0.37
0.38
0.39 	2.694
2.730
2.766 	0.70
0.71
0.72 	3.706
3.732
3.758 	1.03
1.04
1.05 	4.495
4.517
4.539 	1.36
1.37
1.38 	5.165
5.184
5.203 	
0.07
0.08
0.09 	1.172
1.253
1.329 	0.40
0.41
0.42 	2.801
2.836
2.870 	0.73
0.74
0.75 	3.784
3.810
3.836 	1.06
1.07
1.08 	4.560
4.582
4.603 	1.39
1.40
1.41 	5.222
5.241
5.259 	
0.10
0.11
0.12 	1.401
1.468
1.334 	0.43
0.44
0.45 	2.904
2.938
2.971 	0.76
0.77
0.78 	3.861
3.S86
3.911 	1.09
1.10
1.11 	4.624
4.645
4.666 	1.42
1.43
1.44 	5.278
5.297
5.315 	
0.13
0.14
0.15 	1.597
1.657
1.715 	0.46
0.47
0.48 	3.004
3.037
3.069 	0.79
0.80
0.81 	3.936
3.961
3.986 	1.12
1.13
1.14 	4.687
4.708
4.729 	1.45
1.46
1.47 	5.333
5.351
5.370 	
0.16
0.17
0.18 	1.772
1.826
1.879 	0.49
0.50
0.51 	3.100
3.132
3.163 	0.82
0.83
0.84 	4.011
4.035
4.059 	1.15
1.16
1.17 	4.750
4.770
4.790 	1.48
1.49
1.50 	5.388
5.406
5.425 	
0.19
0.20
0.21 	1.931
1.981
2.030 	0.52
0.53
0.54 	3.194
3.224
3.253 	0.85
0.86
0.87 	4.083
4.107
4.131 	1.18
1.19
1.20 	4.811
4.831
4.852 	1.51
1.52
1.53 	5.443
5.461
5.479 	
0.22
0.23
0.24 	2.078
2.124
2.170 	0.55
0.56
0.57 	3.285
3.314
3.344 	0.88
0.89
0.90 	4.155
4.178
4.202 	1.21
1.22
1.23 	4.872
4.892
4.913 	1.54
1.55
1.56 	5.496
5.514
5.532 	

TABLES

165

TABLE 2—Continued
table of theoretical velocity v = -\/2gh corresponding to different
velocity heads h

Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	
1.57
1.58
1.59 	5.550
5.567
5.585 	1.90
1.91
1.92 	6.105
6.122
6.138 	2.23
2.24
2.25 	6.614
6.629
6.644 	2.56
2.57
2.58 	7.087
7.101
7.114 	2.89
2.90
2.91 	7.530
7.543
7.556 	
1.60
1.61
1.62 	5.603
5.620
5.637 	1.93
1.94
1.95 	6.154
6.170
6.186 	2.26
2.27
2.28 	6.658
6.673
6.688 	2.59
2.60
2.61 	7.128
7.142
7.156 	2.92
2.93
2.94 	7.569
7.582
7.594 	
1.63
1.64
1.65 	5.655
5.672
5.600 	1.96
1.97
1.98 	6.202
6.217
6.232 	2.29
2.30
2.31 	6.703
6.717
6.732 	2.62
2.63
2.64 	7.169
7.183
7.197 	2.95
2.96
2.97 	7.607
7.620
7.633 	
1.66
1.67
1.68 	5.707
5.724
5.741 	1.99
2.00
2.01 	6.248
6.264
6.279 	2.32
2.33
2.34 	6.746
6.761
6.775 	2.65
2.66
2.67 	7.210
7.224
7.237 	2.98
2.99
3.00 	7.646
7.659
7.672 	
1.69
1.70
1.71 	5.758
5.775
5.792 	2.02
2.03
2.04 	6.295
6.311
6.326 	2.35
2.36
2.37 	6.790
6.804
6.819 	2.68
2.69
2.70 	7.251
7.265
7.278 	3.01
3.02
3.03 	7.684
7. 697
7.710 	
1.72
1.73
1.74 	5.809
5.826
5.812 	2.05
2.06
2.07 	6.341
6.357
6.372 	2.38
2.39
2.40 	6.833
6.847
6.862 	2.71
2.72
2.73 	7.291
7.305
7.318 	3.04
3.05
3.06 	7.722
7.735
7.748 	
1.75
1.76
1.77 	5.859
5.876
5.893 	2.08
2.09
2.10 	6.388
6.403
6.418 	2.41
2.42
2.43 	6.876
6.890
6.904 	2.74
2.75
2.76 	7.332
7.315
7.358 	3.07
3.08
3.09 	7.760
7.773
7.786 	
1.78
1.79
1.80 	5.909
5.926
5.942 	2.11
2.12
2.13 	6.434
6.449
6.464 	2.44
2.45
2.46 	6.919
6.933
6.947 	2.77
2.78
2.79 	7,372
7.385
7.398 	3.10
3.11
3.12 	7.798
7.811
7.823 	
1.81
1.82
1.83 	5.959
5.975
5.992 	2.14
2.15
2.16 	6.479
6.494
6.510 	2.47
2.48
2.49 	6.961
6.975
6.989 	2.80
2.81
2.82 	7.411
7.425
7.437 	3.13
3.14
3.15 	7.836
7.849
7.861 	
1.84
1.85
1.86 	6.008
'6.024
6.041 	2.17
2.18
2.19 	6.525
6.541
6.555 	2.50
2.51
2.52 	7.003
7.017
7.031 	2.83
2.84
2.85 	7.451
7.464
7.477 	3.16
3.17
3.18 	7.873
7.886
7.898 	
1.87
1.88
1.89 	6.057
6.073
6.089 	2.20
2.21
2.22 	6.570
6.584
6.599 	2.53
2.54
2.55 	7.045
7.059
7.073 	2.86
2.87
2.88 	7.490
7.503
7.517 	3.19
3.20
3.21 	7.911
7.923
7.936 	

166

APPENDIX III

TABLE 2—Continued
table of theoretical velocity v = \/2gh corresponding to different
velocity heads h

Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	1
Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	1
Veloc-
ity
Head
or
Fall, h
Meters 	Veloc-
ity,
Meters
per
Sec-
ond 	
3.22
3.23
3.24 	7.948
7.960
7.973 	3.55
3.56
3.57 	8.345
8.357
8.369 	3.88
3.89
3.90 	8.725
8.736
8.747 	4.21
4.22
4.23 	9.088
9.099
9.109 	4.54
4.55
4.56 	9.437
9.448
9.458 	
3.25
3.26
3.27 	7.985
7.997
8.009 	3.58
3.59
3.60 	8.380
8.392
8.404 	3.91
3.92
3.93 	8.758
8.769
8.780 	4.24
4.25
4.26 	9.120
9.131
9.142 	4.57
4.58
4.59 	9.468
9.479
9.489 	
3.28
3.29
3.30 	8.022
8.034
8.046 	3.61
3.62
3.63 	8.415
8.427
8.439 	3.94
3.95
3.96 	8.792
8.803
8.814 	4.27
4.28
4.29 	9.152
9.163
9.174 	' 4.60
4.61
4.62 	9.500
9.510
9.520 	
3.31
3.32
3.33 	8.085
8.070
8.082 	3.64
3.65
3.66 	8.450
8.462
8.474 	3.97
3.98
3.99 	8.825
8.836
8.847 	4.30
4.31
4.32 	9.185
9.195
9.206 	4.63
4.64
4.65 	9.530
9.541
9.551 	
3.34
3.35
3.36 	8.095
8.107
8.119 	3.67
3.68
3.69 	8.485
8.497
8.508 	4.00
4.01
4.02 	8.858
8.869
8.880 	4.33
4.34
4.35 	9.217
9.227
9.238 	4.66
4.67
4.68 	9.561
9.572
9.582 	
3.37
3.38
3.39 	8.131
8.143
8.155 	3.70
3.71
3.72 	8.520
8.531
8.543 	4.03
4.04
4.05 	8.892
8.903
8.914 	4.36
4.37
4.38 	9.248
9.259
9.270 	4.69
4.70
4.71 	9.592
9.602
9.612 	
3.40
3.41
3.42 	8.167
8.179
8.191 	3.73
3.74
3.75 	8.554
8.566
8.577 	4.06
4.07
4.08 	8.925
8.936
8.946 	4.39
4.40
4.41 	9.280
9.291
9.301 	4.72
4.73
4.74 	9.623
9.633
9.643 	
3.43
3.44
3.45 	8.203
8.215
8.227 	3.76
3.77
3.78 	8.588
8.600
8.611 	4.09
4.10
4.11 	8.957
8.968
8.979 	4.42
4.43
4.44 	9.312
9.322
9.333 	4.75
4.76
4.77 	9.653
9.663
9.673 	
3.46
3.47
3.48 	8.239
8.251
8.263 	3.79
3.80
3.81 	8.622
8.634
8.645 	4.12
4.13
4.14 	8.990
9.001
9.012 	4.45
4.46
4.47 	9.343
9.354
9.364 	4.78
4.79
4.80 	9.684
9.694
9.704 	
3.49
3.50
3.51 	8.274
8.286
8.298 	3.82
3.83
3.84 	8.657
8.668
8.679 	4.15
4.16
4.17 	9.023
9.034
9.045 	4.48
4.49
4.50 	9.375
9.385
9.396 	4.81
4.82
4.83 	9.714
9.724
9.734 	
3.52
3.53
3.54 	8.310
8.322
8.333 	3.85
3.86
3.87 	8.691
8.702
8.713 	4.18
4.19
4.20 	9.055
9.066
9.077 	4.51
4.52
4.53 	9.406
9.417
9.427 	4.84
4.85
4.86 	9.744
9.754
9.764 	

TABLES

167

TABLE 2~-Continued
table of theoretical velocity v = \^2gh corresponding to different
velocity heads h

Veloc- 	Veloc- 	Veloc- 	Veloc- 	Veloc- 	Veloc- 	Veloc- 	Veloc- 	Veloc- 	Veloc- 	
ity 	ity, 	ity 	ity, 	ity 	ity, 	ity 	ity, 	ity 	ity, 	
Head 	Meters 	Head 	Meters 	Head 	Meters 	Head 	Meters 	Head 	Meters 	
or
Fall, h 	per
Sec- 	or
Fall, h 	per
Sec- 	or
Fall, h 	per
Sec- 	or
Fall, h 	Sec- 	or
Fall, h 	per
Sec- 	
Meters 	ond 	Meters 	ond 	Meters 	ond 	Meters 	ond 	Meters 	ond 	
4.87 	9.774 	10 	14.006 	43 	29.044 	76 	38.613 	145 	53.334 	
4.88 	9.784 	11 	14.690 	44 	29.380 	77 	38.866 	150 	54.246 	
4.89 	9.794 	12 	15.343 	45 	29.712 	78 	39.117 	155 	55.143 	
4.90 	9.804 	13 	15.970 	46 	30.040 	79 	39.367 	160 	56.025 	
4.91 	9.814 	14 	16.572 	47 	30.365 	80 	39.616 	165 	56.894 	
4.92 	9.824 	15 	17.154 	48 	30.686 	81 	39.863 	170 	57.749 	
4.93 	9.834 	16 	17.718 	49 	31.004 	82 	40.182 	175 	58.592 	
4.94 	9.844 	17 	18.263 	50 	31.329 	83 	40.352 	180 	59.424 	
4.95 	9.854 	18 	18.791 	51 	31.631 	84 	40.594 	185 	60.243 	
4.96 	9.864 	19 	19.306 	52 	31.939 	85 	40.835 	190 	61.052 	
4.97 	9.874 	20 	19.808 	53 	32.245 	86 	41.074 	195 	61.850 	
4.98 	9.884 	21 	20.297 	54 	32.548 	87 	41.313 	200 	62.638 	
4.99 	9.894 	22 	20.775 	55 	32.848 	88 	41.549 	205 	63.416 	
5.00 	9.904 	23 	21.242 	56 	33.145 	89 	41.785 	210 	64.185 	
5.25 	10.489 	24 	21.698 	57 	33.440 	90 	42.019 	215 	64.944 	
5.50 	10.387 	25 	22.146 	58 	33.732 	91 	42.252 	220 	65.695 	
5.75 	10.621 	26 	22.584 	59 	34.021 	92 	42.483 	225 	66.438 	
6.00 	10.849 	27 	23.015 	60 	34.408 	93 	42.713 	230 	67.171 	
6.25 	11.073 	28 	23.437 	61 	34.593 	94 	42.942 	235 	67.898 	
6.50 	11.292 	29 	23.852 	62 	34.875 	95 	43.170 	240 	68.616 	
6.75 	11.507 	30 	24.260 	63 	35.155 	96 	43.397 	245 	69.328 	
7.00 	11.718 	31 	24.661 	64 	35.433 	97 	43.622 	250 	70.031 	
7.25 	11.926 	32 	25.055 	65 	35.709 	98 	43.847 	255 	70.728 	
7.50 	12.130 	33 	25.444 	66 	35.983 	99 	44.070 	260 	71.418 	
7.75 	12.330 	34 	25.826 	67 	36.254 	100 	44.299 	265 	72.102 	
8.00 	12.528 	35 	26.203 	68 	36.524 	105 	45.386 	270 	72.780 	
8.25 	12.722 	36 	26.575 	69 	36.791 	110 	46.454 	275 	73.450 	
8.50 	12.913 	37 	26.942 	70 	37.057 	115 	47.498 	280 	74. 114 	
8.75 	13.102 	38 	27.303 	71 	37.321 	120 	48.519 	285 	74.773 	
9.00 	13.288 	39 	27.660 	72 	37.583 	125 	49.520 	290 	75.446 	
9.25 	13.471 	40 	28.013 	73 	37.843 	130 	50.500 	295 	76.074 	
9.50 	13.652 	41 	28.361 	74 	38.101 	135 	51.462 	300 	76.726 	
9.75 	13.830 	42 	28.804 	75 	38.385 	140 	52.407 			

1

BTT
M

APPENDIX IV
FRICTION OF GASES FLOWING THROUGH BRICK
FLUES OR MAINS («
by W. A. MOJAROW
in the flow of gases beneath an inverted weir, or, as it may be
designated, inverted flow, the stream of gas may or may not fill
the flue or furnace to its full height; practically, it may be said
that in those cases where the stream of gases does not touch the
hearth or bottom of the flue, the depth or vertical thickness of the
inverted stream will be given by the formula developed by M. J.
Yesmann, Professor of Hydraulics at the Polytechnic Institute of
Petrograd :
in which Q/ = the volume of gas flowing at the temperature t°;
J3 = the length of crest of the inverted weir, that is, the
width of the furnace or flue;
a — sl coefficient which is not constant and varies from
2.97 to 3.62 according to ht and B.
In order to arrive at the actual movement of the gases it is
necessary to take account of the drop in pressure and, likewise,
of the decrease in velocity which occurs at the different parts of
the furnace or flue.
These losses are caused by:
1.	Changes in the direction of flow;
2.	Changes in the cross-sectional area of the channel;
3.	Friction against the walls of the channel.
Information regarding the first two losses and changes of
(1) Revue de laSoriett russe de M&tallurgie, /, pp. 835-371 (1913}. Extrait
de Revue de Metallurgie, XI bis, p. 320, mai 1914.
168

FRICTION OF GASES FLOWING THROUGH BRICK FLUES    169
velocity may be found in the theory of ventilation and these may
be applied; but at the present time there is no series of observa-
tions which will permit the computation of the frictional losses.
Calculations by the author show that these frictional losses
may be evaluated by the following expression:
SL	SL	B	,A.
7 = m --- Vfpt = m--2-qopo = m-^qopQ,   .    .    .    (A)
co	co	co
in which y = millimeters of water column;
m = the coefficient of friction of the gas against the brick;
S = the perimeter  of the  channel in meters,  or that
portion of the perimeter " wet " by the gas;
co = the cross-sectional area of the channel or stream of
gas in square meters;
L = the length in meters of the portion of the channel
considered ;
J3 = SZ/=the superficial wall area of the portion of the channel
considered;
^ = the velocity of flow of the stream of gas at the
temperature t° in meters per second ;
pt = the weight in kilograms per cubic meter of the gas
at the average temperature £°;
t° = the average temperature of the gas in the part of the
channel considered;
go = the volume of the gas at 0° and 760 mm pressure;
po = the specific weight of the gas at 0° and 760 mm.
According to Professor Groume-Grjimailo, under the usual
working conditions of metallurgical furnaces, the gases passing
through the internal channel of these furnaces should always be
considered with reference to the air which forms the external
atmosphere, and the difference between the density of the hot
gases and the air supplies the motive force for the flow of these
gases; therefore, taking as the basis of comparison air at 0°
and 760 mm which has a specific weight po=1.29 kg per cubic
meter, it follows that if Fo=1.0 m per second and L=1.0 m,
the above formula becomes:
in which y=m if -o=1.293.    In other words, the coefficient m is

170

APPENDIX IV

P> ;

only the head, expressed in millimeters of water, corresponding to
the friction loss per second of air at 0° and 760 mm passing through
a brick-lined flue with a velocity of 1 m per second, the sectional area
of the flue corresponding to the equation -~= 1.293.
According to the computations of the author, 0.016 may be
taken as the value of the coefficient m with sufficient precision
for the computations met with in metallurgy. The verification
of this coefficient was made by using it in computations upon
Cowper and Massick and Crook hot-blast stoves.
The formula (A) may be used for all cases in which a current
of gases is flowing through mains or flues.
1. If the current of flowing gas is subdivided into a number of
channels or streams of equal area, the friction loss in each of these
secondary channels is
8    Q

in which

S        ,
= ~   and
n

CO
«.=-;

n being the number of secondary channels or flues.
2.	If the cross-sectional areas of these secondary channels or
flues are not equal (as, for example, in the gas and air flues of an
open-hearth furnace), the values B=SL and co in the formula
(A), for the parts located between the point where the gaseous
currents separate and the point where the secondary flues join
comprise, respectively, the entire surface touched by the gases in
passing and the sum of the average areas of all the channels or
flues through which the gases pass.
3.	If the gas in motion does not fill the furnace to its full
height, the depth of the gaseous stream is computed by the
formula for the inverted weir.   The value given to the perimeter
of the channel should be based upon the depth of the stream of
gases.   As the. lower stream of the gas in motion slides on top of
the immobile layer of the same gas in the bottom portion of the
flue, it is necessary to take account of the frictional resistance by
considering the entire perimeter of the flowing stream of gases,
including the " free lower surface " of the stream, and the cross-
sectional area of the stream as determined by the depth of the
stream in the flue.
2.	
APPENDIX V
MUFFLE FURNACE FOR TEMPERING AND ANNEALING
STEEL AT THE PETROGRAD ARSENAL d>
this furnace supplies an interesting example of the application
of hydraulic laws to the computation of furnaces. An old furnace
of English construction with a cast-iron muffle and four dampers,
working with an updraft, was in operation at the Petrograd
Arsenal. It did not heat well and the heat was poorly distributed.
This furnace was replaced by a very costly one, which was con-
structed according to a German patent and also worked with an
updraft. The muffle was of brick. This furnace, notwithstanding
its complex design, could never be made to heat uniformly.
Upon the request of the superintendent of the forge, Professor
Groume-Grjimailo studied the conditions and recommended the
reconstruction of the old English furnace, in such a manner that
it would work on the downdraft principle. This was done according
to Figs. 133 to 136. The binding of the furnace was not altered.
After reconstruction the furnace worked perfectly. It was
practically impossible to detect any difference in temperature
between "the different portions of the large muffle (3600 X1000 X
100 mm) by the use of two Le Chatelier pyrometers. The tem-
perature of the muffle could be changed as desired, and it could
be made to vary between large limits (900° to 400°) by changing
the setting of the damper in the waste-gas flue.
A short calculation was made later concerning this furnace.
The computed consumption of fuel was 55 kg 80 per hour, about
640 kg per day. The actual consumption per day was 690" kg.
This estimate was based entirely upon the analysis of the gases
at different points within the furnace.
A cast-iron muffle was chosen for this furnace.    A similar
(1) Revue de la Societt russe de Mttallurgie, /, pp. 4%3~426 (1913}. Revue
de Metallurgie, mai 1914 (p. 115, MS.).

172

APPENDIX V

Plan

Bed	Fire
Brick	Brick
fig. 133.—Horizontal Sections.

^^^^^^
fig. 134.—Longitudinal Section.

MUFFLE FURNACE FOR TEMPERING

173

vertical muffle for continuous service, constructed according to
the designs of the author, was in use at the PoutilofI works (Petro-
grad). In the arsenal the daily interruption of the work resulted
in the rapid wearing out of the muffle, and after a run of two
months it was decided to remove the cast-iron muffle and operate
the furnace with a perforated brick hearth through which waste
gases could pass off. The furnace was reconstructed in this
manner, without a muffle, and upon being placed in operation
worked perfectly, heating very uniformly and fulfilling perfectly
all the demands for annealing and tempering which were made
upon it.

/•sv

fig. 135.—Cross-section through
Firebox.

fig. 136.—Cross-section through
Waste Gas Ports.

The following shows the computations which were made:
The volume of the heating chamber, according to the design,
was 3 m3 30;   the temperature of the gas was to be 1000°, the
combustion being neutral, that is to say, without excess air.
The instantaneous  calorific intensity was computed as 2000°,
giving a drop in temperature of the gases of 200° per second, the"
time which the gases remain in the heating chamber being
2000-1000
200
- = 5 seconds.

174	APPENDIX V
The volume of gas per second is found as follows :
0iooo = 3.3 :5 = 0m366

01000

14

The consumption of coal per second is arrived at as follows:
1 kg of coal gives about 9 m3 00 of gas, and; accordingly:

0.14
£ = ;
= 0 kg 0155 per second=about 55 kg 80 per hour.
9.00
The dimensions of the fireboxes were the same as before,
o,=4XlX0.56 = 2m224,
and corresponded with a fuel consumption of 25 kg of coal per
square meter of grate per hour. The rate of combustion was
rather slow, a condition which is particularly favorable for realizing
theoretical combustion.
The area of the hot gas ports from the firebox:
«i = 4XO. 16X0.32 = 0 m2 20.
The velocity in these parts is low:
^iooo = 0.66 : 0.20 = 3 m 20 per second.
The area of the waste gas ports is
co2 = 16XO.24X0.12 = 0 m2 46.
The velocity in these ports is
^iooo = 0.66 : 0.46 = 1 m 43 per second.
These low velocities make it certain that the waste-gas flue
will receive the coolest gases in the chamber and are also very
favorable to the obtaining of a uniform temperature over the
whole hearth of the muffle.
The height of the waste-gas flue according to Yesmaim's
formula is 0 m 38.
The computation for the chimney was not made, as the
existing chimney was amply sufficient and gave a large margin of
safety, the velocity of the gases at its outlet being very nearly zero.

MUFFLE FURNACE FOR TEMPERING	175
These computations have once more confirmed the theory of
#aces developed by Professor Groume-Grjimailo, based upon
Jraulic laws.
Jn the author's opinion the computation for a furnace has
.0me a problem so simple and clear, that, when a furnace has
Yi correctly computed it cannot fail to work properly] it has
-0me possible to guarantee the correct working of a furnace
Jaout any more risk than is involved in the guarantee of the
formance of a turbine or a steam engine. It only remains to
,#in the best types of furnaces for each particular purpose, and
3 is impossible without the cooperation of the works and those
o direct them.

APPENDIX VI

ARCH BRICK WORK
FORMULAS AND TABLES  FOR  FANTAIL  OR TAPER ARCHES
by A. D. WILLIAMS
tables giving the number of shape and straight brick required
to make a complete circle are found in many of the firebrick and
facebrick catalogues. These are very convenient, as far as they
extend, in regard to the standard shapes, but are of comparatively

little assistance in working out
the shapes required for " fan-
tail " or taper arches, which
may be built either of standard
or special shapes as desired,
or for conical or skew arches.
The accompanying tables
were computed to facilitate the
working out of arch shapes,
and it is believed that the
accompanying diagram sup-
plies sufficient information to
fig. 137.	facilitate their use. They have
been carefully computed and
checked, but the writer will be grateful to anyone who will
call his attention to any errors which may have been made in the
tables.
In the diagram the letters and following formulas corre-
spond :
176

ARCH  BRICK WORK	177

2~v       ........   (1)
•   a   0.5Z
S1Q2=— ..........   (2)
,==6.2832rXa(deg.)
360 -   .....   (3)
or
= 0.01754rXa(deg.).
'd=r~v ..........   (4)
r'=r+t ..........   (5)
e=0.01754r'Xa(deg.) .....    (6)
k=c~b ........ -    .    .    (7)
°~e-f-     .........    (8)
s»
-= n = total number of brick in span. .    ...    (9)
k
-== n'=number of taper brick in span.    .    .    (10)
»7
n--72/=n''=number of straight brick in span.     .    (11)
3P I
Thrust, uniform loading   =Tu--~~.
juV
3PI
Thrust, concentrated Io&d=Tc = '-—~.
Pu = uniform load, pounds per square foot.
*   Pc = concentrated load in pounds at center of span.
When several concentrated loads are to be considered, reduce
to an equivalent concentrated center load.

178

APPENDIX VI

TABLE 1
formulas and tables for arch brick
Firebrick Arches; Rise, Length, Radius, for Chord of Unity

No. 1 	No. 2 	No. 3 	No. 4 	No. 5 	No. 6 	No. 7 	No. 8 	
Rise or
Middle
Ordinate
Decimal
of Span
or
Chord 	Loga-
rithm or
Rise or
Middle
Ordinate 	Rise or
Middle
Ordinate
Inches
per 1 Ft
Span or
Chord 	Arc 	Length
of
Arc 	Loga-
rithm of
Length
of
Arc 	Radius
of
Arc 	Loga-
rithm of
Radius
of
Arc 	
V 	log v 	V 	a,
Degrees,
Minutes
and •
Seconds 	b or c 	log b
logc 	r or rr 	logr
logr' 	
0 0300 	8 47712 		13-44-04 	1 00240 	0 C0104 	4 1816 	0 62135 	
0.0313
0.0328 	8.49485
8 51550 	t 	14-19-42
15-00-00 	1.00261
1 00285 	0.00113
0 . 00124 	4.0092
3.8307 	0.60306
0 58327 	
0.0339
0.0350
0.0365
0.0391
0 0400 	8.52961
8.54407
8.56180
8.59176
8 60206 	if
'"ft
if 	15-30-52
16-01-00
16-19-05
17-53-09
18-17-44 	1.00305
1.00327
1.00355
1.00407
1 00426 	0.00132
0.00142
0.00154
0.00176
0 00185 	3.7043
3.5889
3.4429
3.2313
3 1450 	0.58671
0.55496
0.53693
0.50738
0 49762 	
0.0417
0.0443
0 0450 	8.61979
8.64612
8 65321 	i
& 	19-04-11
20-11-00
20-34:-18 	1.00462
1.00522
1 00539 	0.00192
0.00226
0 00233 	3.0254
2.8535
2 8002 	0.47978
0.45538
0 44719 	
0.0469
0.0493
0.0495
0 0500 	8.67094
8.69237
8.69442
8 69897 	ft
'"»' 	21-26-23
22-30-00
22-36-56
22-50-32 	1.00585
1.00645
1 . 00652
1 00665 	0.00253
0.00279
0.00282
0 00288 	2.6887
2.5629
2.5500
2 5250 	0.42954
0.40873
0.40654
0 40226 	
0.0521
0.0547
0 0550 	8.71670
8.73789
8 74036 	I
ft 	23-47-44
24-58-24
25-Q6-34 	1.00723
1.00796
1 00805 	0 . 00313
0.00344
0 00348 	2.4254
2.3125
2 3002 	0.38476
0.36409
0 36177 	
0.0573
0.0599
0.0600 	8.75809
8.77740
8 77815 	&
If 	26-09-01
27-19-34
27-22-16 	1 . 00873
1.00954
1 00957 	0.00378
0.00412
0 00414 	2.2102
2.1168
2 1133 	0.34442
0.32567
0 32497 	
0.0625
0 0650 	8.79588
8 81291 	1
4 	28-30-00
29-37-42 	1 . 01088
1 01123 	0.00470
0 00485 	2.0314
1 9555 	0.30776
0 29126 	
0.0651
0 0658 	8.81361
8 81840 	If 	29-40-22
30-00-00 	1.01127
1 01153 	0.00487
0 00498 	1.9527
1 9319 	0.29063
0 28 W7 	
0.0677
0 0700 	8.83064
8 84510 	tt 	30-50-42
31-52-43 	1.01217
1 01302 	0.00525
0 00569 	1.8802
1 8207 	0.27421
n 9R094. 	

ARCH BRICK WORK

179

formulas and tables for arch brick—Continued
Firebrick Arches; Rise, Length, Radius, for Chord of Unity

No. 1 	No. 2 	No. 3 	No. 4 	No. 5 	No. 6 	No. 7 	No. 8 	
Rise or
Middle
Ordinate
Decimal
of Span
or
Chord 	Loga-
rithm of
Rise or
Middle
Ordinate 	Rise or
Middle
Ordinate
Inches
per 1 Ft
Span or
Chord 	Arc 	Length
of
Arc 	Loga-
rithm of
Length
of
Arc 	Radius
of
Arc 	Loga-
rithm of
Radius
of
Arc 	
V 	log v 	V 	a,
Degrees,
Minutes
and
Seconds 	b or c 	log&
logc 	r or r' 	logr
logr' 	
0.0703
0.0729
0 0750 	8.84703
8 . 86283
8 . 88081 	ft
7
8 	32-00-48
33-06-09
34-07-23 	1.01313
1.01410
1 . 01493 	0.00567
0.00608
0 00644 	1.8132
1.7552
1 7042 	0.25846
0.24432
0 23151 	
0.0755
0.0781
0 0800 	8.87807
8.89279
8 90309 	»
It 	34-20-50
35-30-42
36-21-42 	1.01513
1.01618
1.01698 	0.00652
0.00697
0 00731 	1.6934
1.6396
1 6025 	0.22875
0.21473
0 20479 	
0.0807
0 0820 	8.90703
8 91672 	» 	36-40-23
37-30-00 	1.01728
1.01807 	0.00728
0 00778 	1.5893
1 5555 	0.20120
0 19187 	
0.0833
0.0850
0.0859
0.0885
0 0900 	8.92082
8.92942
8.93418
8.94714
8 95424 	1
1&
1* 	37-50-04
38-35-32
38-59-32
40-08-58
40-49-03 	1.01841
1.01916
1.01956
1.02075
1 02146 	0.00742
0.00824
0.00841
0.00892
0 00922 	1.5422
1.5131
1.4982
1.4567
1 4339 	0.18815
0.17986
0.17656
0.16336
0 15652 	
0.0911
0.0938
0 0950 	8.95974
8.97197
8 97772 	1*
11 	41-18-14
42-30-03
43-08-26 	1.02197
1.02329
1.02389 	0.00944
0.00999
0.01025 	1.4177
1.3795
1.3663 	0.15158
0.13973
0.13355 	
0.0984
0.0990
0 0995 	8.98387
8.99545
8 99763 	1*
1* 	43-39-42
44-47-58
45-00-00 	1.02460
1.02593
1.02617 	0.01055
0.01112
0.01122 	1.3446
1.3121
1.3066 	0.12858
0.11797
0.11613 	
0 1000 	9 00000 		45-14-23 	1.02646 	0.01134 	1.3000 	0.11394 	
0.1016
0.1042
0 1050 	9.00673
9.01773
9 02119 	1*
U 	45-56-36
47-04-35
47-26-20 	1.02731
1.02871
1.02914 	0.01170
0.01229
0.01247 	1.2811
1.2520
1.2430 	0.10760
0.09761
0.09446 	
0.1068
0.1094
0 1100 	9 . 02845
9.03892
9 04139 	1*
1ft 	48-13-44
49-16-16
49-37-47 	1.03015
1.03162
1 . 03196 	0.01290
0.01352
0.01366 	1.2238
1.1995
1.1914 	0.08771
0.07900
0.07604 	
0.1120 	9.04914 	1» 	50-30-12 	1.03312 	0.01415 	1.1721 	0.06895 	

180

APPENDIX YI

F'Ri
I;
ir,'
I
s,' t

formulas and tables for aech brick—Continued
Firebrick Arches; Rise, Length, Radius, for Chord of Unity

No.l 	No. 2 	No. 3 	No. 4 	No. 5 	No. 6 	No. 7 	No. 8 	
Rise or
Middle
Ordinate
Decimal
of Span
or
Chord 	Loga-
rithm of
Rise or
Middle
Ordinate 	Rise or
Middle
Ordinate
Inches
per 1 Ft
Span or
Chord 	Arc 	Length
of
Arc 	Loga-
rithm of
Length
of
Arc 	Eadius
of
Arc 	Loga-
rithm of
Eadius
of
Arc 	
V 	logy 	V 	a,
Degrees,
Minutes
and
Seconds ' 	b or c 	logb
logc 	r or r' 	log r
log/ 	
0.1146
0.1150
0 1167 	9.09512
9.0.6070
9 06664 	M 	51-38-13
51-48-39
. 52-30-00 	1.03466
1.03490
1.03593 	0.01476
0.01490
0.01533 	1.1481
1.1445
1 . 1305 	0.05996
0.05860
0.05326 	
0.1172
0.1198
0 1200 	9.068S8
9.07843
9 07918 	Iff
1& 	52-46-04
53-53-47
53-58-58 	1.03623
1.03784
1 03797 	0.01546
0.01613
0 01619 	1.1252
1.1033
1 1017 	0.05121
0.04270
0 04205 	
0.1224
0.1250
0.1276
0 1300 	9.08777
9.09691
9.10586
9 11394 	1*1
H
l» 	55-01-11
56-08-42
57-15-54
58-17-48 	1.03949
1.04116
1.04287
1 04447 	0.01682
0.01752
0.01823
0 01890 	1.0825
1.0625
1.0434
1 0265 	0.03442
0.02633
0.01846
0 01138 	
0.1302
0.1328
0 1340 	9.11464
9. 12324
9 12702 	1*
i» 	58-22-57
59-29-50
60-00-00 	1.04461
1.04638
1 04715 	0.01895
0.01969
0 02002 	1.0252
1.0077
1 0000 	0.01079
0.00332
9 00000 	
0 1350 	9 13033 		60-26-18 	1 04792 	0 02033 	0 9934 	9 99714 	
0.1354
0.1400 	9.13167
9 14613 	if 	60-37-28
62-43-28 	1.04820
1 05147 	0.02040
0 02180 	0.9907
0 9607 	9.99593
9 98259 	
0.1406
0 1450 	9. 14806
9 16137 	i» 	62-49-26
64-41-19 	1.05190
1 05516 	0.02197
0 02332 	0.9594
0 9346 	9.9&198
9 97061 	
0.1458
0 1500 	9.16386
9 17609 	H 	65-01-39
65-47-30 	1.05576
1 05869 	0.02357
0 02488 	0.9302
0 90S5 	9.96859
9 95825 	
0. 1510
0 1517 	9.17910
9.18091 	1H 	67-13-02
67-30-00 	1.05973
1 06034 	0.02520
0 02545 	0.9033
0 9000 	9.95584
9 95423 	
0 1550 	9 19033 		68-53-37 	1 06288 	0 02649 	0 8840 	9 94643 	
0.1563
0 1500 	9.19382
9 20412 	if 	69-26-13
70-58-44 	1.06392
1 06693 	0.02691
0 02814 	0.8779
0 8613 	9.94344
9 93513 	
0.1615
0 1650 	9.20806
9 21748 	IB 	71-36-06
73-03-06 	1.06816
1 07109 	0.02864
0 02983 	0. 8547
0 8401 	9.93184
9 92432 	

ARCH BRICK WORK

181

formulas and tables for arch brick— Continued
Firebrick Arches; Rise, Length, Radius, for Chord of Unity

No.l 	No. 2 	No. 3 	No. 4 	No. 5 	No. 6 	No. 7 	No. 8 	
Rise or
Middle
Ordinate
Decimal
of Span
or
Chord 	Loga-
rithm of
Rise or
Middle
Ordinate 	Rise or
Middle
Ordinate
Inches
per 1 Ft
Span or
Chord 	Arc 	Length
of
Arc 	Loga-
rithm of
Length
of
Arc 	Radius
of
Arc 	Loga-
rithm of
Radius
of
Arc 	
V 	log v 	V 	a,
Degrees,
Minutes
and
Seconds 	b or c 	- log 6
log c 	r or r' 	logr
logr' 	
0.1667
0 1697 	9.22185
9.22975 	2 	73-44-08
75-QO-OQ 	1.07254
1 07511 	0.03042
0 03145 	0.8334
0 8213 	9.92084
9 9145^ 	
0 1700 	9.23045 		75-00-44 	1 07537 	0 03156 	0 8203 	9 91397 	
0.1719
0.1750
0.1771
0 1800 	9.23521
9.24551
9.24818
9 25527 	2-h
21 	75-53-30
77-09-36
78-01-12
79-11-44 	1.07702
1.07977
1.08165
1 08428 	0.03222
0.03333
0.03409
0 03514 	0.8131
0.8018
0.7943
0 7844 	9.91015
9.90406
9.90001
9 89456 	
0.1823
0.1850
0.1875
0 1882 	9.20077
9.26717
9.27300
9 27459 	2&
21 	80-07-39
81-13-04
82-13-27
82-30-00 	1.08639
1.08890
1.09126
1 09193 	0.03599
0.03699
0.03793
0 03819 	0.7768
0.7682
0.7604
0 7583 	9.89033
9.88546
9.83105
9 87986 	
0 1900 	9 27875 		83-13-38 	1.09365 	0.03888 	0 7529 	9 87673 	
0.1927
0.1950
0.1970
0 2000 	9.28490
9 .29003
9.29648
9 3010<' 	2ft
2| 	84HL3-17
85-13-23
86-22-29
87-12-20 	1 .09625
1.09850
1.10137
1.10347 	0.03991
0.04080
0.04233
0.04276 	0.7456
0.7385
0.7306
0 7250 	9.87253
9.86837
9.86367
9.86034 	
0.2081
0 2050 	9.3077C
9 3117f 	2& 	88-27-14
89-26-10 	1.10660
1.10855 	0.04399
0.04476 	0.7169
0.7106 	9.85543
9.85164 	
0 2071 	9 3161< 		90-00-00 	1.11072 	0.04560 	0.7072 	9.84949 	
0.2083
0 2100 	9.31876
9 32222 	2| 	90-29-34
91-41-32 	1.11196
1.11374 	0.04605
0.04680 	0.7041
0.6969 	9.84762
9.84315 	
0.2135
0.2188
0 2200 	9.3294<
9.3399
9 3424* 	2&
2| 	92-29-24
94-32-12
94-59-5^ 	1.11743
1.12312
1.12444 	0.04822
0.05043
0.05094 	0.6922
0.6807
0.6782 	9.84025
9.83295
9.83135 	
0.2240
0 2265 	9,3501
9 3551 	2« 	96-29-13
97-30-OC 	1.12885
1.13168 	0.05264
0.05372 	0.6703
0.6650 	9.82624
9.82284 	
0.2292
0 2300 	9.3601
9 3617 	2f 	98-30-0
98-48-3 	1.13466
1.1355 	0.05487
0.05521 	0.6600
0.6585 	9.81953
9.81854 	

P? ;	I
A	!
5*
i{ f
P"	1   ,
|jff	' •
&*	' !
ill!	!
5	i ,

182	APPENDIX VI
formulas and tables for arch brick—Continued
Firebrick Arches; Rise, Length, Radius, for Chord of Unity

No. 1 	No. 2 	No. 3 	No. 4 	No. 5 	No. 6 	No. 7 	No. 8 	
Rise or
Middle
Ordinate
Decimal
of Span
or
Chord 	Loga-
rithm of
Rise or
Middle
Ordinate 	Rise or
Middle
Ordinate
Inches
per 1 Ft
Span or
Chord 	Arc 	Length
of
Arc 	Loga-
rithm of
Length
of
Arc 	Radius
of
Arc 	Loga-
rithm of
Radius
of
Arc 	
V 	logv 	V 	a,     '
Degrees,
Minutes
and
Seconds 	6 or c 	log b
log c 	r or rf 	logr
logr' 	
0.2344
0.2396
0 2400 	9.36991
9.37946
9 38021 	2tt
2J 	100-28-08
102-24-54
102-33-50 	1 . 14061
1.14667
1 14714 	0.05714
0.05944
0.05962 	0.6505
0.6415
0 6408 	9.81323
9.80720
9 80675 	
0.2448
0 2465 	9.38880
9 39195 	2« 	104-20-44
105-00-00 	1 . 15284
1 15621 	0.06177
0 06304 	0.6330
0 6302 	9.80142
9 79950 	
0.2500
0.2600
0.2604
0.2673
0 2700 	9.39794
9.41497
9.41567
9.42693
9 43136 	3
3| 	106-15-36
109-53-51
110-04-25
112-30-00
113-28-34 	1.15912
1.17150
1 . 17200
1.18072
1 18429 	0.06413
0.06874
0.06893
0.07215
0 07346 	0.6250
0.6108
0.6101
0.6013
0 5980 	9.79588
9.78588
9.78541
9.77912
9 77667 	
0.2708
0.2800
0.2813
0 2821 	9.43270
9.44716
9.44909
9 45041 	34-
3S 	113-45-36
117-25-40
117-26-54
120-00-00 	1.18533
1 . 19746
1 . 19920
1 20027 	0.07384
0.07826
0.07889
0 07928 	0.5970
0.5851
0.5850
0 5774 	9.77597
9.76722
9.76717
9 76144 	
0.2900 	9 46240 		120-30-04 	1.21102 	0 08315 	0 5759 	9 76035 	
0.2917
0 3000 	9.46489
9 47712 	3i 	121-02-15
123-51-18 	1.21336
1 22495 	0.08399
0 08812 	0.5744
0 5667 	9.75919
9 75333 	
0 3100 	9 49136 		127-08-33 	1 23926 	0 09316 	0 5584 	9 74691 	
0 3109 	9 49265 		127-30-00 	1 24059 	0 09363 	0 5575 	9 74624 	
0.3125
0 3200 	9.49485
9 50515 	3f 	128-01-18
130-28-37 	1.24289
1 25391 	0.09443
0 09827 	0.5563
0 5506 	9.74527
9 74086 	
0 3300 	9 51851 		134-19-16 	1 26892 	0 10343 	0 5425 	9 73443 	
0.3333
0.3341 	9 . 52288
9.52386 	4 	134-^5-44
135-00-00 	1.27395
1 27517 	0.10515
0 10557 	0.5417
0 5412 	9.73373
9 73335 	
0 3400 	9 53148 		136-51-46 	1 28428 	0 10866 	0 5377 	9 73050 	
0 3500 	9 54407 		139-58-05 	1 29997 	0 11393 	0 5321 	9 72603 	
0.3541
0.3600 	9.54921
9.55630 	4i 	141-13-56
142-14-08 	1.30650
1 31599 	0.11611
0 11925 	0.5301
0 5284 	9.72431
9 72299 	

MISCELLANEOUS TABLES
MISCELLANEOUS TABLES
TABLE 2

183

	Chamber 	Volume 	
Operation 	Cubic Meters
per 1000 Kg. of
Coal Burned
per Hour 	Cubic Feet
per 1000 Pounds
of Coal Burned
per Hour 	
Kilns, Ordinary brick 	 	1000 	16 018 	
Porcelain 	 	120 	1 923 	
Refractory brick 	 	35 	560 	
Glass, bottles 	 	35 	560 	
Puddling furnaces 	 	11 	177 	
Crucible steel furnaces 	 	3 	50 	
Rcverberatory furnaces, Iron melting. 	2 	35 	
Steel melting 	 	1 	17 	

	Ratio between
Grate Area and
Hearth Area 	
Roasting of ores, etc 	 	15 	
Copper inciting 	 	5 	
Iron molting 	3 	
Puddling ...                                         .                     .             ... 	2 	
Stool melting 	 	1 	
From Le Chatelier, Le Chauffage Industriel.
TABLE 3
bessemer converters
Blast pressure about 25 pounds per square inch = 1 kg 76 per square centimeter-
Blast volume about 900 to 1100 cubic feet of free air per ton per minute =
25 m3 50 to 31 rn3 20 per tonne.
Blast pressure must be about seven times the pressure due to the static
head of the molten metal.
Molten metal weighs about 430 pounds per cubic foot=6888 kg per cubic
meter.
Depth of metal in vessel about 12 inches = 300 mm.
Static head of metal about 3 pounds per square inch = 0 kg 21 per square
centimeter.
Tuyere blocks are about 24 inches=600 mrn in depth.
Tuyere holes an* about 0.5 inch = 12 to 15 mm diameter.   Five to 7 holes

184

APPENDIX VI

TABLE 4
chimney draft (Lange)
BG(l+atQ)
700-fn
700+tn

tgi-

du—do

0.008 to 0.010,

in which F0 = area of bore of chimney at top in square meters;
B — kilograms of coal burned per hour;
G = kilograms of flue gases per kilogram of coal;
a = 1-^273 = 0.00367;
to = temperature of gases at base of chimney;
7 = 1.293 = weight of a cubic meter of air at 0° and 760 mm;
5=ratio between the weight of flue gases and air;
do = diameter of bore of chimney at top;
t? =3.1416 for a circle;
3.3137 for an octagon;
4.00 for a square;
Z = length of flue in meters;
a=flue coefficient 0.03 to 0.14 (usually 0.04);
Hr—height of chimney above grates in meters;
z=mm of water or kilograms per square meter;
71 = weight of flue gases per cubic meter at 0° and 760 mm;
du = diameter of bore of chimney at base in meters
tm—average temperature of flue gases;
p= kilo grams of coal burned per second;
Q=waste gases per kilogram of coal, cubic meters;
un=velocity of gas flow, meters per second (from 3 to 15).

MISCELLANEOUS TABLES	185
TABLE 5
hot blast stoves, empirical data
B'ast temperatures range from 500° to 1000°.
Heating surface ranges from 7 to 25 square meters (average 20 square meters)
per cubic meter per millimeter of blast.    (Withwell Stoves.)
Cowper stoves.    Velocity of cold blast in checker 1.50 to 2.00 m per sec.
Velocity of hot blast in checker 5.00 to 8.00 m	per sec.
Volume to be taken at the temperature and pressure.
Le Chatelier states that the heat interchange rate is
650 cal. per square meter per hour for 250° temperature difference.
TABLE 6
fuhnace temperatures
From Le Chatelier and Damour:
Glass tank, bottle glass		1425°
Annealing lehr		585°
Gas retort setting, top		1190°
Bottom		1060°
Porcelain kilns, hard porcelain		1400°
Chinaware		1275°
Brick kilns, various sources:
Building brick, cones 015a to 2a		800°-1170°
Vitrified pavers, cones la to 14		1150°-1410°
Glazed brick, cones 6a to 9a		1250°-1310°
Firebrick, cones 6 to 20		1250°-1530°
From Harbison and Walker Co., Catalogue:
Glass furnace between the pots		1375°
In pots, refining		1310°
In pots, working		1045°
Tanks melted for casting		1310°
Annealing glassware		444°- 555°
Crucible steel furnace, Siemens varies from		1460°-1590°
. A rough method of estimating temperatures:
Just glowing in the dark		525°
Dark red		700°
Cherry red		908°
Bright cherry red		1000°
Orange		1150°
White		1300°
Dazzling white		1500°

186	APPENDIX VI
TABLE 7
fuel consumption of furnaces, pounds per M (from various sources)
Brick kilns, Hoffman kilns, well built		280 to 340
Grates and troughs		340 to 450
Ruabon kiln		420 to 660
Staffordshire kiln		340 to 450
Buhrer continuous tunnel		230 to 280
C. E. Longnecker, pulverized coal consumption, pounds per ton (Iron Age,
Feb. 6, 1919):
Puddling		1000
Busheling	    400 to 500
Bfllet heating	    160 to 180
Forging	    400
Sheet annealing	    200
Sheet and pair	    300
Tin plate mill	    170
Open-hearth	   500 to 600
Copper reverberatory	    300
Tin smelting		1400
Galvanizing pots	    100
Tire furnaces	    330
Wheel	    600
Continuous bloom furnaces	    100 to 150
Rivet making	    90
Steam boilers		,3.5 pounds per bhp per hour
Soaking pits, hot ingots	    100 to 125
Reheating cold blooms	    140 to 200
Continuous furnaces, cold billets	    140 to 195
Open-hearth furnaces (G. L. Luctschcr):
.    Natural gas	 5600 to 6000 ft3 per ton
Coal	    500 to   650 pounds per ton
Oil	      45 gallons per ton
Basic furnaces	    790 pounds per ton
Acid furnaces	    780 to   860 pounds per ton
Billet heating 4 inches square cold	    200 to   250 pounds per ton

MISCELLANEOUS TABLES

187

TABLE 8
velocity of convection currents resulting from various average
temperature  differentials acting  for different heights

	Velocity in Feet per Second 	
Temperature 		
Difference, 					
Degrees F. 	Height, 	Height, 	Height, 	Height, 	
	3 Inches 	1 Foot 	10 Feet 	40 Feet 	
1 	0.1811 	0.3622 	1.145 	2.291 	
2 	0.2561 	0.5123 	1.620 	3.240 	
3 	0.3137 	0.6275 	1 . 984 	3.968 	
5 	0.405 	0.810 	2.561 	5 . 123 	
10 	0.5727 	1.1455 	3.622 	7.245 	
20 	0.810 	1.620 	5.123 	10.245 	
30 	0.992 	1.984 	6.275 	12.55 	
40 	1 . 1455 	2.291 	7.245 	14.49 	
50 	1,2808 	2.561 	8.10 	16.20 	
60 	1.403                 2.806 	8.873 	17.745 	
70 	1.515 	3.031 	9.582 	19.165 	
80 	1.620 	3 . 240 	10.245 	20.49 	
90 	1.718 	3.436 	10.867 	21.735 	
100 	1.811 	3.622 	11.455 	22.91 	
150 	2.218 	4.436 	14.03 	28.06 	
200 	2.561 	5.123 	16.20 	32.40 	
300 	3.137 	6 . 275 	19.84 	39.68 	
400 	3.622 	7.245 	22.91 	45.82 	
500 	4.05 	8.10 	25.61 	51.23 	
600 	4.436 	8.873 	28.06 	56.12 	
700 	4.791 	9.582 	30.305 	60.61 	
800 	5.123 	10.245 	32.40 	64.80 	
900 	5.434 	10.867 	34.365 	68.73 	
1000 	5.727 	11.455 	36.225 	72.45 	
1200 	6.275 	12.55 	39.68 	79.36 	
1400 	6.776 	13.552 	42.86 	85.72 	
1600 	7.245 	14.49 	45.82 	91 . 64 	
1800 	7.684 	15.368 	48.60 	97.20 	

188

APPENDIX VI

TABLE 9
velocity in meters per second of convection currents resulting
from various average temperature differentials acting for
different heights
Velocity in meters per second=v = -\/2gHat

To-Ti,
To-h.
Degrees 	# = 0.10 	# = 1.00 	# = 10.00 	
1 	0.0848 	0.2683 	0.8485 	
2 	0.1200 	0.3794 	1.200 	
3 	0.1470 	0.4648 	1.470 	
4 	0.1697 	0.5367 	1.697 	
5 	0.1897 	0.6000 	1.897 	
6 	0.2078  • 	0.6571 	2.078 	
7 	0.2245 	0.7100 	2.245 	
8 	0.2400 	0.7590 	2.400 	
9 	0.2546 	0.8050 	2.546 	
10 	0.2683 	0.8485 	2.683 	
20 	0.3794 	1.200 	3.794 	
30 	0.4648 	1.470 	4.648 	
40 	0.5367 	1.697 	5.367 	
50 	0.6000 	1.897 	6.000 	
60 	0.6571 	2.078 	6.571' 	
70 	0.7100 	2.245 	7.100 	
80 	0.7590 	2.400 	7.590 	
90 	0.8050 	2.546 	8.050 	
100 	0.8485 	2.683 	8.485 	
200 	1.200 	3.794 	12.00 	
300 	1.470 	4.648 	14.70 	
400 	1.697 	5.367 	16.97 	
500 	1.897 	6.000 	18.97 	
600 	2.078 	6.571 	20.78 	
700 	2.245 	7.100 	22.45 	
800 	2.400 	7.590 	24.00 	
900 	2.546 	8.050 	25.46 	
1000 	2.683 	8.485 	26.83 	

MISCELLANEOUS TABLES	189
METRIC CONVERSION TABLE
Logarithm
1m 00	=3.2803 ft	 0.5159842
I	=39.37 in	  1.5951654
= 1000 mm.	 3.000 0000
1.00 ft	=0 m 30 480	  9.484 0158-10
= 304 mm 80	  2.484 0158
= 12 in	  1.079 1812
]	1.00 in	=25mm40005	  1.4048346
i	1m2 00	= 10.7639 sq ft	  1.0319683
= 10,000 cm2	 4.000 0000
1 sq ft	=0.0929034 m2	 8.968 0316-10
= 929 cm2 034	 2.968 0316
= 144 sq in	.'	 2.158 3624
1 cm2 00	= 0.155sq in	 9.1903308-10
|	.    = 100 mm2 00	*	 2.000 0000
!	1 sq in	=6 cm2 45163	 0.809 6692
= 645 mm2 163	 2.809 6692
1m3 00    .	=35.3145 cu ft	  1.5479525
•	=1000 liters	 3.000 0000
I	=1.58219 oz mols	 0.1992583
= 44.80287 gr mols	  1.651 3058
= 264.170 gallons U. S	 2.421 8842
= 220.083 gallons British	 2.342 5870
l.OOcuft	=0m3 028317	 8.4520475-10
= 28.317 liters	  1.452 0475
= 1728 cu in	 3.237 5437
,	-7.48052 gallons U.S	  0.8739317
f	=6.23210 gallons British	  0.794 6345
= 1.26868 gr mols	  0.103 3533
= 0.044803 oz mol	  8.651 3058-10
i	1.00 gram mol    =22.32 liters	  1.348 6942
I	=0 m3 02232	  8.348 6942-10
= 0.788219 cu ft	 9.896 6467-10
= 0.035314 oz rnol	  8.547 9525-10
1 OOozmol         =22.32cuft	  1.3486942
= 0 m3 63236	  9.800 7417-10
= 632.36 liters	  2.800 7417
= 28.317 gram mols	  1-452 0475
4	1 kg 00	=2.20462 Ib	  0.343 3340
f	=1000 grams	 3.0000000
=35.27392 oz	  1.5474540
1 00 Ib	=0 kg 453953	 9.656 6660-10
=453 gr 593	  2.656 6660
i	=16oz	  1.2041200

190

APPENDIX VI

METRIC CONVERSION TAELE—Continued
Logarithm
1.00 oz	=28 gr 3490	   1.452 5461
= 0.0625 Ib	  8.795 8800-10
= 437.5 grains	  2.640 9781
1 kg 00 per m2     =1 mm 00 of water	  0.000
= 0 kg 0001 per cm2	  6.000 0000-10
= 10 gr 00 per cm2'. .,	  0.000 0000
= 0.03937 in of water	  8.595 1654-10
= 0.001422 Ib per sq in	  7.153 0032-10
= 0.204817 Ib per sq ft	  9.311 3657-10
1 kg 00 per cm2   = 1 metric atmosphere	  0.000
= 0.967777 atmosphere	  9.985 7752-10
= 735 mm 51 of mercury	  2.866 5888
= 10000 kg 00 per m2	  4.000 0000
= 10 m 00 of water	  1.000 0000
= 14.2234 Ib per sq in	   1.153 0032
= 2048.171bpersqft. . . ,	  3.311 3657
= 32.8083 ft of water	  1.515 9842
= 393.699 in of water	  2.595 1654
= 28.9570 in of mercury	   1.461 7542
1.00 atmosphere =760 mm of mercury	  2.880 8136
= 29.9212 in of mercury	   1.475 9790
= 1 kg 0332 per cm2	  0.014 2248
= 14.697 Ib per sq in	   1.1672280
= 10 m 332 of water	  1.014 2248
= 33.9007 ft of water	  1.530 2090
l.OQoz per sq in =0.0625 Ib per sq in	  8.7958800-10
=9.00 Ib per sq ft	  0.9542425
= 1.732 in of water	  0.238 5479
=34 mm 90413 of water	  1.542 8768
=34 kg 90413 per m2	  1.542 8768
1.00 Ib per sq in =0 kg 0703067 per cm2	  8.846 9968-10
= 703 kg 067 per m2	  2.846 9968
=0.068041 atmosphere	  8.832 7720-10
= 16.00 oz. per sq in	   1.204 1200
= 144.00 Ib per sq ft	  2.1583625
=27.67975 in of water	  1.442 1622
=2.30665 ft of water	  0.362 9810
=2.0359 in of mercury	  0.308 7510
=51 mm 7113 of mercury	  1.713 5856

MISCELLANEOUS TABLES	191
METRIC CONVERSION TABLE—Continued
Logarithm
1.00 Ib per sq ft =4 mm 88241 of water		0.688 6343
= 4 kg 88241 per m2		0.688 6343
= 0.0069444 Ib per sq in		7.841 6175-10
= 0.11111 oz per sq in		9.0457575-10
= 0.19222 in of water		9.2837997-10
= 0.0180184 ft of water		8.2046185-10
= 0.0141380 in of mercury		8.150 3885-10
1 kg 00 per m3    =0.0624283 Ib per cu ft		8.795 3816-10
1 gr 00 per cm3   =1000 kg 00 per m3		3.000 0000
= 1 kg 00 per liter		0.000
= 62.4283 Ib per cu ft		1.795 3816
=8.36469 Ib per gallon U. S		0.922 4499
= 10.043 Ib per gallon British		1.001 7471
= 0.036127 Ib per cu in		8.557 8379-10
1.00 Ib per cu ft =16 kg 0184   per m3		1.204 6184
= 0kg 01618 per liter		8.2046184-10
= 0.13368 Ib per gallon U. S		9.1260683-10
= 0.16046 Ib per gallon British		9.205 3655-10
= 0.0005787 Ibper cu in		6.7624563-10
= 0.0092592 oz per cu in		7.9665763-10
1.00 Ib per cu in = 27 gr 6797 per cm3		1.442 1621
=27 kg 6797 per liter		1.442 1621
=27,679 kg 744 per m3		4.442 1621
= 1,728 Ib per cu ft		3.237 5437
= 231.00 Ib per gallon U. S		2.363 6120
=277.274 Ib per gallon British		2.442 9092
Weight of Air 0° (32° F.) and 760 m/m (29.92 in) mercury.
1 m3 00 air	=1 kg 2928		0.111 6154
=2.85069 Ib		0.4549500
l.OOcuftair      =0.080723 Ib		8.9069975-10
= 0 kg 036615		8.563 6635-10
1 kg 00 air	=0 m3 77336		9.888 3840-10
=22.3109 cu ft*.		1.436 3365
1.00 Ib air	=12.3880 cu ft		1.093 0025
= Om»3S08		9.5459500-10
1.00 gr mol air    =0 kg 02886		8.460 3096-10
= 0.06363 Ib		8.803 6442-10
•l.OOozmolair   =0 kg 8172		9.9123517-10
= 1.80171b		0.2556917
=28,827 oz		1,459 8117

192

APPENDIX VI

METRIC CONVERSION TABLE—Continued

Logarithm
1.00 calorie
1.00 B.t.u.
1.00 calorie per m3
3.96832 B.t.u		0.598 6065
0.2519959 calorie		9.4013935-10
0.11238 B.t.u. per cu ft		9.050 6540-10
=0.02232 calorie per gr mol		8.348 6942-10
= 2.50812 B.t.u. per oz mol		0.399 3482
1.00 B.t.u. per cu ft    =8.8991 calories per m3		0.9493460
=0.1984 calorie per gr mol		9.297 6568-10
= 22.32 B.t.u. per oz mol		1.348 6942
1.00 calorie per gr mol = 44.803 calories per m3		1.651 3058
= 5.0379 B.t.u. per cu ft		0.702 3532
= 112.472   B.t.u. per oz mol		2.0510447
1.00 B.t.u. per oz mol=0.0448 B.t.u. per cu ft		8.651 3058-10
= 0.1593 calorie per m3		9.2021352-10
= 0.00889 calorie per gr mol		7.948 9553-10
1.00 calorie per kg
1.00 B.t.u. per Ib
= 1.8 B.t.u. per Ib		0.2552725
0.5555 calorie per kg		9.744 7275 — 10
CONVERSION OF METRIC FORMULAS TO ENGLISH UNITS
Many readers will prefer to use the English units of measurement and
Fahrenheit temperatures. This may readily be done in many of the con-
putations. In some of the formulas, however, the temperature enters as a
direct factor. These formulas may be transposed to English units by the
use of a conversion factor, but the Centigrade temperatures must be retained,
as no means has been found to use Fahrenheit temperatures.
P. 11. 1 cu ft of air = 0.0807 Ib. 1 cu ft of waste gases at 0° and 760 mm
or 32° F and 29.92 in weighs from 0.0805 to 0.0830 Ib per cubic foot.
P. 13. When H is expressed in feet, 5 will be expressed in pounds per
square foot, when the specific weights are expressed in pounds per cubic
foot. Pounds per square foot may be converted to inches of water column
by multiplying by the factor 0.19245.
P..27. The formula, Q = K\K«&V2gh, is the same in English units, the
coefficients ki and *2 are practically the same for gases and fluids flowing at
high velocities from thin or sharp-edge orifices, when the area of the orifice
is small. The larger the orifice the less the relative value of these coefficients
affects the flow or the nearer the value of the coefficients approaches unity.

P. 32.

ro.c
}-   o.s
j    lo.c
1 kg 00 per m2
1 mm of water
0.03937   in of water
204817 Ib per sq.ft
001422 Ib per sq in
1 atmosphere   =760 mm of mercury
= 29.92 in of mercury
=    1 kg 0333 per cm2
= 33.9007ft of water
= 14.697   Ib per sq in

MISCELLANEOUS TABLES	193
P. 41.    When dimensions are in feet, the formula of Yesmann is
-t	(E)
\ a"-i
or as given on p. 256.
The values of B on page 41 are:  1 m 00= 3.28 ft.
2 m 00 = 6.56 ft.
5 m 00 = 16.40 ft.
The values of ht = 0.30 = 0.984 ft.
0.50 = 1.64   ft.
0.75=2.46   ft.
1.00 = 3.28   ft.
P. 52.    For English units these formulas read as follows:
P. 56.    This formula is the same as given on p. 52.
P. 76.    The volume of gases given off by the combustion	of the coal
specified on this page will be:
Cubic Feet Cubic Feet
per kg	per Ib
Theoretical air	       319	145
1.25 times theoretical air supply	       396	180
1.50 times theoretical air supply	       473	215
1.75 times theoretical air supply	       551	250
2,00 times theoretical air supply	       627	285

APPENDIX VII
DESIGN OF OPEN-HEARTH FURNACES
By A. D. WILLIAMS
in designing an open-hearth furnace the first point to be settled
is the size of the hearth. Molten metal weighs 430 Ib per cubic
feet, so that 5.23 cu ft of bath will be required per ton of metal
capacity. The depth of bath permissible depends upon the work
to be done. With a shallow bath the reactions will be completed
faster than in a deep bath. The boil will be more violent and the
depth allowed for the molten cinder will be greater. Furnaces of
the mixer type, used in the Talbot and duplex process, are much
deeper than those used in the regular process.
In the pig and ore process the boil will increase the volume of
the bath to from 2 to 2.5 volumes. In the scrap process the bath
may boil to 1.5 to 1.7 its original volume.' The manner of handling
the cinder, whether it is retained in the furnace until the heat is
tapped or is to be drawn off by a cinder skimming notch, affects
the depth. In the early furnaces room had to be provided for all
of the cinder, and overflows were not infrequent. One advantage
of the Campbell tilting furnace was the facility it offered for
running off a portion of a heavy cinder. Later furnaces were
built with a cinder notch which permitted draining any excess
amount of cinder.
Table 1 gives the approximate hearth area in square feet
required for bath depths ranging from 1 to 3 ft. It was com-
puted by the formula:
nV    4
in which V—volume of molten metal in charge;
d = depth of bath, metal only;
yi=area of hearth.
194

Number of Furnaces
2335625' 21      12
10      20     30      40     50     60      70      80      90     100
Capacity of Furnace, Tcxns

fig. 138.—Graphical Comparison of the Approximate Depth of Molten Metal
in Bath of various Open-hearth Furnaces.

Number of Furances
2335C252112	3	1        1

0       10     20       30     40      50      GO      70      80      90     100
Capacity of furnace in Tons

fig. 139.—Graphical Comparison of the Length of Hearth in Various Open-
hearth Furnaces.

196

APPENDIX VII

While it is necessaiy to provide additional depth to cover the
depth of cinder and the boiling of the charge, additional area is
not required for these purposes.
An old rule of thumb made the length of the furnace twice its
width. This was all very well with small furnaces, although a
longer hearth gives better combustion conditions. The tempera-
ture of the metal in the bath is between 1525° and 1600° C. The
cinder will be slightly hotter than the metal, the difference ranging
from a few degrees just previous to tapping, to 100° or more.

17
16
15
M
1! ^
.212.
In
Jd
°,0
•o
* 9
8
7
6
5 	Number of Furnaces
2335625      21      12           3            1       1 	

									] 	

						i 	2 			

					M 	? 				

					•ft 		0 			

				V 	> 	\y\ 	\ 				

			/ 		fr 		( 				

			/'/! 	/ 	( 	> 					

		°/ 	/ 								

		/ 									

											

20      30     40      50      60      70      80     90   100
\	Capacity af Furnace in Tons
Fii. 140.—Graphical Comparison of the Width of Hearth in Various Open-
**	hearth Furnaces.
The gases leaving the hearth will range between 1600° and 1700°.
Told states that the gases should remain in the hearth 2 seconds;
Groume-Grjimailo, that the temperature drop through the
hearth should be assumed as 200° C. per second. The theoretical
flame temperature of a very good producer gas with both the air
and the gas preheated to 1000° and 40 per cent excess air will be
between 2100° and 2140°.
These data would seem consistent.  It requires between one and
two seconds for the reaction of combustion to be completed as the

DESIGN OF OPEN-HEARTH FURNACES

197

large jets of air and gas from the ports must be given time to mix.
With too short a furnace the flame will extend beyond the hearth.
With too long a furnace the gases of combustion will tend to drop
below the bath temperature.
There are three limitations on the width of the furnace:
1.	The distance material can be thrown through the door by
expert manipulation of a shovel or a dolomite gun.
2.	The width the flame can be spread.
3.	The limitation due to the strength of the roof.
The first controls patching and making bottom. Furnaces
have been built to 16.75 ft wide. This is rather close to the limit.
Table 2 gives the hearth dimensions of a number of furnaces
in service. It shows a considerable diversity in the ideas regarding
this portion of the furnace. Table 3 gives the minimum and
maximum values from Table 2.
TABLE 1
hearth area op open-hearth furnaces for various depths of molten
metal

		Depth of Bath of Molten Metal, In. 	
Capacity 	Cu Ft of 		

						i 			
of
Furnace,
TV\T1C! 	Molten
Metal 	12 	15 	18 	21 	24 	27 	30 	33 	36 	
jl ons 		(Hearth area in square feet) 	
15 	78.45 	235 	188 	157 	135 	118 					
20 	104 . 60 	314 	252 	212 	180 	157 	139 				
25 	130.75 	392 	314 	262 	225 	196 	174 				
30 	156.90 	471 	376 	314 	270 	235 	209 	189 			
35 	183.05 	549 	440 	356 	316 	275 	244 	220 	201 		
40 	209 . 20 	628 	504 	420 	360 	314 	278 	256 	229 	209 	
50 	261 . 50 	785 	629 	525 	450 	392 	350 	325 	286 	262 	
60 	313.80 	941 	755 	629 	542 	471 	418 	377 	343 	314 	
75 	392.25 	1177 	940 	785 	674 	588 	523 	470 	429 	392 	
90 	470.70 	1412 	1130 	945 	812 	706 	628 	567 	515 	471 	
100 	523.00 	1569 	1255 	1050 	900 	785 	697 	629 	573 	523 	

Allow from 3 to 6 in for cinder and boil.
y
volume of molten metal in charge;
Formula:   3— ~A.    In which
d
d = depth of bath ; metal only ; A = area of hearth required.   Weight of molten
metal, 430 Ib per cubic foot; 5.23 cu ft per ton.

198

APPENDIX VII

TABLE 2
hearth data op open-hearth furnaces from practice

Tons 	Refer-
ence
Number 	Length,
Ft,
L 	Width,
Ft,
W 	Area,
SqFt
A 	L
W 	A 	% 	

	

	
	Tons 	
	
10 	01-A 	19.25 	6.50 	163.6 	2.96 	16.36 	0.95 	
10 	02-F 	13.50 	7.54 	101.0 	1.82 	10.12 	1.59 	
15 	01-GS 	21.32 	8.52 	181.0 	2.50 	12.06 	1.31 	
15 	02-GO 	22.37 	9.57 	215.0 	2.33 	14.35 	1.10 	
15 	03-R 	19.67 	9.83 	191.7 	2.00 	12.78 	1.23 	
20 	01-GS 	23.45 	9.18 	215.3 	2.56 	10.75 	1.46 	
20 	02-GO 	24.61 	10.33 	254.0 	2.39 	12.70 	1.24 	
20 	03-A 	20.00 	10.50 	210.0 	1.92 	10.50 	1.50 	
25 	01-GS 	26.25 	9.84 	258.4 	2.67 	10.30 	1.52 ' 	
25 	02-GO 	27.87 	11.07 	304.6 	2.53 	12.20 	1.29 	
25 	03-A 	25.00 	10.50 	262.5 	2.38 	10.50 	1.49 	
25 	04-A 	25.00 	12.00 	300.0 	2.08 	12.00 	1.31 	
25 	05-A 	25.63 	10.50 	268.0 	2.44 	10.70 	1.46 	
30 	01-GS 	27.89 	10.50 	290.6 	2.63 	9.6 	1.62 	
30 	02-GO 	29.20 	11.81 	344.5 	2.48 	11.4 	1.36 	
30 	03-B 	21.00 	9.30 	195.0 	2.26 	6.5 	2.41 	
30 	04-A 	22.00 	12.5 	275.0 	1.77 	9.17 	1.71 	
30 	05-A 	21.88 	12.25 	267.9 	1.77 	8.93 	1.76 	
30 	06-B 	27.00 	10.00 	270.0 	2.70 	9.0 	1.75 	
35 	01-A 	24.00 	12.00 	288.0 	2.00 	8.20 	1.92 	
35 	02-A 	21.87 	12.25 	267.0 	1.79 	7.62 	2.06 	
40 	01-GS 	31.00 	11.48 	355.0 	2.70 	8.85 	1.77 	
40 	02-GO 	32.41 	12.89 	417.7 	2.52 	10.50 	1.51 	
40 	03-F 	24.00 	11.00 	264.0 	2.20 	6.60 	2.38 	
40 	04-A 	26.33 	12.50 	329.0 	2.11 	8.23 	1.90 	
40 	05-A 	24.00 	12.00 	288.0 	2.00 	7.20 	2.18 	
50 	01-GS 	34.45 	12.46 	430.6 	2.77 	8.6 	1.83 	
50 	02-GO 	35.96 	13.98 	502.7 	2.58 	10.0 	1.56 	
50 	03-A 	32.00 	10.00 	320.0 	3.20 	6.4 	2.46 	
50 	04-A 	27.00 	13.9 	376.0 	1.96 	7.5 	2.08 	
50 	05-A 	29.75 	15.00 	446.0 	1.99 	8.90 	1.76 	
50 	06-A 	32.00 	14.00 	448.0 	2.28 	8.96 	1.75 	
50 	07-A 	30.00 	15.00 	450.0 	2.00 	9.00 	1.74 	
50 	08-A 	30.50 	13.00 	396.5 	2.36 	7.92 	1.98 	
50 	09-A 	31.00 	15.00 	465.0 	2.08 	9.30 	1.68 	
50 	10-A 	28.00 	12.75 	357.0 	2.20 	7.14 	2.20 	
50 	11-A 	31.00 	14.00 	434.0 	2.22 	8.58 	1.81 	
50 	12-A 	35.00 	14.00 	490.0 	2.50 	9.80 	1.60 	
50 	13-A 	26.75 	13.40 	361.1 	2.00 	7.20 	2.18 	
50 	14-A 	27.67 	13.30 	368.7 	2.08 	7.38 	2.12 	
50 	15-A 	26.75 	12.58 	336.5 	2.12 	6.73 	2.33 	

DESIGN OF OPEN-HEARTH FURNACES

199

TABLE 2—Continued
hearth data of open-hearth furnaces from practice

Tons 	Refer-
ence
Number 	Length,
5 	Width,
Ft,
W 	Area.
SciFt, 	L
W 	A
Tons 	•j 	
50 	16-A 	32.00 	14.00 	448.0 	2.28 	8.96 	1.75 	
50 	17-A 	27.00 	13.90 	375.8 	1.95 	7.50 	2.08 	
50 	18~A 	29.00 	15.00 	435.0 	1.95 	8.70 	1.80 	
50 	19-A 	32.00 	14.00 	448.0 	2.28 	8.96 	1.75 	
50 	20-A 	33.67 	13.00 	438.0 	2.59 	8.76 	1.79 	
50 	21-F 	28.00 	10.25 	287.0 	2.73 	5.74 	2.74 	
60 	01-GS 	36.75 	13.12 	484.4 	2.80 	8.1 	1.95 	
60 	02-GO 	38.39 	14.76 	566.2 	2.60 	9.3 	1.68 	
60 	03-A 	30.00 	15.00 	450.0 	2.00 	7.5 	2.09 	
60 	04-A 	38.00 	15.00 	470.0 	2.54 	9.5 	1.65 	
60 	05-A 	43.00 	16.75 	720.0 	2.55 	12.0 	1.30 	
60 	06-A 	40.00 	16.00 	640.0 	2.50 	10.67 	1.47 	
60 	07-A 	34.40 	12.30 	423.0 	2.80 	7.05 	2.23 	
60 	08-B 	32.75 	11.80 	387.0 	2.77 	6.45 	2.43 	
60 	09-A 	32.00 	14.75 	472.0 	2.18 	7.67 	2.00 	
60 	10-A 	29.00 	14.92 	432.0 	1.94 	7.20 	2.18 	
60 	11-A 	40.00 	15.25 	610.0 	2.63 	10.16 	1.54 	
60 	12-A 	32.00 	15.00 	480.0 	2.13 	8.00 	1.96 	
75 	01-A 	40.00 	16.00 	640.0 	2.50 	8.53 	1.84 	
75 	02-A 	34.00 	13.50 	460.0 	2.53 	6.14 	2.56 	
75 	03-A 	40.00 	16.00 	640.0 	2.50 	8.53 	1.84 	
90 	01-A 	39.50 	15.25 	600.0 	2.56 	6.67 	2.36 	
100 	01-A 	40.00 	16.00 	640.0 	2.50 	6.40 	2.45 	
100 	02-F 	32.00 	12.50 	400.0 	2.56 	4.00 	3.92 	
150 	01-A 	41.00 	15.00 	615.0 	2.74 	4.06 	3.83 	
200 	01-A 	42.00 	15.75 	665 . 0 	2.66 	3.32 		
200 	02-A 	40.00 	16.00 	640.0 	2.50 	3.2 		
200 	03~B 	47.20 	13.00 	616.0 	3.64 	3.08 		
200 	04-A 	40.00 	13.00 	520.0 	3.07 	2.60 		
300 	01 -B 	47.20 	14.75 	695.0 	3.19 	2.32 		
A = American.    F=foreign.   B = Boche (German-Hungarian, etc.)
GS = Groume-Grjimailo scrap process.
GO = Groume-Grjimailo ore process.

 

200

APPENDIX VII

TABLE 3
maximum and minimum values from table 2

Capac-
ity,
Tons 	Length, Ft 	Width, Ft 	Area, Sq Ft 	L
W 	A
Ton 	S7
*A 	

	.3
§ 	X*
d
§ 	G
3 	X
=3
>?H
<< 	.3
S 	X
d
§ 	d
§ 	3
a 	3
S 	X
c3
IS 	.5
a 	9
a 	
10 	13.50 	19.25 	6.50 	7.54 	101.0 	163.6 	1.82 	2.93 	10.12 	16.36 	0.98 	1.55 	
15 	19.67 	22.37 	8.52 	9.83 	181.0 	215.0 	2.00 	2.50 	12.06 	14.35 	1.10 	1.31 	
20 	20.00 	24.61 	9.18 	10.50 	210.0 	254.0 	1.92 	2.56 	10.50 	12,70 	1.24 	1.50 	
25 	25.00 	27.87 	9.84 	12.00 	262.5 	304.6 	2.08 	2.67 	10.30 	12.20 	1.29 	1.52 	
30 	21.00 	29.20 	9.30 	12.50 	195.0 	344.5 	1.77 	2.70 	8.93 	11.40 	1.36 	2.41 	
35
40
50 	21.87
24 00 	24.00
32 41 	12.00
11.00 	12.25
12 89 	267.0
264 0 	288.0
417 7 	1.79
*>, 00 	2.00
*>, 70 	7.62
6 60 	8.20
10 50 	1.92
1  51 	2.06
9, 38 	

	26.75 	35.96 	10.00 	15.00 	287.0 	502.7 	1.95 	3.20 	5.74 	10.00 	1.56 	2.74 	
60 	29.00 	43.00 	11.80 	16.75 	387.0 	720.0 	1.94 	2.80 	6.45 	12.00 	1.30 	2.43 	
75
90 	34.00 	40.00
39 50 	13.50 	16.00
15.25 	460.0 	640.0
600.0 	2.50 	2.53
9 5fi 	6.14 	8.53
6 67 	1.84 	2.56
2.36 	

	
TABLE 4
open-hearth  furnace  heaeth and  heating  chamber proportions,
according to groume-grjimailo

	Scrap Process 	Ore Process 		
			Heating 	
Capac- 									Cham- 	
ity, 				Height 				Height 	ber, 	
Tons 	Length, 	Width, 	Area, 	Above 	Length, 	Width, 	Area, 	Above 	CuFt 	
	Ft 	Ft 	SqFt 	Bath, 	Ft 	Ft 	SqFt 	Bath, 		
				Ft 				Ft. 		
15 	21.32 	8.52 	181.7 	5.25 	22.57 	9.57 	215.3 	4.43 	954 	
20 	23.45 	9.18 	215.3 	5.91 	24.61 	10.33 	254.0 	5.00 	1271 	
25 	26.25 	9.84 	258.4 	6.15 	27.85 	11.07 	304.6 	5.21 	1581 	
30 	27.89 	10.50 	290.6 	6.56 	29.20 	11.81 	344.5 	5.53 	1907 	
40 	31.00 	11.48 	355.2 	7.56 	32.41 	12.89 	417.7 	6.09 	2543 	
50 	34.45 	12.46 	430.6 	7.15 	35.96 	13.98 	502.7 	6.32 	3178 	
60 	36.75 	13.12 	484.4 	7.87 	38.39 	14.76 	566.2 	6.73 	3814 	

DESIGN  OF OPEN-HEARTH FURNACES

201

Number of Furances
25       21      12
The diagrams, Figs. 138,139,140 and 141 show, respectively, the
approximate depth of bath in feet; the length of the hearth in
feet; the width of the
hearth in feet and the
area of the hearth in
square feet. Two lines
have been plotted on
these diagrams, show-
ing the dimensions of
the furnaces given in
Table 4, which was
abstracted from Profes-
sor Groume-Grjimailo's
paper, in the Journal de
la Societe Russe de
Metallurgie. This table
was given in The Iron
Age of Dec. 26, 1917.
100 —s
Fig. 142 shows the
profile of one side of
the hearth suggested
in this paper for a 30-
30      40     50      GO      70      80     90
Capacity of Furnace iu Tons
10      20
ton     furnace.      These
fig. 141.—Graphical Comparison of the Hearth
Area of Various Open-hearth Furnaces.
furnace hearths show a
certain   consistency  in
their   design,   a  larger
hearth and a shallower bath being suggested for the ore process
than for the scrap process.
One feature of the open-hearth and similar furnaces that has
caused sorrow, and tribulation is that the bottom of the furnace
forms a valley below the level of the port sills. One of the basic
principles of furnace design is that the flame must lick the hearth
or bottom of the furnace. The gas pressure in the heating chamber
must be equal to the atmospheric pressure. This last means that
a nice balance must be maintained between the volume of gas and
air entering the chamber and the gases removed from the chamber.
When the pressure in the furnace is permitted to drop below the
atmospheric pressure cold air will tend to flow into the furnace
around the doors and through all cracks and openings. This
chills the bath and causes excessive oxidization to occur.

202

APPENDIX VII

I

It is well known that when patching bottom it is necessary
to keep the doors closed as much as possible in order to avoid
chills, which are likely to develop into cracks and leaks in the
bottom. Many beautiful octahedral steel crystals have been
discovered in tearing out old furnace bottoms.
3600 (11.8 ft.)
When the pressure in the furnace gets higher than the atmos-
phere a sharp sting of
flame is developed and
fuel must be burned
to maintain it. Some
m e 11 e r s and many
heaters keep the doors
of their furnaces deco-
rated with a halo of
flame. In some cases
it is necessary to main-
tain this sting owing to
the defective design of
3200 (10.50 ft.)	I	, 1	/.	rni
Scrap Process
/^///////////^
fig. 142.—Sections Showing Profile of Hearth
Slope According to Professor Groume-
Grjimailo.
the furnace. There is
no question whatever
that this method of
working will prevent
cold air being drawn
into the furnace. It is
te easiest way "; the
company pays for the
excess fuel, and the
melter or heater has plenty of time to sit down and "watch
'er burn." In foreign plants the technical control of the furnaces
is more closely maintained than in this country because fuel is
expensive.
In order to sinter the bottom of the furnace in place it is
necessary to direct the jet of flame so that it will lick the hearth.
In order to do this the air and gas ports must be given a suitable
inclination toward the hearth and the velocity of the flame must
be sufficient to carry it down to the bottom. The velocity which
will be impressed upon the jet of air entering the furnace will be
fixed by the height from the bottom of the regenerators to the port
and by the area of the port and the flues leading to it. In the case
of the gas a slightly greater head is available as it enters the

DESIGN OF OPEN-HEARTH FURNACES

203

regenerator under pressure from the producer. The gas pressure
can be and usually is increased toward the end of a campaign when
the regenerators are partially blocked.
The inclination of the ports is fixed when the heads are built.
It frequently happens that these heads are changed several times
before they work in a satisfactory manner. In fact, a number of
furnace drawings which have been published show heads which
must have been altered considerably in order to make the bottom.
In the open-hearth furnace the ports are just below the roof,

f

						°8 						
						°6 						
	G 	xsP( 	rts 			o^ 		Lit I 	orta 			
						«*> 						
						*>o 						
					£ 	18 				• 	
					S 	16 				I 	
					2 	14 						
					< 							
						10 						
	» 					o 		• 				
						Q 			• 			
							• 					
		» 	• 									
				a 								
60    50    40    30    20     10	10    20     30    40    50    60
Sumaco Capacity, Teas
fig. 143.—Graphical Comparison of the Port Areas of Various Open-hearth
Furnaces.
and the hearth forms a pocket below the level of the port and door
sills and above the level of the tapping hole. This pocket will
become filled with the coolest gases in the heating chamber. In
order to sweep these gases out of the pocket and permit the
sintering of the bottom of the furnace in place it is necessary to
utilize the jet of flame issuing from the ports. This jet must
describe a parabola having a middle ordinate equal to the vertical
distance from the tapping hole to the port sills. In the earliest
types of open-hearth furnace it was endeavored to attain this

204

APPENDIX VII

result by depressing the roof of the furnace. The serious objec-
tions to this poor construction arose from its tending to strangle
the furnace during the heat and from the extremely short life of
the roof. Later experience showed that the flame might be jetted
into this pocket by the direction of the ports and the velocity of
the gas and air. In European furnaces these velocities range
between 12 and 18 m (40 to 60 ft) per second, while in American
furnaces the velocity is as high as 50 m per second.
TABLE 5
open-hearth furnaces

Reference
Number,
Ton 	Square Feet,
Port Areas 	Reference
Number,
Ton 	Square Feet,
Port Areas 	

	Gas 	Air 	
	Gas 	Air 	
10-01-A 	2.43 	10.12 	50-04-A 	10.50 	18.0 	
			50-05-A 	7.66 	19.2 	
15-03-B 	1.07 	4.68 	50-07-A 	5.75 	13.8 	
			50-09-A 	7.50 	13.7 	
20-03-A 	2.80 	3.50 	50-10-A 	6.60 	13.1 	
			50-11-A 	4.92 	14.53 	
25-04-A 	3.25 	9.00 	50-12-A 	11.59 	17.72 	
			50-13-A 	12.50 	18.0 	
30-04-A 	4.75 	13.75 	50-14-A 	6.80 	15.38 	
30-05-A 	3.70 	14.60 	50-15-A 	9.85 	16.14 	
			50-16-A 	5.62 	17.80 	
35-01-A 	,    3.4 	6.40 	50-16a-A 	7.00 	20.00 	
35-Ola-A 	3.75 	5.98 	50-17-A 	10.50 	12.33 	
			50-18-A 	8.00 	16.42 	
40-05-A 	15.70 	21.00 	50-19-A 	7.40 	13.30 	
40-06-A 	3.5 	7.00 		< 		
40-04-A 	8.00 	14.25 	60-05-A 	6.75 	29.31 	
			60-06-A 	8.00 	25.74 	
			60-13-A 	7.74 	25.37 	
A number of different arrangements of the ports of the Siemens
furnace have been devised and used with more or less success.
The early Siemens furnaces were designed for the use of producer
gas, which required preheating. Later these furnaces were used
with various manufactured and natural gases and fuel oils, while

DESIGN OF OPEN-HEARTH FURNACES	205
latterly pulverized coal has been employed.    These various fuels
require furnace modifications, mainly in tl\e ports and heads, as
k	only the air supply is preheated.
Pulverized coal is only suited for use in furnaces where the ash
carried into the furnace with the fuel will not be objectionable.
One trouble with early open-hearth or Siemens furnaces was
caused by the dirt carried over into the regenerators. This was
particularly the case when the chambers were located immediately
!	below the furnace and the uptakes rose directly from the chamber
arch.    In later designs the chambers were placed below the charg-
ing platform and the uptakes were carried up from a  cinder
!	pocket or slag chamber.    This reduced, but did not eliminate, the
cinder trouble.
*	The carrying power of a flowing stream varies as the sixth
1	power of its velocity;  that is, when the velocity is doubled, the
j	mass of the particle which the stream can carry increases sixty-
I	four times.    The inertia of these larger particles tends to carry
I	them into any eddies where the stream changes direction, but the
]	finer particles will be carried farther.    The ports must be inclined
and the velocity of the flame must be sufficient to allow the bottom
to be made.    This also tends to direct the flame on the surface
of the bath and the higher the impinging velocity the greater the
tendency to pick up cinder, etc., which will be thrown up during
Sf	the boil.
Possibly--the best illustration of the action of the jet of flame
impinging upon the top of the bath may be obtained by observing
the action of a stream of water from ai nozzle impinging upon a
flat plate'.; When the stream is directed at right angles to the
plate there will be !a circular flare or - film of water traveling out-
ward at a high velocity and a short distance out a tumultuous
ring of eddying w^ter eight or teii times as thick as the film it
surrounds. The distance out to this ring will depend upon the
velocity of the stream. When:the jet strikes the plate at an
4*	angle it .will form a triangular high-velocity film breaking up
into a -turbulent eddy at the base or side furthest from the apex
where-the   siiream strikes  the  plate.    The  distance  from the
stream to the eddy will be affected by two factors, the velocity
X	of the stream and its angle of incidence.    If a water surface is
substituted for the flat plate the action is complicated by the
fact that-the jet displaces a certain amount of the surface water

206

APPENDIX VII

fig. 144.—Arrangement of Ports of a 25-Ton Open-hearth Furnace at
Lyswa, Russia.

. sy77/f///////fsss..

fig. 145.—Arrangement of Ports of a 50-Ton Furnace at Homestead. This
furnace was fired with natural gas but was arranged for producer gas
firing.

DESIGN  OP OPEN-HEARTH FURNACES

207

and the size of the turbulent eddy is considerably increased. If a
second stream of water be directed so that it impinges upon the
first stream just before the first stream impinges on the plafce the
condition of the formation of the flames in the furnace will be
approximated. The main difference between the action of the
two streams of water and that of the streams of air and gas forming
the flame will result from the fact that as the reaction of combus-
tion takes place there is a great increase of temperature which

1
1 	 	^ 	 *s 	'i. 	
"1 		 r_ 	 	 	
1
1
1
1
1
1 		 	1
1 Gas
1    1
L_i 	
Air 	I 	
m
SECTION THROUGH AIR PORTS

'&**
fig. 146. — Arrangement of Ports on Many American Furnaces.
velocity and high gas velocity.

Low air

makes the volume of the flame approximately double that of the
reacting gases.
A study of the effect of the velocities of the two streams upon
their mixing will reveal many interesting facts, particularly if the
streams are colored so as to supply a contrast while they remain
distinct and a third color by their complete mixture. The degree
of the mixing at various points will be revealed by the various
tints formed as one or the other color predominates.
The function of the ports is to bring the combustible and the

208

APPENDIX VII

fig. 147.—Dropped Roof of Early Furnace Design.

fig.. 148,—Heating Chamber with Raised Roof.

fig. 149.—Heating Chamber with Baised Straight Hoof.
cornburent to a point where they will combine in the flame.
In the early types of Siemens furnaces there were usually five
ports side by side, two for gas and three for air. Figs. 144, 145
and 146 show later designs of ports which were used respectively

fig. 150.-—Heating Chamber with Straight Hoof.
with the heating chambers shown in Figs. 148, 149 and 150.
Figs. 144 and 148 were used at the Lyswa Works (Qural), Russia,
while Figs. 145, 149, 146 and 150 were used in American fur-
naces, the last being the later design. A noticeable feature of
the Russian furnace is that .the bath occupies about 0.60 of the

DESIGN  OF  OPEN-HEARTH  FURNACES	209
length of the heating. chamber. This gives a space at each end
of the heating chamber for the formation of the flame. The
;	velocities of the gas and air entering the heating chamber are
approximately the same. The air ports are located on each side
of the gas port. This furnace works hot and has a good output.
The ports shown in Fig. 145 were designed for use with natural
gas, which was jetted into the port at right angles with the stream
of preheated air and close to the bottom of the port. These ports
]	were also intended to permit the use of producer gas in case of the
j	failure of the natural gas supply, there being two regenerator
chambers at each end of the furnace.    With natural gas both
\	chambers were used for air.    With producer gas the uptakes
nearest the heating chamber were for gas and those further back
were for air. With this design of port the stream of gas impinges
upon the stream counter to the air current. This would tend to
form a mixing eddy at point of junction.
The port arrangement shown in Fig. 146 is that used in many
American furnaces. In this design the air velocity is com-
paratively low, while the gas velocity is from four to ten times the
air velocity. One of the reasons that has been advanced for this
port arrangement is that it forms a blanket of air between the
:;	flame and the roof, reduces the wear on the roof and protects the
!;	bath from the oxidizing effect of the air.    This design of port
&	gives an extremely long flame.    The flame is forced away from the
port and the ends of the heating chamber work alternately hot
and cold.    The introduction of this design of port resulted in an
increase in the length of the heating chamber in order to prevent
the flame passing beyond the heating chamber.    Then the gas
velocity was increased to force the flame to the end of the chamber.
Fig. 143 is a diagram in which have been plotted the areas of
the gas and air ports as tabulated in Table 5.    The wide difference
in the ideas of port areas is well illustrated.
With oil, pulverized coal, coke-oven and natural gas, the fuel
/	is piped to the furnace and used without preheating.    The fuel is
introduced at the end bulkhead or through the sides of the heads.
Blue water gas has been used in some foreign furnaces. As this
gas contains practically no hydrocarbons it may be preheated.
A few attempts have been made to utilize blast-furnace gas in the
open-hearth. It may be clone by preheating to a higher tem-
perature than is usual with the ordinary mixed producer gas.

210

APPENDIX VII

Regardless of whether the fuel is used cold or preheated it must bo
brought into contact with the preheated air so that the flame
formed will permit the sintering of the bottom, and the heads of
the furnace must be designed to obtain this result.
One of the reasons why blue water gas and blast-furnace gas
have not been considered on their heating possibilities is that they
burn with a non-luminous flame, it being considered that to obtain
high temperatures in the open-hearth and reverberatory furnace a
flame with a so-called high radiating effect is necessary. By this
is meant a luminous flame. Ifc is well known that the transmission
of heat by radiation varies as the difference between the fourth
powers of the temperatures of the radiating and recipient surfaces
and a coefficient varying from unity for the ideal black body to a
very small fraction of unity for a polished surface. Conduction
varies with the temperature difference. Convection depends
upon the temperature head or difference in temperature and the
flow of the fluid.
In the early designs of Siemens furnaces the roof was depressed
from each end to the center, as shown in Fig. 147. It was sup-
posed that this type of roof enhanced the heating effect by forcing
the flame into contact with the bath and assisted in the sintering
of the bottom. This type of roof had a short life, as it had a
tendency to burn out, and it was frequently damaged when
charging the furnace. Its worst defect was that it choked the
furnace. Later designers were obsessed by the radiant-heat idea
and this resulted in the forms of roof shown in Figs. 148 and 149.
Cooling Rib.
-S«t after Eoof
is Completed
It was soon found, however, that this
type of roof resulted in an increased
fuel consumption, and the straight
roof (Fig. 150) is now used. Fig. 151
shows a form of skewback designed to
prevent the wall expansion from in-
terfering with the roof. Twelve-inch
roofs are widely used and many
American furnaces employ the Orth
fig. I51.-Skewback Construe- roof which permits the use of a repair
fannto?irdedatt°opPernlltblock Whe* the intermediate shapes
burn out.   It is possible that a roof
with cooling ribs spaced closer together than in the Orth roof
would be more satisfactory.

DESIGN OF OPEN-HEARTH FURNACES	211
It is a basic principle of furnace design that satisfactory results
cannot be obtained unless the flame licks the sole of the furnace.
It is likewise well known that bottom cannot be made in an open-
hearth furnace unless the flame can drop down far enough to
sinter the bottom in place, no matter how luminous the flame may
be. One of the hottest flames is that of the oxy-acetylene torch.
Acetylene burned in air gives a very luminous flame, but when this
flame is supplied with oxygen it becomes a blue non-luminous
flame. The luminous acetylene flame does not emit an excessive
amount of radiant heat to any recipient surface. It is rather
noticeable that when the oxy-acetylene torch is used in welding
it is necessary for the flame to impinge upon the work, and that
the work has a tendency to become luminous, while the flame
itself has a very slight luminosity, and that at the tip only. The
mixed producer gas which is used in numerous Siemens furnaces
derives its heating value mainly from carbon monoxide and
hydrogen. These two combustibles are the main constituents of
blue water gas. In fact, blue water gas bears a fairly close resem-
blance to a good mixed producer gas from which the nitrogen has
been removed.
Radiant heat from a luminous flame may also be considered
from another viewpoint. The roof, side walls and bath are at a
high temperature and emit a certain amount of light, depending
upon their temperature and emissivity. The flame is sufficiently
transparent, when the furnace is at a high temperature, to permit
the opposite wall and the slag surface to be seen. The red and
yellow portion of the flame, which emits the most visible light, is
not transparent and is at a lower temperature than the blue
transparent portion. A smoky flame is caused by the presence
of soot or unignited carbon. Soot may be caused by the disso-
ciation of carbon monoxide when this gas is chilled by impinging
upon cold metal.
Stratification is frequently observed in the flame. Cool gases
tend to collect below hotter gases. The hottest gases tend to
rise to the roof where they are cooled. The coldest gases would
have a tendency to collect on the surface of the bath, but the
jet of flame from the ports tends to sweep them away. Convec-
tion currents are rarely appreciated at their true value. A
temperature difference of 1° C. is sufficient to impress a velocity
of 0.268 m (0.88 ft) per second and this velocity will increase as

212

APPENDIX VII
the square root of the difference in temperature. This tends to
give an angular direction to currents.
The open-hearth furnace works very close to the yield point
of the refractories, but it is only recently that water-cooling has
been adopted for these furnaces, although it has been used for
years in the blast furnace. Water-cooling adds to the life of the
brickwork by increasing the thermal gradient through the wall
and removing the heat. It adds little if anything to the fuel
consumption and increases the life of certain portions of the
furnace, thereby reducing the amount of time the furnace is down
for local repairs. This means increasing the output. Water-
cooled doors and frames were used a number of years ago, but the
extended use of cooling devices is rather recent.
In early designs of furnaces the regenerator chambers were
under the furnace and the uptakes rose direct to the ports. As a
result the upper portion of the checkerwork blocked up rapidly
and its life was reduced. The first -cinder pockets were small
chambers parallel with the regenerator chamber designed to
distribute the gases to the checkerwork by a number of small
ports and their functioning as cinder pockets was accidental.
The way the cinder lodged in them showed the advantage of
increasing their size, and ample space for this purpose became
available when the checkerwork was removed from below the
furnace and placed under the charging platform. The main fault
with many of these pockets is their lack of depth. Removable
cinder pockets have been devised.
Regenerative methods of firing or the preheating of the incom-
ing gases and the air-for combustion have made it possible to
attain high furnace temperatures. The numerous furnaces
utilizing the heat of the products of combustion for the preheating
of the gas and air supply are a grand memorial to the Siemens
brothers.
In the designing of any furnace with regenerators it is important
to have sufficient regenerator capacity and equally important to
avoid overdoing the matter. The products of combustion leave
the heating chamber of open-hearth furnaces at a temperature of
about 1700°. The incoming air enters the valve at 10° &nd the
temperature of the producer gas in the main will range from 500°
to 600°. Coke oven gas, natural gas or any gaseous fuel con-
taining hydrocarbons cannot be passed through a regenerator

I
11 f

DESIGN  OF OPEN-HEARTH FURNACES

213

without a considerable loss in its heating power due to the dis-
sociation of the hydrocarbons. Furnaces fired with these gases,
as well as those fired with oils or tars, are designed to preheat the
air supply only, but it is usually desirable to design the regenera-
tors for these furnaces in such a manner that producer gas may be
substituted without extensive and costly alterations.
VOLUME OF CHECKER BRICK
There seems to be a considerable diversity of opinion regarding
the amount of checker brick which should be used. Table 6
gives the data covering the volume of the checker brick in a
number of furnaces. These data have been plotted in Fig. 152

JLW
130
120
110
100
jao
3
70
60
50
40
3C 					, 						

								0 			

								e 			

											

		9 						* 			

			9 								

				D 							

				. : 			9 				

	0       10       20      30      40       50      GO      70       80      90      10
Tons 	
fig. 152.—Graphical Comparison of the Volume of Air Plus Gas Checker
Brickwork in Cubic Feet per Ton of Nominal Capacity for Furnaces of
Various Capacities.
which compares the total amount of the air and gas checkerwork
per ton of nominal capacity. Table 7 gives the maximum and
the minimum volumes of checkerwork.
In all data of this kind there are two uncertain factors. The
nominal and the actual capacity of an open-hearth furnace are
different. It happens quite frequently that the actual capacity

214

APPENDIX VII

is 10 to 40 per cent in excess of the nominal capacity. When
crane and ladle capacity is available this excess can be turned
into output; otherwise it may be troublesome. The other uncer-
tain factor is in the checker brickwork itself, the way it is set
and its material, the space allowed for the passage of gas and air
and thickness of the brick.
A number of more or less empirical rules have been proposed
for arriving at the volume of checker or regenerator capacity.
A. Consett makes the total regenerator volume 2 cu m per tonne
(70 cu ft), and makes the air chamber 10 per cent larger than the
gas chamber, for furnaces designed to make four melts per twenty-
four hours. In Notes et Formules it is stated that " for slow
furnaces the empirical relation between the volume of the regen-
erator and the charge of the furnace in tonnes is 0.8 cu m (28 cu ft)
to 1.3 cu m (46 cu ft) per tonne; and for fast working furnaces
from 53 to 64 cu ft per tonne." H. H. Campbell says from 50
to 100 cu ft per tonne of melting capacity. Gruner says 50 to
70 kg of checker brick per kilogram of coal burned per reversal.
Told suggests 6 cu m or 2850 kg of checker brick per cubic meter
of air pe?r second per 100° C. rise in temperature. Another sug-
gestion is the provision of 50 sq m (537.5 sq ft, of checker surface
per tonne (metric) of coal per twenty-four hours.
In Euchene's investigations on the carbonizing of coal he
developed a formula for the heat-storage capacity of checker
brickwork which may be stated as follows:
Qo' = 0.20H-0.000062*2,
in which Qo* = kilogram calories per kilogram of checker brick
between zero and t degrees C.; and in which t = temperature to
which the brickwork is raised, degrees C.
Breslauer cites the regenerator data of a number of furnaces,
giving the number of cubic meters of regenerator per ton of steel
per hour.
His figures are given for a number of different plants as follows:
cubic meters of regenerator per ton of steel per hour

Dowailis	  14.60
Krupp, large.. ..  18.32
Krupp, 3 ton.... 36.00

Graz		15.50
Landore		20.00
Terre Noire		30.00
Borsigwerke....	44.00

Haleside		16.75
Pateg		20.60
Swedish		36.60
Steelton, Pa		37.45

DESIGN OF OPEN-HEARTH FURNACES	215
The wide variety of rules for the proportioning of the regen-
erators affords an ample opportunity for choice, and in part
explains the variation in volume of checkerwork used by different
designers. Empirical rules, basing the proportioning of a part
by a direct ratio with the capacity of the furnace are very easy
to apply, and require very little thought in their use. In addition
they save time, as it only takes a few minutes to arrive at the
regenerator volume required. Unfortunately, this is not the case
when logical methods are employed.
HORIZONTAL  OR VERTICAL PASSAGES
Regenerators may be built with the gas passages arranged
horizontally or vertically. Where head room is limited a hori-
zontal pass regenerator, at first sight, appears to possess certain
advantages, but a consideration of the behavior of heated gases
when cooling and of cold gases when being heated, will show that a
horizontal regenerator or recuperator introduces a considerable
amount of friction in the path of the gases, necessitating an initial
pressure for introducing the air and gas and a strong suction to
remove the waste gases.
At Steelton, Pa., it was found necessary to use a blower
with horizontal regenerators. The writer recently had occasion
to investigate the action of some horizontal regenerators. It was
found that the products of combustion were flowing mainly through
the upper passes and their heat was conveyed to the lower passes
by conduction through the brickwork. The air supply flowed
through the entire height of the checker. The Motional resistance
was excessive. These regenerators, however, contained an
enormous weight of brick for the amount of work to be done by
them, and for that reason gave very little difficulty in operation.
A basic principle of regenerator design is: the gas passages
should be vertical; the cooling gas should pass downward through
the checkerwork; the gas being heated should pass upward through
the checkerwork. When the gases circulate in this manner they
have a tendency to subdivide themselves between the different
passes proportionally to the local heating and cooling of the brick-
work, with the result that the cooling and heating of the gases will
be practically uniform. A few years ago A. E. Maccoun made a
series of temperature observations on a Cowper hot-blast stove at

'• \   \

I   I,

216

APPENDIX VII
TABLE
volume   of   checker   brick

Reference
Number,
Tons 	Gas Checkers 	

	Length,
Ft 	Width,
Ft 	Area,
SqFt 	Volume,
CuFt 	Volume,
CuFt
per Ton 	Height,
Ft 	
10-01-A
15-03-B
20-03-A
20-04-A
25-03-A
25-04-A
25-05-A
30-05-A
30-04-A
35-01-A
35-02-A
40-03-F
40-07-E
50-04-A*
50-17-A
50-20-A
50-16-Af
50-21-F
50-07-A
50-22-A
50-23-A
5CM)9-A
50-10-A
50-11-A
50-13-A
50-16-Af
50-04-A*
50-05-A
50-18-A
50-19-A
60-11-A
60-13-A
60-03-A
60-04-A
60-05-A
60-06-A
60-07-A
60-08-B
60-14-E
75-03-A
75-O2-A
75-01-A
80-01-E
100-03-E 				297
504
517
240
689
732 	29.7
33.6
25.8
21.0
27.6
29.3 		

	

	

	7.00
18.00 	4.00
4.50 	28.0
81.0 	

	

	

	
	8.5 	

	

		

			532
703
665
656
734
840
1040
930
1400
1740
1070
2590
2088
2093
3300
896
1936
1235
1912
1188
1928
1980
2156
2510
2027
1953
1616
2417
2515
2780
2630
1260
2515
3278
3334
1680
2100 	17.7
23.4
19.0
18.7
18.4
21.0
20.8
18.6
28.0
34.8
21.4
51.8
41.8
41.8
66.0
17.9
38.7
24.7
38.2
23.7
38.6
39.6
43.1
42.0
33.8
32.5
26.9
40.3
41.9
46.3
43.8
21.0
33.5
43.7
44.5
21.0
21.0 		

	
	ioioo
8,50
9. 26
15.00
7.83 	

	12.00
12.17
15.00
8.00
22.00 	5.58
6.33
5.29
7.00
6.00 	66.5
77.0
79.0
56.0
132.0 	

	

	25.50
22.00
12.25
18.25
18.00
17.00 	5.50
7.92
9.50
10.17
8.17
10.08 	140.0
174.0
116.0
185.0
144.0
172.0 	
	
	10.00
10.00
9.25
14.00
14.50
12.17 	

	

		

	

				

				

	

	

				

		

	

				
	
	16!i7 	

	31.25 	7.92 	247.0 	

	

	

				

	

	

				
	
	is! 83
13.83
15.00 	

	24.00
23.00
12.00 	8.4
8.4
7.0 	202.0
193.0
84.0 	

	

	16.00 	9.33 	149.0 	
	
	22.00 	

	12.50
14.00 	9.00
10.00 	112.0
140.0 	
	
	15.00
15.00 	
: Original and rebuilt.

DESIGN OF OPEN-HEARTH FURNACES

217

ASCERTAINED   FROM   PRACTICE
Air Checkers

Length,
Ft 	Width,
Ft 	Area,
SqFt 	Volume,
CuFt 	Volume,
CuFt
per Ton 	Height,
Ft 	Air-fUas,
Cu Ft per
Ton 	
			391 	39 1 		68 8 	
			616 	41 0 		74 6 	
			780 	39.0 		64 8 	
7.00
18.00 	4.50
6.00 	31.5
108.0 	472
818
1020 	23.6
32.7
40.8 	15.00
8.50 	44.6
60.3
70 1 	
			3000 	120 0 		120 0 	
			708 	23 6 		41 3 	
			937 	31.2 		54 6 	
12.00
12.17
15.00
8.00
22.00 	7.58
8.33
7.00
7.83
10.00 	90.5
101.5
105.0
63.0
220.0 	905
860
970
944
1735
1590 	25.9
24.6
24.3
23.6
34.7
31.8 	10.00
8.50
9.25
15.00
7.83 	44.9
43.3
42.7
44.6
55.5
50.4 	
25.50
22.00
12.25
18.25
18.00
17.00 	8.00
10.83
9.50
12.00
12.17
12.08 	204.0
238.0
116.0
218.0
218.0
203.0 	2040
2380
1070
3130
3160
2470
3300 	40.8
47.6
31.4
62.6
63.2
49.4
66.0 	10.00
10.00
9.25
14.00
14.50
12.17 	68.8
82.4
62.8
114.4
105.0
91.2
132.0 	
			1681 	33.6 		51.5 	
			2904 	58.1 		96.8 	
			1900 	38.0 		62.7 	
			2621 	52.4 		90.6 	
			1980 	39.6 		62.3 	
			2310 	46.2 		84.8 	
			2693 	53.8 		93.4 	
			3310 	66.2 		109.3 	
31.25 	10.83 	340.0 	3460
5662 	57.7
94.4 	10.17 	99.7
128.2 	
			2393 	39.8 		72.3 	
			2835 	47 2 		74.1 	
	..... 		4198 	70.0 		110.3 	
			3443 	57.4 		99.3 	
24.00
23.00
12.00 	12.60
12.60
7.83 	302.0
290.0
94.5 	4160
4000
1416
3442 	69.4
66.7
23.6
44.5 	13.83
13.83
15.00 	115.7
110.5
46.6
78.0 	
16.00 	12.50 	200.0 	4400
5265 	58.7
70.2 	22.00 	102.4
114.7 	
12.60
14.00 	10.00
11.25 	126.0
157.5 	1888
2360 	24.8
23.6 	15.00
15.00 	45.8
44.6 	
f Original and rebuilt.

218

APPENDIX VII

P \

the Edgar Thomson Works (American Iron & Steel Institute meet-
ing, May 28, 1915), which showed that the checker openings
close to the shell took more gas when heating and less air on
blast.
In his work, Fours d Flamme, Professor Groume-Grjimailo
gives a mathematical demonstration of the reason why the portion
of the checkerwork close to the wall, losing a considerable amount
of heat by radiation, exerts a greater cooling effect on the hot
gases of combustion flowing downward and tends to concentrate
their flow through this portion of the checker, while the air, which
is being heated, tends to seek the central and for that reason more
slowly cooled portion of the checkerwork. It is interesting to
note that Professor Groume-Grjimailo cites the Cowper stove, as
follows: " For example, the checker openings of the Cowper
hot-blast stove located nearest to the shell lose a great deal of
heat by radiation; they therefore exercise a stronger cooling
effect upon the current of gas flowing through them and by reason
of this the velocity of the descending current of gas is increased,
since if fe<^i then V2>vi."
Convection currents in gases and air, due to small temperature
differences, are by no means inconsiderable. A temperature dif-
ference of 1° C. is sufficient to impress a vertical velocity of
0.268 m (0.88 ft) per second on a gas. This velocity will be
increased directly as the square root of the difference in tempera-
ture. Convection currents will act to carry the cooled gas or the
heated gas or air away from the heating or cooling surface. These
currents will exist in any chamber, regardless of whether a current
of gas is circulating through the chamber or not. When a hot gas
is giving up its heat to a surface the convection currents will be
downward, while when a cool gas is absorbing heat from a surface
the convection currents will be upward. It naturally follows that
the working current or circulation of the air or gases should be in
the same direction as the convection currents, as in this case they
wi]l tend to reduce the friction loss. When the convection cur-
rents are in the opposite direction to the working current they form
recirculating loops which entail a direct loss of heat capacity in the
checkerwork.

DESIGN OF OPEN-HEALTH FURNACES	219
PERIOD  BETWEEN" IOEVERSALS
The period between reversals has a direct bearing upon the
design of the checker in two important particulars: the heating
and cooling time determines the weight of checker brick required
and the thickness of the brick composing it. There is a limit to
the quantity of heat which may be absorbed and given out by the
brickwork. The practical limit is reached when the entire mass of
brickwork is raised to a temperature at which heating gases pass
through the checker with a "very slight or no drop in temperature.
The economical limit is reached when fche heating gases leave the
checkerwork at such, a temperature that during the period when
the checker is giving up heat the brickwork temperature does not
drop below the initial temperature of the incoming gases plus the
temperature differential necessary for heat transfer.
The most important variable, the period between reversals, is
beyond the control of the designer. The furnaces are operated
by two or three shifts of men. Each shift usually has certain
definite portions of the furnace to keep in repair and will so operate
the furnace, when it is possible so to do, in a manner to favor their
section and throw the burden of repair work upon the other shifts.
This leads to irregular working. Sidney Cornell (Chemical and
Metallurgical Engineering, May, 1913) cites the case of a 60-ton
furnace. There were 509 reversals in a week. The average time
period between reversals was 10 minutes. The longest period
was 70 minutes, the shortest 2 minutes. Consecutive periods
differed widely in their duration. The following time periods in
minutes were scaled from a diagram he presented:
R 15 R 25 R 20 R 15 R 16 R 23 R 24 R 24 R 34 R 22 R53
R 12 R 9.
(R stands for reversal.)
Quick reversals are necessary at certain stages of the operation,
but it is certainly desirable that the work should be divided, as
nearly equally as possible, between the two ends of the furnace.
When the time factor depends entirely upon the human element
it is absolutely impossible to avoid considerable irregularity in
operation. At the same time melt variations will prevent auto-
matically timed reversals, except during certain stages of the heat.
However, reversing machines are available which will operate
the valves in a predetermined sequence and time the reversals

220

APPENDIX VII

regularly. These reversing machines also permit the operator to
reverse the furnace at any time he sees fit. Machines of this type
have been installed at a number of by-product coke-oven plants,
but there seems to be a tendency upon the part of the " heaters "
to cut out the automatic timing device. It is hardly necessary
to state that a certain amount of passive or impassive opposition
might be expected to the use of a machine of this kind, a species of
sabotage which is extremely difficult to overcome. Under
ordinary working conditions there should be two to eight reversals
per hour, and it is necessary to proportion the checkerwork to
suit the longest time period.
TABLE 7
maximum and minimum volume of checker brick ascertained prom
practice

Capac- 	Gas 	Air 	Air+Gas 	
ity, 				
Tons 				. 			
	Minimum 	Maxiniuni 	Minimum 	Maximum 	Minimum. 	Maximum 	
10 	29.7 		39.1 		68.8 		
15 	33.6 		41.0 		74.6 		
20 	21.0 	25.8 	23.6 	39.0 	44.6 	64.8 	
25 	27.6 	29.3 	32.7 	40.8 	60 .,3 	70.1 	
30 	17.7 	23.4 	23.6 	31.2 	41.3 	54.6 	
35 	18.7 	19.0 	24.6 	25.9 	43.3 	44.9 	
40 	18.4 	21.0 	23.6 	24.3 	42.7 	44.6 	
50 	17.9 	66.0 	31.4 	66.0 	50.4 	132.0 	
60 	21.0 	46.3 	23.6 	94.4 	44.6 	128.2 	
75 	33.5 	44.5 	44.5 	70.2 	78.0 	114.7 	
80 	21.0 		24.8 		45.8 		
100 	21.0 		23.6 		 	44.6 		
The time factor has a definite bearing on the thickness of the
checker brick. This is shown by the curves of Fig. 153. These
curves were plotted for a fire-clay brick. For a silica brick or
brick of other material the co-ordinates would be different, but
the curves would be similar to those shown. These curves show
the rise in temperature at the center line of a brick in per cent
of the rise in temperature at the surface, when both faces of the
brick are heated during various time intervals. In these curves

DESIGN OF OPEN-HEARTH FURNACES	221
the ordinates are given per cent values to permit their application
to any initial temperature. These curves are computed by a
formula developed from Fourier's conduction equation. They
show that the rate of temperature rise at the center of the brick
will vary according to the square of the thickness of the brick.
These curves apply equally to the cooling period. A curve
showing the complete heating and cooling cycle will resemble the
hysteresis loop, which shows the heating effect of cyclic magnetic
changes upon an iron core.
The firebrick makers in this country list a special checker
brick, 10.5X4.5X4.5 in (265X115X115 mm), and a checker
brick 2.9X2.75X2.75 in (107X70X70 mm), and some designers
use 9-in straights, which give a 2.5-in (63-mm) wall. With a
30-minute period between reversals, the temperature change on
the central plane of these bricks may be approximated as follows:
Assuming that the initial temperature throughout the bricks
is practically uniform, and the surface is heated through any
temperature range for a period of 30 minutes. At the end of this
period the temperature of the central plane will have increased
to 59 per cent, 94 per cent and 96.5 per cent of the surface tempera-
ture, respectively, according to Fig. 153. So that the cooling
cycle starts with an initial drop in temperature on the central
plane of 41, 6 and 3.5 per cent, respectively.
Fig. 153 shows that the period of time required for these
drops will be, respectively, 21, 3 and 2 minutes. During this
period the portion of the brick between the center and the surface
will be transmitting heat both toward the center and the surface
of the brick.
In other words, the thinner the checker brick the higher its
heat-storage capacity as compared with the volume it occupies,
the greater the amount of heating surface for the given weight of
brickwork and the smaller the heat-storage capacity per unit of
surface. When the checker brick are too thin the heat gradient
from top to bottom of the checker becomes a curve instead of a
straight line. The brick, instead of working on the sloping portion
of the curve (Fig. 153) work over on to the flat upper portion of
the curve.
A great many of the formulas covering the heat transfer from
one substance to another contain a factor which covers the
velocity of flow of the gas or liquid which is absorbing or giving

222

APPENDIX VII

up heat to the stationary surface. For some reason or other
there seems to be an impression that the higher the velocity
of flow the better. Undoubtedly there is a certain velocity of
flow that will result in the maximum heat transfer per unit of
heating surface, and in the case of properly designed heat transfer
elements, be they regenerators, recuperators, steam boilers, etc.,
it is extremely probable that the natural convection currents will

10   20    30   40   50   60
Time., Minutes

70   80    90  100  110  120 130 140 150
Time, Minutes
fig. 153.
Density	p = l.8l
Specific heat, c=0.250
Conductivity in
cal/sec/cm2/! °cm =
0.00367
Diffusivity.. h* =0.00811
Rise in Temperature on
the Median Line of
Fireclay Brick in Per-
centage of Surface
Temperature. Both
faces exposed to heat.
Ordinates, percentages;
abscissae time in min-
utes.

assume this velocity themselves. Higher velocities, as well as
lower velocities, will reduce the rate of heat transfer. The
higher velocities may be obtained by forcing the gas or liquid past
the surface, when the velocity is too low, that is, when the heated
gases are not carried away from the chamber above the regenerator,
or the cooled gases cannot flow away from below the checkerwork,
recirculation will take place in the form of convection eddy
currents.

DESIGN  OF OPEN-HEARTH FURNACES

223

Concerning forced circulation, it is easy to conceive that a
current of hot gas may pass a finite surface at such a high velocity
that its temperature drop or loss of heat may be extremely small.
In this case the rate of heat transfer will be very low per unit of
surface. On the other hand, it may be conceived that the gas
passes the heating surface so slowly that it loses practically all
of its heat, and has a large drop in temperature. In both of these
cases an inordinate amount of heating surface will be necessary.
With the high velocity a very great length of surface will be
required. With the low velocity an extremely wide surface will
be required. Probably the best analogy to these conditions is
supplied by the electrical circuit. A series circuit may have such
a high resistance that its power transmission value will approx-
imate zero. A multiple circuit may have such a low resistance

				r\ 																											
* s\ 			r\ 	I 	y 	"**. 	*\ 		A 			f 	S 	\ 							n 	f 	s 		A 						
X'~ 	V 	/ 	\ 	j\ 			in< 	\l 	/ 	V; 		1 	/ 		\ 	\ 		i 	\\ 	j 	) 	t- 		J 	/ 	Cv 		a 			
		N^ 						u 		\ 	y 	! 		

	

										1 					
		V 												
11357       9     11     13579      11      1357
.M.              P.M.                                 A.M.                                P.M. 	
fig. 154.—Temperature Head or Differential between the Hot Gases in a
Fire Box and a Point 1 In. from the Surface of the Wall Exposed to
Heat.
that it forms a short circuit and its power transmission value will
approximate zero.
The heat differential or temperature head necessary for the
heat transfer is a factor concerning which there is considerable
disagreement. There is the film theory of high surface resistance
due to layers of gas adhering to the surface. Such data as are
available indicate that a temperature drop of 300° or more is
necessary for gas to gas heat transfer. The curves of Fig. 154
were copied from a pamphlet, " The Plow of Heat Through
Furnace Walls" (Bulletin No. 8, U. S. Bureau of Mines) by
Ray and Kreisinger. The full line shows the fluctuation in the
firebox temperature of the experimental furnace as indicated by a
thermo couple and the dotted line gives the temperatures of a
couple embedded in the brickwork 1 in from the surface exposed
to heat. It will be noticed that the brick temperatures lag behind

:H
h * 1

224

APPENDIX VII

the furnace temperatures and, due to the heat-storage capacity
of the brick, a smoother curve is obtained. The temperature
gradient between the two curves includes the resistance of 1 in

p
11

fig. 155.—Curves Showing the Temperature Changes in the Hot Gases
Cooling, the Cool Gases Heating and the Checker Brick.
These curves showing these temperature changes during the normal or ideal period or
cycle are indicated by the legends. The abnormal cycle or the changes due to overheating
and overcooling are marked with reference letters. The latter condition is the one that
occurs when a cold checker is heated in starting.
Ag    cooling curve of hot gases passing through a cold checker;
JBff    cooling curve of hot gases passing through a checker with too long a heating
period;
Off    cooling curve of hot gases passing through a checker after it has absorbed its
maximum amount of heat;
Aa    heating curve of cold gases passing through an overheated checker;
Ba,    heating curve of cold gases passing through a checker with too long a cooling
period;
Co,    cold gases passing through a cold checker;
Db    cold checker prior to heating;
Eb    checker initial heating curve.    The upper portion after becoming heated trans-1
mits heat to lower portion by conduction;
Fb    checker overheated in upper portion.    Heat is transmitted by conduction to
raise temperature of lower portion;
Hb    overheated checker prior to cooling.
of brick as well as any surface resistance which may exist, and
this difference rarely exceeds 150°. This would seem to indicate
that a heat differential of less than 300° might be obtainable under
good working conditions from gas to gas.

DESIGN  OF OPEN-HEARTH FURNACES

225

Blocking up of the checkerwork by dust deposits occurs
progressively, and a number of schemes have been tried for increas-
ing the time between clean-outs. This dust collects upon the
upper portion of the checkerwork and causes more trouble in the
air checker than it does in the gas, for the reason that the gas
usually enters the regenerators under pressure and this pressure
can be increased to overcome increased resistance. The air,
however, enters the checker under atmospheric pressure, and its
flow is induced by the chimney effect caused by the heat it absorbs
acting through a vertical height equal to the distance from the
bottom of the checkerwork to the port. It naturally follows that
increased resistance will have a considerable effect in reducing the
air supply, and it is frequently necessary to put a fan on the air
supply after 400 to 500 heats. Running the gas through the air
checkers has been the subject of a patent, the idea being based
upon the reducing action of the gas, but this deposit contains very
little iron ore when there are adequate cinder pockets. The
composition of this deposit at the Donetz-Jurjewka works was:
composition of deposit in checkers

	Gas 	Air 	
Additions and limestone, per cent 	 	26 0 	37 0 	
Furnace lining, per rent 	 	 	0 8 	1 5 	
Cinder per cent 	28 2 	16 0 	
Silicct brick per cent 	45 0 	45 5 	
			
Frank Orth has designed a checker in which the size of the
pass increases in four steps, being widest at the top and narrowest
at the bottom. While G. L. Danforth, Jr., arranges the top of the
checkerwork in a series of blocks surrounded by channels about
6 in wide and about 2 ft deep. Another arrangement, by Dan-
forth, provides a number of pits in the top of the checkerwork.
The number, perimeter and depth of the pits giving an entry area
eqxial to the entry area at the top of the checkerwork. In both
cases the purpose is to provide space for the deposit and at the
name time prevent it from blocking up the checkerwork. .The
dust deposit will in time attain a thickness of 1.0 to 2.0 in at
the top of the checker and its effect in increasing the resistance

226

APPENDIX VII

TABLE 8
temperatures, pressures, velocity, time data from various sources

	E. Juon at Donetz-Jurjewka
Works 	

	Pressures
in mm of
of Water 	Temperatures,
Average,
Degrees C 	
Gas in main ...                  	 	+ 15
+ 2 to +11
+5
+4
+7
+ 5 to +10
-1
TO
+3
TO
-3
- 2 to - 3
+ 1.5
-14 to -15
-14 to -15
-19
-18
-33 	600
650 to   750
700
1100 to 1300
1200
1250
1200 to 1300
550
400 to   700
1225
1100 to 1350
1300
1250 to 1400
1800
1700
1700
1600
1600
750
700
600 	
Gas in flues under regenerators 	 	

Average 	 	

Gas at top of regenerators 	

Gas at top of uptake 	 	

Air under regenerators 	

Air at top of regenerators 	 	

Air at top of uptake . 	

Hearth chamber, top and bottom 	 	

Waste gases top of uptake — Gas 	 	

—Air 	

Top of gas regenerator 	 	

Top of air regenerator 	 	

Below gas regenerator 	

Below air regenerator 	

At base of stack 	 	

	Temperatures According to 	

	Told 	Le
Chatelier 	Harbison
Walker 	
Gas in flues 	 	400
850
625
30
270
950
610
1600
300 	720
1200
1000 	720
1200
1000 	
Leaving regenerator 	 	

	
Average temperature in regenerator 	 	

	
Air at reversing valve 	 	

	
In flues leading to regenerator 	 	

	
Leaving regenerators 	 	

	
Average temperature in regenerator 	 	

	
Waste gases entering regenerators ... 	

	
After reversing valve 	 	

	

DESIGN  OF OPEN-HEARTH FURNACES
TABLE 8—-Continued

227

	From 	Told 	
	Velocity,
m per
Second 	Time
in
Seconds 	
Air and gas passing through the valves 	3 50 		
Entering regenerators 	 	3 00 		
Passing through regenerators, less than 	 	1 00 		
Air in regenerator chamber . 		5 00 	
Checkerwork ...         .   .           .       .... 		3 00 	
Gas in regenerator chamber 	 		4 00 	
Checkerwork 		3 00 	
Air and gas parsing through checkerwork, less than. .
Air and gas passing through chamber over checker. .
Air and gas issuing from the ports 	 	 	2.00
0.50
8.00 		
Gases in the hearth 		2 00 	
			
through the regenerator may be gaged by the following record of
the gas pressure below and above the checkerwork published by
E. Juon.
measure of resistance to flow through checkers

	Pressure in mm 		Pressure in mm 	
Heat Number 	of Water 	Heat Number 	of Water 	
	Below 	Above 		Below 	Above 	
156-159 	-1-6 	H-5 	600-602 	+ 18 	0 	
160-164 	4-5 	+5 	603-606 	+ 18 	+1 	
165-168 	+4 	+4 	607-610 	+17 	0 	
169-172 	+4 	-4-4 	611-613 	+16 	0 	
173-176 	+5 	-i-o 	614-617 	+ 17 	0 	
			618-621 	+16 	+1 	
The dust deposit is difficult to cope with, as much of it is
extremely fine. It is very difficult to reduce the velocity of the
gas current and throw this dust down in the limited space avail-
able, but a considerable amount of it will be deposited in a well-
designed cinder pocket.

il

228

APPENDIX VII

Taking up the design computations for a 50-tonne open-
hearth furnace regenerator, the following assumptions are made:
Melting capacity of furnace	    50 tons
Number of heats made per week	    15
Average time per heat, charge to tap	      8 hours 20 minutes
Coal consumption per ton of steel		300 kg (660 Ib)
.Average number of reversals per hour....:	      3
Secondary air supply, per cent of theoretical	      140
gases of combustion on burning 100 volumes of haw producer gas

	Vol.                Calories 	02 	C02 	H2O 	N2 	
H2 	11 26X 58 2= 655 	5 63 		11.26 	22.52 	
CH4
CO 	3.24X195.2= 632 .
29 65 X 68 2=2022 	6.48
14 83 	3.24
29 65 	6.48 	25.92
59.32 	
O2 	0 19 					
CO2 	1 25            . 		1.25 			
N2 	50 69      	 					
H2O 	3 72 			3 72 		
						
	100.00                 3309 	26.94
0.19 	34.14 	21.46 	158.45
0.76 	
		26.75 	34.14 	21.46 	157.69 	
combustion of 100 molecular volumes of gas

Air

Products of Combustion in Molecular Volumes

4 1
Jf

Supply,
Per 	Molec-
ular 	Excess
Air 	02 	C02 	H20 	Excess 	N2 	Total 	
Cent 	Volumes 					2 			
100 	133.75 	0.00 	0.00 	34.14 	21.46 	0.00 	157.69 	213.29 	
120 	160.50 	26.75 	5.35 	34.14 	21.46 	21.40 	179.09 	240.09 	
140 	187.25 	53.50 	10.70 	34.14 	21.46 	42.80 	200.49 	266.79 	
180 	240.75 	107.00 	21.40 	34.14 	21.46 	85.60 	243.29 	320.29 	
These values may be evaluated as cubic feet, cubic meters, etc.
A portion of this air is required for the oxidization of certain
elements in the charge and additions.

DESIGN OF OPEN-HEARTH FURNACES

229

Total coal consumption = 300X50 = 15,000 kg (for the 500
minutes). The average coal consumption will be 30 kg per
minute, or 0.5 kg per second. The maximum rate of coal con-
sumption will be approximately 1.25 kg per second. This coal
gasified in a producer supplies 3.5 cu m of gas per kilogram of coal
gasified and this gas, burned with 40 per cent excess air, requires
1.87 volumes of air per 1 volume of gas and the products of
combustion will be 2.68 volumes. Fig. 183 shows the heat capacity
and calorific intensity curves of the producer gas, the air supply
and the waste gases, as computed according to the methods of
Mallard and Le Chatelier. These curves are based upon the
combustion or burning of 100 molecular volumes or 2,232 cu m
of the gas fuel under consideration for use in the furnaces.

	Required 	Available from 	
	for 	Products of 	
	Heating 	Combustion 	
	Gas 	Air 	Gas 	Air 	
	Checker 	Checker 	Checker 	Checker 	
Temp, top of checkerwork, degrees. . . 	200 	1200 	1700 	1700 	
Temp, bottom of checker, degrees .... 	600 	300 	800 	600 	
Temp, increase or decrease, degrees. . . 	600 	900 	900 	1100 	
Heat capacity in calories at. ...   1700° 			4140 	4140 	
(Based upon 100 molecular        %™o 	960 	1700 	1750 		
volumes of the gas burnt •            0
from curve of Fig. 183) . .
oUU 	450 	480 		1250 	
Heat  in  calories  per  100  molecular 					
volumes of gas burnt to be given or 					
absorbed from checkerwork 	 	510 	1220 	2390* 	2890* 	
Heat in calories per cubic meter of gas 					
burnt to be given out by or absorbed 					
by checkerwork 	228.5 	546.6 	1071* 	1295* 	

	

* These values give the total amount of heat available in 'the products of combustion of
100 molecular volumes or 1 cu m of the gas cooled through the assumed temperature range
of either the gas or the air checker, and which must be divided between the. two checkers.
By assuming that 2 cu m of gas are burned the proportion of
the products of combustion required for the heating of the two
checkers may be arrived at:

230

APPENDIX VII

	Heat
Required
for 	Heat
Available
Products
Combust 	

	Gas 	Air 	Gas
Checker 	Cl
Y*
66
1C
12
.99
.01
12
e
8€ 	
For gas: 228.5X2 	 	457 	1093.2
0.2
70.52 	1071
23
697.5 	
	
For air:   546.6X2 	 	

	
	
Available in products of combustion . .
Total required and available 	 	155
29.48 	

	
Per cent of total required 	 	

	
	
Heat available required for the gas
checker = 2366X29 48   .. 	

	
	
Heat  available  required  for the air
checker =2366X70.52 	 			

Volume of products of combustion re-
quired for gas checker, 697. 5 -4- 1071,
per cent 	 			65.13 	
	
Volume of products of combustion re-
quired for air checker, 1668 . 5 -r 1295
per cent 	 			

Total per cent waste gases 	 			193
6
67.00
33.50
359
0.9* 	
	
Correction to make 200 per cent 	 			

Corrected per cent values 	 			

Reducing these to a 100 per cent basis
Calories per cubic meter of gas burned
Volumes per cubic meter of gas burned 	228.5
1.00 	546.6
1.87 	

*2.68 volumesX0.335 and 2.68X0.665.
The surplus heat over that required for the preheating o
gas and air will be
For the gas checker: 359-228.5 = 130.5 calories
For the air checker:  861 — 546.6=314.4 calories
This surplus supplies the heat lost by radiation, condu<
and convection from the checker or regenerator chamber
should these losses be not sufficient to absorb this amount of
the final temperature of the products of combustion leaving
checkers will automatically increase until the heat carried
into the furnace by the air and gas plus these losses equals

DESIGN OF OPEN-HEARTH FURNACES

231

amount of heat given to the checkerwork by the products of
combustion.
The maximum quantity of gas required will be
3.5 (cu m per kg) X 1.25(kg coal) =4.375 cu m per second.
The maximum quantity of air required will be
4.375X1.87 = 8.182 cu m per second.
The maximum volume of the products of combustion will be
4.375X2.68 = 11.725 cu m per second.
These volumes are reduced to zero C. and 760 mm of barometric
pressure.
The average volumes will be as follows:
of gas:   3.5X0.5(kg of coal) = 1.75 cu m per second
of air:   1.75 X1.87 = 3.273 cu m per second
of products of combustion: 1.75X2.68 = 4.69 cu m per second
Reversal Period = t

20 Minutes,
1200 Seconds

30 Minutes,
1800 Seconds

Gas:
Maximum calories=4.375X228.5X2= .
Air:
Maximum calories=4.375X546.6XZ= .
Gas:
Average calories = 1.75 X 228.5 X t = .
Air:
Average calories    = 1.75 X 546. 6X t = .

1,200,000
2,871,000
480,000
1,148,000

1,800,000
4,306,000
720,000
1,722,000

Allowing for a range of 200° in the checker brick
and 90 per cent of its weight as effective, the
weight of brick required will be
For gas:
20 min.: 1,200,000-s- (200X0.25X0.90) =	
30 min.: 1,800,000-K200X 0.25X0.90) =	
For air:
20 min.: 2,871,000-s- (200X0.25XQ.90) =	
30 min.: 4,306,000-r (200X0.25X0.90) =	

26,667kg
63,800 kg

40,000 kg
95,680 kg

232	APPENDIX VII
The brick will weigh about 1800 kg per cubic meter; therefore
the volume occupied will be
Reversal Period
20 Minutes       30 Minutes
1200 Seconds    1800 Seconds
For gas:
20 min. period, 26,667-^1800, cu m	    14.32
30 min. period, 40,000^1800, cu m		22.23
For air:
20 min. period, 63,800-^1800, cu m	    35.45
30 min. period, 95,680-^1800, cu m		53.13
Increase in temp, in checkerwork, degrees     Gas	Air
Gas: 1200-600=	      600
Air:   1200-300=		900
Average temp, in checkerwork, degrees:
Gas: (1200+600)^2 =	      900
Air:   (1200+300) -5-2 =		750
Average time in checkerwork, seconds:
At 100° increase in temp, per second.         6	9
At 200° increase in temp, per second.	3	4.5
Gas: Aver, volume per sec, at 900°, m3,
1.75X(l+ai) =	      7.53
Air:  Aver, volume per sec. at 750°, m3,
3.273X (l+at) =		12.28
With 200° per second increase in temp.,
the volume required for the passes will
be, cu m.
Gas:   7.53X3    =	    22.59
j	Air: 12.28X4.5=		55.26
I
With a temperature rise of 100° per second the volume required
for the passes will be double the above.
Fig. 153 shows that with the usual period between reversals
there will be no economy in increasing the thickness of the checker
brick over 2.5 in (63 mm), which is a standard shape.
The volume occupied by the checker brickwork will be the
sum of the brick volume added to the pass volume, and requires
no explanation. With a different producer gas and a different
air proportion there would be a corresponding change in, the
amount of heat interchange required and in the volumes required
for the brickwork and for the passes.
The height of the checkerwork should be made as great as

DESIGN OF OPEN-HEARTH FURNACES	233
possible, say, 5 m (16.4 ft) as a minimum. The flues below the
checker should be proportioned to permit free flow to the passes
at a low velocity. If desired, the height of these flues may be
stepped down, proportionally to the distance from the inlet.
This, however, introduces complications in the brickwork with
comparatively little gain.
The vertical velocity of the gases leaving the checkerwork
may be considerable and it is necessary to provide sufficient space
above the checker to get rid of the eddies which will be formed.
Unless sufficient space is provided these eddies will cause con-
siderable interference with the flow of the gas from the checker
chamber into the slag pocket, converting what should be a smooth
regular flow into a series of bursts or blow-throughs. These bursts
may have entirely different periods in the air and gas chambers
and result in considerable irregularity of combustion and waste
of fuel.
In any regenerative fired furnace it is impossible to reduce the
temperature of the waste gases leaving the regenerator to the
temperatures of the incoming air and gas. This results in a
considerable loss of heat up the chimney. Frequently one-third
of the heat passes uselessly up the stack, and the amount of heat
lost is more often in excess of this value than it is less.
The theoretical temperature of the waste gases at the base of
the stack is about 300°. The actual temperature at the base
of the stack ranges from 600° to 1000°, and rarely runs below 700°.
This would seem an ideal opportunity to install a steam boiler
and recover a portion of the heat, but until a comparatively few
years ago such an installation was not considered, although the
installation of boilers on puddling furnaces had been common
practice for many years. To-day few open-hearth furnaces are
built without waste heat boiler equipment and it is extremely
probable that such boilers could be profitably installed in con-
nection with many of the other furnaces.
Considerable notice has been taken of these waste heat installa-
tions in the various technical papers, but it has been in the main
simply tabulations of the installations as made with very little
real information as to the underlying reasons which led to the
selection of the particular equipment installed. A noticeable
departure from this practice was presented by the paper of
Thomas B. Mackenzie before the Iron and Steel Institute, in 1918.

234	APPENDIX VII
PROVISION FOR EXPLOSIONS
One of the operating difficulties with the open-hearth furnace
lies in the fact that explosions of gas are likely to occur whenever
the furnace is reversed. This difficulty is also met in all regenera-
tive furnaces. These explosions vary in their intensity from slight
puffs to heavy explosions and are due to the gas trapped in the
gas regenerator meeting the air that is drawn into the stack flue.
When the furnace is connected directly with the stack the puff of
the explosion passes up the chimney and is rarely noticed. Similar
explosions are not infrequent in blast furnace practice, and
experience in that line has demonstrated the absolute necessity
of providing explosion doors to relieve explosion pressures, as well
as the necessity of making all the flues and settings gas tight and
building them with buck stays of sufficient strength to stand the
explosion stresses.
When boilers or economizers are connected with the furnace
these explosions become of serious import and unless relief valves
are provided of sufficient area to prevent excessive rises in pressure
the settings will be damaged and numerous cracks will admit cold
air, greatly reducing the efficiency of the waste heat installation.
Another cause of unsatisfactory results with waste heat boilers
arises from the loss of sensible heat by the gases in passing through
the flues. These flues are generally underground and close to the
surface, and the ground above the flue is frequently so hot that
it remains dry, except when very heavy rains occur. Exactly
what the heat loss from this source will be depends upon the
construction of the flue, the depth below the surface and the
length of the flue. With waste heat utilization it is desirable
that the flues should be well insulated and as short and direct as
possible.
The waste-gas flues are frequently far from tight, and when
waste-heat boilers are installed the air leakage into the flues is
much more serious than when they connect directly to the stack.
Low temperatures at the bottom of the chimney in most metal-
lurgical high-temperature furnaces should be viewed with suspicion,
until checked by an analysis of the waste gases.

DESIGN OF OPEN-HEARTH FURNACES

235

LEAKAGE  THROUGH VALVES  AND  DAMPERS
Leaky valves and dampers are another source of trouble
when -waste-heat boilers are installed. The simple butterfly
valve is the oldest form of reversing valve. When carefully made
and new these valves are tight, but they do not remain in that
condition very long when exposed to hot gases. In modern prac-
tice the butterfly valve is rarely used, except for reversing the air,
the gas being reversed by valves better designed for the prevention
of leakage.
Gas
K 	Air
L 	
There are a number of valves on the market which have proved
more or less successful in operation. Many of these valves have
water seals, which prevent leakage as long as the water supply is
maintained and the pressure differential between the flues or the
flue and the air is less than the seal. All water-seal valves lose
their seal during the reversal period, and while this period, when
the sealing lip is lifted above the water surface, may be only a
fraction of a minute, a certain amount of loss occurs which cannot
be prevented. All water-seal valves add perceptibly to the
moisture in the hot gases
which pass through thorn.
Chimney
Damper
Fi<«. 156.—An Arrangement of Flues and
Valves Used in the United States.
Refer to sequence of valve operation.
Fig. 150 shows an ar-
rangement of valves and
flues which has boon used in
the United States. It is
rather costly, involving the
installation and upkeep of
eight valves and two dam-
pers. A method of reversal
which experience has shown
to be satisfactory-with this
valve system is as follows: assuming that the air and gas
are entering the furnace through the checkers K and L and
passing out through the checkers / and .7, the sequence of opera-
tion is:
1.	Steam is cut off from the producers;
2.	Air-stack valve F is closed;
3.	Gas-inlet valve A is closed;
4.	Air-inlet valve Cy Is closed;
1.	
236	APPENDIX VII
5.	Gas-stack valve B is opened.    (This passes the gas
trapped in the gas checker K to the flues and boiler,
thence to the stack);
6.	Gas-stack valve G is closed;
7.	Air-inlet valve E is opened.    (This admits air to the
furnace);
8.	Gas-inlet valve H is opened;
9.	Air-stack valve D is opened;
10. Steam is turned on to the producers.
The important feature of this system of valve operation is the
time interval between the opening of the gas and the air stack
valves on the same side of the furnace. This interval must be
sufficient to permit the inflammable gases in the gas checker to
pass into the flues and to the stack before the air-stack valve is
opened. In the plant where this system was introduced the
number of explosions was reduced from about 40 per day to 4 in
411 reversals in a period of five clays.
Several other systems are in use, and in some installations
the valves are. interconnected in sets which are operated simul-
taneously. Different arrangements of flues and different valves
will require some modification of this system, the essential point
being the interval between the opening of the gas-stack valve and
the air-stack valve.
This sequence of valve operation will not eliminate explosions
unless the valves and the flues are sufficiently tight to prevent
any air entering the system while the gas trapped or pocketed in
the checker chamber is passing to the stack.
FAULTY BOILER SETTINGS
Probably the most important portion of the waste-heat boiler
installation is the arrangement of the boiler setting with regard
to the manner in which the gases pass through it—that is, the
baffling and the location of the gas inlet and outlet. The design
of boiler settings and their baffling has been the subject of much
experimenting, but unfortunately most of these experiments have
been made without any very clear conception of the action of the
hot gases while flowing past cool metallic surfaces.
The ruling temperature in steam boilers is very low.   For this

DESIGN OF OPEN-HEARTH FURNACES	237
reason it would require designing talent of an extremely high order
and much serious study to produce a boiler which would not work.
Practically all of the boilers which have been built and installed
present extremely gross violations of some of the simplest and
most elementary laws of physics, not only in the circulation of the
heated gases but in the circulation of the water and steam. Owing
to their low ruling temperature these boilers work—that is, they
produce steam when hot gases pass through them, but their
utilization of the heat is comparatively inefficient when the
possibilities of such low-temperature applications are considered.
Some three years ago the writer, in the course of a discussion
before the Cleveland Engineering Society, stated that it seemed
to him that commercial boilers were much better designed for the
production of soot, a form of lampblack, than they were for the
production of steam. Since then he has seen no occasion to reverse
his opinion. At the same time he will admit that the low rate of
evaporation presents a certain margin of safety in boiler operation
—that is, the operating safety of a steam boiler depends upon the
maintenance of the supply of feed water. When the water supply
fails a very few minutes elapse before the water in the boiler
will be evaporated to a point where portions of the heating surface
will become dry. This is the danger point, and the higher the
rate of evaporation as compared with the volume of water con-
tained in the boiler, the quicker it will pass this danger line.
When the method of baffling steam boilers is examined, it will
be found that the hot gases are introduced at the lowest point of
the setting, that these gases rise in two of the passes and drop
through the middle pass, and are carried away from the highest
point of the setting. Experience with regenerators and similar
heat-absorbing structures has shown that this arrangement of gas
passages is absolutely illogical. Some waste-heat boilers without
baffling have been installed in connection with copper-smelting
furnaces, but in these installations the baffling was removed in
order to reduce the resistance to the passage of the gases through
the boiler, and the manner in which the gases were introduced and
carried away from the setting was not calculated to obtain the
best results. The main idea in the design appeared to be that
the gases should pass through the boiler setting as rapidly as
possible without any consideration of the utilization of their
sensible heat, while two boilers were placed in series in order to

238

APPENDIX VII

reduce the temperature of the outgoing gases.    The precedent
of this design has been followed in other cases.
There is a considerable diversity of opinion in regard to the
manner in which waste-heat boilers should be rated. In America
boilers are usually rated at 10 sq ft (0.933 m2) per horsepower,
which is equivalent to an evaporation of 3 Ib (14.6 kg) per square
meter of heating surface. Some have considered that this rating
should be reduced to 7.30 kg for waste-service service, in spite
of the fact that many boilers are in service at rates of evaporation
considerably in excess of the above figures. When it comes to the
selection of a boiler for any given waste-heat installation a con-
sideration of some of the installations which have been made
indicates wide differences in regard to the area of heating surface
required.
waste heat boilers installed on open-hearth furnaces
(Thomas B. Mackenzie, Iron, and Steel Institute, 1918)

	I 	III 	V 	VII 	IX 	
Nominal capacity of furnace,
tons 	 « 	 	30 	45 	100 	60 	60 	
Heating surface, * sq m 	
Economizer heating surface,
so m 	 	151.00
66.2 	170.00
89 4 	204.00
111.9 	204.00
111 9 	204.00
111 9 	
Steam pressure, absolute, per
so cm, ke: 	7 14 	8 35 	5 20 	6 18 	8 64 	
Feed water, initial temp ....
Feed water, final temp 	 	11.6
117.8 	6.95
120.6 	40.8
133 5 	9.5
133 00 	29.3
129 00 	
Gas temperatures, deg. C.:
Entering boiler 	504 00 	585 00 	422 00 	577 00 	439 00 	
Leaving boiler ... 	254 00 	273 00 	232 00 	303 00 	304 00 	
Drop in boiler 	 	250.00 	212.00 	190.00 	274 00 	135 00 	
Leaving economizer 	 	169.00 	182.00 	184.00 	172 00 	264 00 	
Drop in economizer 	84 00 	91 00 	48 00 	131 00 	40 00 	
Draft in mm of water :
At boiler inlet 	 		23 00 	40 00 	25 00 	25 00 	
At boiler outlet 	 		62.00 	78 00 	63 00 	95 00 	
Drop through boiler 		39 00 	38 00 	38 00 	70 00 	
At draft fan 	20 00 	87 00 	80 00 	76 00 	146 00 	
Drop through economizer .
Probable  volume   of  gases
passing through boiler per
second, cu m at zero and
760mm 	 	9.74 	25.00
10.35 	2.00
15.50 	13.00
15.50 	51.00
24.60 	
* Boilers all Babcock & Wilcox type.

DESIGN" OF  OPEN-HEARTH  FURNACES
othkk waste ukat boilkii data

239

Test Number .                    	 	 	1* 	»> 	3 	4 	
					
Plant 	111. St.
(.Jo. 	Indiana
St. Co. 	Beth-
lehem
Co. 	Lacka-
wanna
Steel Co. 	
Rated furnace capacity, tons. ........
Aotujil furnace capacity tons. ..,,... 	<>r>
72 1 	75
85 	80
82 (i 	oo.oot
00 <)() 	
Type, of boiler 	                  ...... 	Stirling 	Hunt 	B & W 	B <fe W 	
Boiler hunting surface, Kq m. ........
Steam pressure ab.Holute, kg per sq em.
Superheat, de^  (!, .              .     	 	371.0
9 . 70
71  00 	453.3
9. SO
9S 00 	480.0
07 00 	502.3
54 00 	
huh at boiler inlet        	 	 	004 00 	024 00 	730 00 	530 00 	
( »iis at boil(»r outlet          	 	327 00 	277 00 	250 00 	242 00 	
Drop in temperature. . . . 	 	 	
Draft at boiler inlet, nun    .   ...   ... 	337.00 	347.00
37 00 	483.00
30 00 	288.00
45 00 	
Outlet 	 	 	 	. 	100.00 	83.00 	92.5 	
Draft- iohh in boiler 	•15 2 	03 00 	44 00 	47 5 	
Weight of kiih passing; through boiler,
kg per second 	<) 22 	10 00 	0 50 	10 00 	
					
noh. 1, 2 and 3 from (•. J. Bacon'H paper at 1915 meeting of the
American Iron and Steel Institute*.
Tiwt No. 4, Arthur I). Prati, American Society of Mechanical Kn$ineerB,
December, 1910.
The following method of arriving at the amount of boiler-
heating surface required for absorbing the waste heat from an
open-hearth furnace1 is simply an extension of the method used by
the author in arriving at the regenerator capacity required and
reference taunt be made to the heat-capacity curves given in the
preceding .section of this work.
In practice it might l>e desirable to divide* this heating surface
between an economizer or feed-water heating section and a boiler
or steam-producing section. Thin method of construction will
result in a reduction of the size of the; boiler and its cost, and
possibly may reduce the total cost of the installation. When
the cost of the* foundations arid other structure required
to install the*, economizer in considered it is probable that the

APPENDIX VII

	Gas
Checker 	Air
Checker 	
Temp, products of combustion at bottom of checker-work,
degrees C 	             	 	800 	600 	
Products of combustion per cu meter of gas burnt, cu m . .
Products of combustion == 0 90+1 78=             	 	0.90
2 	1.78
68 	
Average temperature products of combustion
= [(800X0 90) + (600X1 78)] -^ 2 68 	 	6( 	>5 	
			
(No allowance is made for a heat loss in the flues, although in practice a
temperature drop of 50° to 100° will occur between the bottom of the checker-
work and the boiler inlet. The heat capacities given by the curves are
based on the consumption of 100 molecular volumes or 2.232 cu m. of gas.
These values have been reduced to those for a cubic meter of gas burnt in
this computation.)
Heat capacity products of combustion of 1 cu m of gas
at the bottom of the checkerwork, average £ = 665,
calories	 635
Heat capacity products of combustion of 1 cu m of gas
at the boiler outlet, average 2=200, calories	 162
Heat available for production of steam, calories	473
Assuming that one-third of this heat will be lost in flues
and boiler setting, net amount of heat available will
be, calories	 316
Heat required for evaporation of 1 kg of water at 5.54
kg per sq cm absolute (78.76 Ib per sq in) = 156+500,
calories	 656
Products of combustion from 1 cu m of gas will evapo-
rate: 316-^656, kg	 0.481
1 sq m of boiler heating surface is equivalent to the
evaporation of 15 kg of water per hour; or 0.00417 kg
of water per second
Area of the heating surface required to evaporate 0.481
kg of water per second will be: 0.481 -f-0.00417 sq m. 116
(This being the area of the heating surface required to
absorb the heat in the products of combustion from
1 cu m of the gas burnt)
As the average amount of gas burnt per second is 1.75
cu m, the area of the heating surface required will be:
116.00X1.75	 203
Quantity of gas burnt per second, p. 231.

DESIGN OF OPEN-HEARTH FURNACES

241

total cost will be about the same for both methods of installa-
tion.

Another factor that has
to be considered, is the area
of the gas passage through
the boiler must be sufficient
to permit the maximum vol-
ume of the products of com-
bustion to pass without adding
unduly to the draft resistance
through the boiler.
In the foregoing computa-
tion the temperature of the
boiler feed water was taken
as zero C. In practice this
will not  be the case, if	the	^     „ „„    ^	, «    .
.     ,	,	.	,,	fig. Io7.—Proposed Setting of Marine
average temperature   of	the	Type of Waste Heat Boiler,
water is considered.
THE MATTER OF THE DRAFT
Stationary or land practice has persistently used brick boiler
settings in spite of their many disadvantages. Brick settings are
undoubtedly less costly than air-tight steel-sheathed boiler settings,
and the fact that the weight of the boiler setting on land is unim-
portant has led to the almost exclusive use of the porous brick
setting, owing to its lower cost. There are a number of places
where the extremely low-draft pressure makes the brick setting
comparatively unobjectionable, but in open-hearth and other
waste-heat installations where a large draft differential is required
the porosity of the brick setting is objectionable. In addition
the brick setting will be badly damaged by any explosions which
may occur; the brickwork is readily cracked and these cracks
admit air which will produce explosions at each reversal.
Practically all waste-heat boilers installed upon open-hearth
furnaces have necessitated the installation of an induced draft fan.
With the commercial types of boiler set and baffled to the makers'
drawings, these fans will be necessary, or else an unduly high
chimney. The pressure in the heating chamber of the furnace
is equal to the atmospheric pressure and it is necessary to supply

If!

242	APPENDIX VIIJ
a draft depression below the regenerators sufficient to remove
the-products of combustion from the furnace; additional draft
depression must be supplied to overcome any friction in the pas-
sages through which the waste gases pass. There are limits to
the height of chimney which it is desirable to install in connection
with an open-hearth furnace and any further increase in the draft
depression must be secured by the installation of a draft fan.
When these fans are operated by steam they will consume about
one-fifth of the total steam generated and the balance will be
available for the gas producers and for supplying the other power
demands of the plant.
The primary function of the open-hearth furnace is the produc-
tion of steel and this should be kept in mind in the design of the
waste-heat boiler setting and flues. The boiler should be by-
passed so that any failure in these portions of the equipment will
not necessitate the shut-down of the furnace. In some cases
steam-jet apparatus has been installed to provide against the
failure of the fan or its motive power.
The venturi coned ejector form of chimney has been employed
in some installations. This type of chimney may be used in either
of two methods, the fan may be reduced in size and only handle
a portion of the waste gases, or the Louis Prat method may be
employed, in which the fan handles cold air only. This latter
method is analogous to that of the hydraulic head increaser
designed by Clemens Herschel for use with low head hydro-
plants.
One of the incidental advantages of introducing induced draft-
in the operation of the furnace arises from the fact that the fan
draft may be increased to compensate for the blocking up of the
checkers and the operation of the furnace will be entirely inde-
pendent of those barometric and weather conditions which affect
chimney draft.
Reversing valves for regeneratively fired furnaces have been a
source of much trouble. Many different valves have been
designed and placed upon the market, and a number of different
flue arrangements have been devised to eliminate the reversing
valve and accomplish the reversal with a multiplicity of mushroom
valves and dampers. The simple Siemens butterfly valve was the
first four-way valve used on these furnaces. When in use, how-
ever, and exposed, on one side, to the hot gases and on the other,

DESIGN  OF  OPEN-IIEARTII  FURNACES

243

to the cool gas or air passing to the regenerators, it soon warps
and becomes leaky. These leaks permit air to pass directly to the
stack and cool down the waste gases; or, if the valve is used for
gas, there is continual leakage of gas, which burns either in the
valve or in the stack flue.
While many reversing valves are water-scaled, most of them,
like the butterfly valve, during the* operation of the valve, open a
direct connection, practically the full area of the valve from gas
main or air to the stack. Then* have been a few valves which cut
the furnace, gas and air entirely off from one another and the
stack, but these valves have not come into extended use.
Water-sealed valves are used extensively.    As long as the seal

fkj. 15H.
fhj. 159.
fh»s. 15H arul 159, -Pyrometer Diagrams of Stack Temperature's, Abnormal
conditions shown by suddctn upward kick in Fig. 159 jiro probably dun
to nir ioukiiKft mid the combustion of chcjokdr ^rhc^h passing along the
fhio to the* Black,
holds they are tight, but there are usually structural limitations
to the? depth of the seal When exposed to gas pressure; on one
side and to the stack depression on the other, the seal is unbalanced
and may readily be* broken by surges or explosions. In Home eases,
a considerable! water area is exposed to the entering gas or air,
as well as to the waste gases.
The producer gas and the stack gases are several hundred
degrees hotter than boiling water and will absorb a considerable
amount of moisture from a very small area of water surface.
Other valves expose very little water surface. With nil of those*
vulvas the sealing lip must bo raised to clear the water surface
and the port rims, whenever the valve in operated. From the

244

APPENDIX VII

time the seal is broken until it is reestablished, the full suction
of the stack acts to pull air or gas, and in some cases both, into the
stack.
With some valves, the furnace itself is directly connected to the
stack through both regenerators, at reversal, so that a portion of
the stack-pull tends to draw air in at the doors. This may or
Hamber of Furnaces of Each Size
113224	13     4	4
16
15
14
B
12
11
§10
I9
so s
a
g. 7
I6
^ 5
4 																						

																						

																						

																						

																						

																						

											6 					0 						

																					_2 	

																						

											r, 											

																						

											2 											

								3 														

																						
S 																						

2 																						

I 																						

n 																						
0      10     20     30     40     50    60     70     80     90    100   200
Tons., Nominal Capacity of. Furnace
fig. 160.—Graphical Comparison of Gas Valve Areas of Various Open-hearth
Furnaces.
may not be seriously objectionable, according to the distance
between the valve and the furnace and the rapidity with which the
valve may be operated.
Moisture absorbed from water seals is a direct loss of the
amount of heat required to evaporate it and superheat it to the
temperature at which it passes out of the regenerator to the stack.
In addition, its dissociation probably occurs in the checkers, which
may release some oxygen to combine with other combustibles at

DESIGN OF OPEN-HEARTH FURNACES

245

this point. The reactions here are complex, as certain hydro-
carbons dissociate in the checkers, as well as C02. A further
increment of moisture occurs in certain elements of the charge,
and an open-hearth furnace is not particularly efficient as a dryer.
At the same time, moisture is carried in by the air supply. All of
this water leaves the regenerator for the stack as highly super-
, of F.arnaces of Each Size
16 			I  1 	L 	? 	Z S 	t 	I 		1 	3 	4 			^ 	I 				4 	1 	
																						
IK 											t 											
																						
11 																						
																						
1Q 																						
											0 					0 						

																						
																						
*ain 																						
											T.HS 											
																						
« ^ 											» 		3 							, 	, 	
§• 																						
																						
~ 							< 															
s' 					j 																	
-4 																						
u>b 							1 	o 														
£, 																						
*^ 5 							? 															
																						
4 																						
																						
3 																						
																						
2 																						
																						
1 																						
0 																						
0      10     20    30     40     50     60     W    80     90    100   200
Tons, Nominal Capacity of Firraac.e
fig. 161.—Graphical Comparison of Air Valve Areas of Various Open-hearth
Furnaces.
heated steam, and its amount is considerable, particularly with
large furnaces. In " The Heat Balance of the Open-Hearth/'
by Sidney Cornell (Chemical and Metallurgical Engineering, May,
1913), the weight of moisture passing in the flue gases was given
as about 26 per cent of the weight of ingots produced. The water
seals in the valves increased the amount of moisture in the pro-
ducer gas 1 per cent.
The water seal depends upon its water supply, and a very slight

246

APPENDIX VII

stoppage breaks the seal. Frozen water lines in winter frequently
cause the superintendent to consign the plant to the tropical
regions, particularly when they occur on a cold Sunday morn-
ing. Water vapor absorbed by the flue gases reduces not
only their temperature, but also the stack draft and the
amount of heat available for the waste-heat boiler to convert
into steam.
As to the valve area required for a furnace, there is as much
diversity in practice as there is with the other portions of the
furnace. Figs. 160 and 161 are a graphical comparison of reversing
valve practice, while Table 10 shows the same data in tabular
form. The reference numbers in the table correspond with those
given in preceding chapters.
TABLE 9
reversing valves

Nominal Diameter Valve 	Nominal Area of Valve 	
In 	Ft 	nun 	Sq In 	8(1 Ft, 	rn2 	
18
21
24 	1.5Q
1.75
2.00 	450
525
610 	254
346
452 	1,77
2.40
3.14 	0.164
0.223
0.292 	
27
80
33 	2.25
2.50
2.75 	685
760
840 	572
706
855 	3.90
4.91
5.93 	0.362,
0.456
0.548 	
36
40
42 	3.00
3.33
3.50 	915
1000
1070 	1017
1256
1385 	7.07
8.73
9.62 	0.657
0.808
0.894 	
48
54
60 	4.00
4.50
5.00 	1220
1370
1525 	1809
2290
2827 	12.57
15.90
19.63 	1.168
1.477
1.823 	
66
72 	5.50
6.00 	1675
1830 	3421
4071 	23.76
28.27 	2.210
2.930 	

DESIGN  OF OPEN-HEARTH FURNACES

247

TABLE 10
reversing valves and chimneys in practice

		Valve 	Area 		( 	Chimney. 		
Nominal
Furnace
Capacity, 			SqFtp 	er Ton 		Area oi 	SqFt 	
Tons 	Gas,
SqFt 	Air,
SqFt 	Gas 	Air 	Height,
Ft 	Bore,
SqFt 	Per
Ton 	
10-1
15
20-A 	3.12
3.12
3 90 	4.87
3.12
3 90 	0.312
0.208
0 195 	0.487
0.208
0.195 	100
90
100 	9.63
12.56 	0.963
0.837 	
20-3 	3 07 	4 00 	0 154 	0 200 				
20-D 	3 90 	5 90 	0 195 	0 295 				
20-4 						5 85 	0.293 	
25-4
25-3
30-5-4
35-2 	4.90
5.65
4.90
5 90 	4.90
6.90
4.90
5 90 	0.196
0.226
0.163
0 169 	0.196
0.276
0.163
0 169 	125
125
125 	12.56
19.64
14.20 	0.502
0.786
0.473 	
35-A
35-1
35-D 	4.90
4.90
4.90 	5.90
4.90
7.10 	0.169
0.140
0.140 	0.169
0,140
0.203 	114
130 	17.00
15.90 	0.487
0.474 	
40-7 						9.00 	0.225 	
40-4 					140 	19.64 	0.491 	
50-4
50-10 	7.06
7.06 	7.06
15.00 	0.141
0.141 	0.141
0.300 	150 	23.70
21.50 	0.474
0.430 	
50-11
50-8
50-13-15
50-16
50-X 	5.94
9.60
9.60
9.60
5 22 	9.18
12.50
9.60
12.50
7 75 	0.119
0.192
0.192
0.192
0 104 	0.184
0.250
0.192
0.250
0 155 	150
150
150
160 	26.27
28.25
25.80
20.00 	0.525
0.565
0.516
0.400 	
50~4a 	8 13 	8 13 	0 163 	0 163 				
50-19
50- 5 	9.60
7 00 	9.60
9 52 	0.192
0.140 	0.192
0.190 	150 	20.00 	0.400 	
50-D 	5 90 	8 70 	0 118 	0 174 				
60-13
60-3-5 	7.06
7.06 	12.58
8.72 	0.118
0.118 	0.210
0.145 	180
153 	33.18
28.27 	0.553
0.471 	

248	APPENDIX VII
TABLE 10—Continued
reversing valves and chimneys in practice

		Valve 	Area 			Chimney 		
Nominal
Furnace
Capacity, 			SqFtr 	>er Ton 		Area o: 	*SqFt 	
Tons 	Gas,
SqFt 	Air,
SqFt 	Gas 	Air 	Height,
Ft 	Bore,
SqFt 	Per
Ton 	
75-1 	9 42 	13.00 	0.126 	0.173 				
75-A 	9 42 	12 56 	0 126 	0 167 				
75-3 	8 70 	12 56 	0 116 	0 167 				
75-D 	7 10 	10 50 	0 095 	0 140 				
75-2 					165 	20.36 	0.271 	
80-1 						15.80 	0.198 	
100-3 						19 60 	0.196 	
100-H
100-E
100-4
100-D 	10.00
8.75
9.42
8 70 	10.00
8.75
15.90
12 60 	0.100
0.088
0.094
0 087 	0.100
0.088
0.159
0 126 	180
180
160 	28.25
50.00
28.25 	0.285
0.500
0.283 	
150-1 					150 	23.70 	0.158 	
200-4 	7.00 	12.56 	0.035 	0.063 	180 	38.50 	0.385 	

I' \

Some of these valves are so heavy as to require electric motors,
or some other form of power, for their operation. In these cases
the control is located on a pulpit at a central location on the charg-
ing floor, in the rear of the furnace. Smaller and lighter valves
are operated by cables or levers led into the pulpit. Heavy valves
have considerable inertia, and for this reason cannot be operated
as rapidly, even by power, as the smaller valves with lighter moving
parts.
Furnaces fired by natural gas, oil, coke-oven gas or tar require
reversing valves for the air only, the fuel being reversed by shut-
ting off the jet at one end of the furnace and turning on the jet
at the opposite end. Some of these furnaces are supplied with one
checker chamber at each end, while others are so constructed,

DESIGN OF OPEN-HEARTH FURNACES	249
with two chambers at each end, that they may be converted with
little difficulty to producer-gas firing.
Those furnaces in which only the air is preheated have a slight
advantage over those in which both the gas and the air are pre-
heated, in that no unburned gas has to be wasted up the stack at
reversal. The amount of fuel lost in this manner depends upon the
gas-filled volume between the reversing valve and the port, and
the frequency of reversal. When the gas is preheated this loss
cannot be avoided.
This gas likewise creates an explosion hazard; when the condi-
tions are right, it burns and passes up the stack as a puff of flame.
Again it may become mixed with air, the mixture being below the
ignition temperature; when a portion of this mixture is suddenly
ignited an explosion of more or less violence occurs. These
explosions damage the walls of regenerative chambers, flues and
waste-heat boilers so that large amounts of air are drawn into the
system, reducing the stack draft and the output of the boiler by
reason of the lowering of the temperature of the waste gases.
One of the factors in regard to valve area that meets with
little consideration is the velocity of the gases passing through the
valve. In addition, most valves involve a change in direction of
flow, totaling 360°, 180° in the valve and two 90° changes in the
flues. When a stream of flowing gases passes through passages
involving changes in area, velocity changes are involved. The
velocity of flow in the normal section of the flue may be repre-
sented by Fmin and in the contracted area of the valve by Fmax.
The corresponding velocity heads will be Amin and Amax- That is,
a velocity head = Amax—Amin will be required to produce the increase
in velocity. The pressure, in kilograms per square meter or in
millimeters of water, required to produce the increase in velocity
will be
8 = (ftmax — hmln) A*,
in which d = pressure in kilograms per square meter or millimeters
of water;
Aj=the weight of 1 cu m of the gas in motion at a tem-
perature of t°.
When the pressure is desired in inches of water, the weight of
the gas being in pounds per cubic foot, the formula is
5 = 0.192(ftmax-~ Amln) At*

250

APPENDIX VII

The coefficient of contraction varies from unity, when the
areas of the two passages are the same, to 0.83, when the area of
the smaller passage is 0.01 of the area of the larger passage.
This slightly increases the pressure required, but ordinarily a
large margin is available to cover this increase. The loss of
pressure due to changes of direction may be expressed by the
formula,
in which r is a function of the angle through which the stream is
deflected. The following values are given by Weisbach for short
bends in pipe:

Angular change a =    20°        40°        45°
r = 0.046    0.139    0.188

60°
0.364

80°   90°
0.740 0.984

v= velocity in meters per second;
2g = gravitational constant =2X9.81.
When the loss of pressure clue to directional changes is desired
in inches of water column, the formula is
in which v = velocity in feet per second ;
20 = 2X32.2;
Aj = weight per cubic foot of gas in motion at t°.
The losses, due to directional changes of 180° in the valve and
90° in the flues each side of the valve, are approximately from two
to four times as great as the loss due to restricted valve area.
For this reason, changes of diameter of valve of 6 in (150 mm)
or so have a comparatively small effect upon operation. These
losses vary with the square of the velocity in the valve and the
flues. Many furnaces are, undoubtedly, choked by the small area
of the valves used, and much operating trouble is doubtless due
to lack of consideration of these details.
A valve small enough to choke the furnace is an expensive
luxury, as it exacts its toll every minute the furnace is working.
Added chimney height or forced draft must be provided to over-
come its resistance. There is very little doubt that the erratic
working of some furnaces with different weather conditions is

DESIGN  OF OPEN-HEARTH FURNACES

'   251

311
dumber of Furnaces of Each Size
1112121        12

xuu
180
170
160
150
-s140
*
^130
J3 120
110
100
90
£0
TO 																									

																					2 	— 			

	

																									

																						— 	- 	— 	

											3 											

	

											8 		3 												

																					— 				

				

								1 																	

						2 																			

																	— 								

								

							' 																		

																									

	o 																								

																									

																									

10      20      30      40      50      60     70       80     90     100     150    200
Tons, Nominal Capacity of Furnace
fig. 162.—Graphical Comparison of Chimney Heights of Various Open-hearth
Furnaces,
Number of Furnaces of Each Size
1112222      14      4	11	4       1       1
50
"30
20
1Q
10    20    30     40     50     60    70     80    90    100   150   200
Tons, Nominal Capacity of Furnace
fig. 163.—Graphical Comparison of Chimney Areas of Various Open-hearth
Furnaces.

252    '	APPENDIX VII
largely due to the fact that the close balance between draft and
resistance is disturbed by barometric and temperature conditions.
These various losses will be discussed in more detail in the design
computations for a furnace.
Figs. 162 and 163 give a graphical comparison of chimney
areas and heights which are tabulated in Table 10. Open-hearth
practice in the United States tends to the use of self-supporting
steel chimneys lined with firebrick. Even with waste-heat boilers
and induced draft, the straight chimney is used, while abroad
many of the venturi cone (Prat type) chimneys are used. The
chimney is a necessity, as the waste gases must be carried to a
sufficient height to prevent their becoming a nuisance, not only
in the works, but to its neighbors.
Another factor which must be considered, in connection with
the draft required to operate the furnace, is that the gases must be
pulled out of the furnace through the ports, down through the
checkers and through the valves and flues; that is, the waste-
gas end of the furnace is below atmospheric pressure, and there is a
constant tendency for cold air to be pulled into the system.
When this brickwork is new and tight the leakage of air into the
system may be slight, but after a few explosions have shaken
things up, the brickwork is liable to leak like a sieve. For this
reason, gas samples taken at the base of the stack are liable to
show a condition of affairs quite different from that which actually
exists in the gases leaving the heating chamber or the regenerators.
A great many tests and considerable investigation of open-
hearth furnaces have been made, from time to time, at different
plants. Tests of this kind cannot be permitted to interfere with
furnace operation. They must be carried on night and day, over
several melts. When it is decided to run such a test the question
of cost must be considered, not only in apparatus, but in per-
sonnel. A large number of observations and chemical analyses
must be made and the results analyzed.
Very slight details are liable to vitiate the value of such tests
and it is extremely difficult to impress upon the available assistants
the factors that are really essential; frequently, in fact, the busy
executive is unable to devote the preliminary attention he desires
to the test scheme, and, as a result, only a portion of the data
desired is obtained. Comparatively few of these tests are made
known, hence there is much repetition of the work of others.

DESIGN OF OPEN-HEARTH FURNACES

253

THE DESIGN OF OPEN-HEARTH FURNACES
Design computations for an open-hearth furnace do not require
any large amount of mathematical knowledge, for the principles
involved are comparatively simple. As in all other engineering
and chemical propositions, it is necessary to effect a compromise
between a number of different requirements and co-ordinate them
in the right manner to secure a desired result. All of the different
elements of the problem are closely interrelated, and changes and
modifications at one point necessitate carrying a corresponding
modification through the entire system which it affects.
In order to establish a point of departure, it has been assumed
that a furnace having a nominal capacity of 100 tons is to be
designed, that it is to be fired with producer gas, and that the
actual hearth area will be 650 sq ft. The computations will be
limited to those required to establish the design lines. Certain
factors may bp more or less arbitrarily fixed without regard to
current practice or whether they are desirable or not, merely
for the purpose of furnishing a working base, the purpose of the
computation being to illustrate the formulas used and their
application.
The reactions in the open hearth are well known. Their main
effect, as far as the flue gases are concerned, is an increase in C02
and in the moisture content, the latter in the first part of the
heat, and the former during the boil and after the limestone is
added. The fuel consumption will vary with the furnace, the
method of working, etc. Ranging from 220 kg (485 Ib) per ton,
using molten pig, up to 350 kg (770 Ib) per ton and higher. The
fuel consumption is not uniform during each furnace cycle, from
charge to charge, but varies about as follows:

Percentage of
. Cycle (Time) 	Percentage of
Fuel Consumed 	
63.00 	76.00 	
17.00 	15.20 	
14.00 	8.40 	
1.00
5.00 	0.40 	
		
100.00 	100,00 	

254

APPENDIX VII

TABLE 11
combustion of producer gas (SC-DSW)

	B.t.u. 	B.t.u. 		Products of Complete 	
Volumetric 	per 	per 		Combustion, Cubic Feet 	
Composition 	Cubic 	100 	02 		
of Gas, 	Feet 	Cubic 	Required 				
Per Cent 	of
Element 	Feet
of Gas 		C02 	II2O 	N2* 	
Hs       12.10 	X 293.2 	= 3,548 	6.05 		12.10 	24.20 	
CH4      2.60 	X 983.4 	= 2,557 	5.20 	2.60 	5.20 	20.80 	
CWBU     0.40 	X1610.0 	=     644 	1.20 	0.80 	0.80 	4.80 	
CO      21.78 	X  343.6 	=  7,484 	10.89 	21.78 		43.56 	
O2         0.02 			-0.02 			-0.08 	
COo      5 68 				5.68 			
H2O      3 82 					3.82 		
No       53 60 						53 60 	
							
100.00 	Low 	14,233 	23.32 	30.86 	21.92 	146.88 	
H20    18.10 	X    54.06 	=     988 					
	High 	15,221 					
Theoretical air supply = 23.32X5.00 = 116.60 cu ft per 100 cu ft of gas.
* Assuming the atmosphere to consist of 80 per cent N« and 20 per cent Os.

Air
Per
Cent 	Supply
Volumes 	Excess
Air 	Products of Combustion of 100 Volumes of Gas 	

	
	02 	CO, 	H20 	N2 	Total 	
100 	116.60 	0.00 	0.00 	30.86 	21.92 	146.88 	199.66 	
120 	139.92 	23.32 	4.64 	30.86 	21.92 	165.53 	222.98 	
140 	163.24 	46.64 	9.09 	30.86 	21.92 	184.19 	246.30 	
180 	209.88 	93.28 	18.18 	30.86 	21.92 	221.50 	292.94 	
			Percentage Basis (Wet) 	
100 			0.00 	15.64 	11.11 	73.25 		
120 			2.00 	14.03 	9.97 	73.94 		
140 			3.75 	12.72 	9.03 	74.50 		
180 			6.31 	10.71 	7.50 	75.37 		
			Percentage Basis (Dry) 	
100 			0.00 	17.60 		82.40 		
120 			2.29 	15 . 58 		82.13 		
140 			4.12 	13.97 		81.91 		
180 			6.83 	11.59 		81.58 		

DESIGN  OF OPEN-HEARTH  FURNACES	255
For the case in hand it is assumed that the fuel consumption will
be about 300 kg (660 Ib) per ton converted into producer gas of the
following composition: H2, 12.10; CH4, 2.60, C2H4, 0.40;
CO, 21.78; 02, 0.02; C02, 5.68; H20, 3.82; N2, 53.60, having
a thermal value of 1265 calories per m3 or 142 B.t.u. per cubic foot
(low values), the high values being 1352 calories per m3 or 152
B.t.u. per cubic foot. The heat capacity of this gas, the air
supply required for its combustion and for the products of com-
bustion are shown by the curve (Fig. 184). Table 11 gives the
combustion and air-supply data for this gas. One pound of coal
produces 70 cu ft of gas, 1 kg, 4 m3 39 of gas. Its specific weight
is 1 kg 125 per m3 (0.07024 Ib per cubic foot). Its products of
combustion, with 40 per cent excess air, weigh 1 kg 32 per cubic
meter (0.08241 Ib per cubic foot). At the maximum rate of
working, the gas will be burned at the rate of 5 m3 32 (188 cu ft)
per second, requiring 8 m3 51 (301 cu ft) of air for combustion,
and the products of combustion will be 12 m3 77 (451 cu ft),
all volumes at 0° C., 761 mm barometer. As the volumetric
corrections for pressure are comparatively small, they will be
neglected in the computation, and the temperature corrections
alone will be used.
As the capacity of the furnace is to be 100 tonnes, the metal
volume will be 523 cu ft, and the hearth area has been fixed at
650 sq ft. The approximate depth of the bath will be:
«,
depth  of bath = eZ = — = ^p = 2.41  ft = 29  in of metal.
1	a       650
As the bottom will slope toward the tap hole and be banked
at both ends and sides, the actual metal depth will depend upon
the way this is done. There will be at least 12 inches of bottom.
Therefore, the depth to the brick will be about 42 inches from the
sills of the charging doors, and the port sill or bridge will be
fixed as 6 inches higher, making the total depth that the flame
must drop below the port 48 inches, or about 1200 mm.
The brick lines of the hearth will have to be fixed outside of
the bath area of 650 sq ft. Therefore, the inside width between
walls will be made 5 m 00 (16.40 ft), and the length between port
sills 13 m 50 (44.25 ft), giving an area of 67 m2 50 (726 sq ft). If
the length is cut to 13 m 00 (42.65 ft.) the area will be reduced to

256

APPENDIX VII

65 m2 00 (700 sq ft). The width might be reduced slightly by
increasing the length. There are advantages in reducing the span
of the roof, as well as disadvantages in making the furnace too
long, but it is possible that a length of 14 m 00 (45.90 ft) with a
width of 4 m 650 (15.25 ft), giving an area of 65 m2 11 (701 sq ft),
would be satisfactory.
The temperature in the heating chamber will be 1800° C.
(3272° F.) for the gases, the roof being 50° to 100° C. (90° to
180° F.) cooler, and the bath from 150° to 250° C. (270° to 450° F.)
cooler. The height of the chamber may be approximated by
Yesmann's formula
in which ht=the thickness of .the layer of gas in motion in meters
(or feet) ;
Qi=the volume of gas in cubic meters (or cubic feet) at
t° temperature;
jB = the width of the furnace in meters (or feet);
A = &   coefficient  which   varies  for   each   value   of   h
and Bj
t = temperature Centigrade
TABLE 12
table giving the values of A for metric units

	Values of B 	
ht 	1 mOO 	2 mOO 	5m 00 	
Om 30 	3.42 	3.54 	3.62 	
Om 50 	3.29 	3.46 	3.57 	
Om75 	3.13 	3.37 	3.54 	
1 m 00 	2.97 	3.28 	3.53 	
This formula may be translated to English units as follows:

DESIGN OF OPEN-HEARTH FURNACES

257

TABLE 13
table giving the values of A for english units

r      Tj'rtyv*- 	Values of B 	
hi, .beet 	3 Feet 	6 Feet 	9 Feet 	12 Feet 	16 Feet 	
1.0 	2.275 	2.36 	2.40 	2.42 	2.43 	
1.5 	2.215 	2.32 	2.38 	2.40 	2.41 	
2.0 	2.15 	2.29 	2.35 	2.38 	2.39 	
2.5 	2.08 	2.245 	2.32 	2.36 	2.38 	
3.0 	2.01 	2.20 	2.30 	2.35 	2.375 	
For the case in hand,
Q, = Q(l+orf)=  12 m3 77X7.606 = 97 m3 14
451 cu ft   X 7.606 = 3430 cu ft
5 = 5 m 00 (16.4 ft) or 4 m 650 (15.25 ft)
Z=1800°C. (3275° F.)
A = 3.53 and 3.48 (approximately for metric units)
= 2.37 and 2.34 (approximately for English units)
The formula may now be written with numerical values, as
follows:
For 5=5m 00 (16.4ft),
Or, for English units,
For 5=15.25 ft (4m 65),

34302
15.252X1800
, = 2.34^-

= 7.11 ft (2m 169).

This will be the distance from the surface of the bath to the
center of gravity of the roof segment; it will give an approximate
height of the skewbacks above the door sills of 5 ft 4 in (1630 mm)
for the wider chamber and 5 ft 7 in (1700 mm) for the narrower
chamber.
With a chamber area of 65 m2 00 (700 sq ft) the chamber
volume will be approximately 144 m3 00 (5087 cu ft) for the

258	APPENDIX VII
wider chamber and 149 m3 50 (5280 cu ft) for the narrower cham-
ber. The gases will remain in the chamber approximately 1.50
seconds, which, with a temperature drop of 200° C. (360° F.) per
second, means a temperature of approximately 1500° C. (2732° F.)
for the gases leaving the chamber. Referring to the curve
(Fig. 184) and allowing for a drop in calorific intensity of about
200°, it will be seen that a preheat of the air and gas of between
800° and 1000° C. (1472° to 1832° F.) will be required. Allowing
for a possible loss of temperature in the necks, cinder pockets and
uptakes, the checkerwork will be proportioned to supply a preheat
of 1200° C. (2192° F.).
The distance the jet of flame must drop below the bridge or
port sill, in order to permit 'the sintering of the bottom, has been
fixed at 1200 mm (48 in). A resultant velocity of the air and gas
can be assumed, and this will fix the resultant angle of the two
jets. The higher the resultant velocity is assumed, the less the
resultant angle will be, and the further beyond the center of the
chamber will be the point where the maximum depression of the
jet of flame occurs.
High velocities, in addition, cause the incoming end of the
chamber to work cold and the outgoing end to work hot, while
it is desirable that both ends of the chambers work as uniformly
as possible. High velocities for either the gas or the air mean
reduced port areas, and high velocities for the outgoing products
of combustion, which in turn call for an increased draft depression
in order to pull the gases through the ports. This draft depression
creates a suction acting to pull air in through the valves, flues
and chamber walls. At the same time, it is necessary to have
sufficient draft to draw the waste gases out of the chamber and
down through the checkerwork, but the lower this draft depression
the less the tendency to induce air leakage or infiltration.
As the flame has to drop 1200 mm (48 in) in one-half of 14 m 00
(46.00 ft), which is the length of the furnace, an angle somewhat
greater than 10° must be allowed for the trajectory of the jet.
Yesmann's formula for this case is
.., , .	Tr   *>2sin2 8
Metric:	H = —	X
2g	m-t
r?    r u	tt    ^2sin2 5    459+*,
English:	H =	X -—--*,

DESIGN OF OPEN-HEARTH FURNACES	259
in which H = the middle ordinate of the parabola, in this case
1 m 200 or 4.00 ft;
*; = the resultant velocity of the two jets uniting to form
the flame;
sin 5 = the sine of the resultant angle of the two jets;
2g = gravitational  constant = 2X9.81 = 19.62  in metric
units or 2X32.2 = 64.4 in English units;
ti = the temperature of the gases within the chamber;
Zm = the temperature of the gases in the jet of flame.
When a furnace is heating up, the stream of flame tends to
follow the roof, until the interior of the chamber becomes raised
to a temperature sufficient to permit it to drop, and the drop of
the flame is an index of the progress made in heating the furnace.
It is likewise desirable to be able to sinter the bottom, when the
furnace, for any reason, is cooler than usual, or the ports are
eroded. The temperature of the jet of flame, tm, may be assumed
as 1800° C. (3272° F.) and that of the gases in the chamber as
800° C. (1472° F.)=fc; velocities of 0=15 m 00, 20 m 00 and
25 m 00 (49.2, 65.6 and 82.0 ft) per second will be tried out in the
formula, solving for sin 5. The resultant angle for these velocities
will be as follows:
For v = 15 m 00 (49.2 ft) per second, 5 = 18° 12'
2; = 20 m 00 (65.6 ft) per second, 5 = 13° 33'
y = 25 m 00 (82.0 ft) per second, 5 = 10° 46'
In solving to obtain these angles
fc = 800° C. (1472° F.)    273+*, = 273+800 = 1073
2m-Z<= 1800-800 = 1000
#=lm200 (4.00ft)    20 = 2X9.81 = 19.62
The formula may now be written:
«? sin* SX1078
n-*-•*>     19.62X1000 '
which becomes		
.    s       /2T794   4.684
sin 5 = A/—~— =	.
\    v2	v
For v=15 m 00 (49.2 ft) per second, sin 5 = 0.3123
v = 20 m 00 (65.6 ft) per second, sin 5 = 0.2342
v = 25 m 00 (82.0 ft) per second, sin 5 = 0.1873

260

APPENDIX VII

These computations may be made in the English units, if desired.
Should U be given a higher value than 800° C. (1472° F.), the
angle will be less. Two components may be selected to suit the
resultant angle and velocity, but this cannot be intelligently done
until the pressures available for impressing velocity upon both
the gas and the air have been approximated. For the air, the
pressure available will be entirely due to the chimney effect of the
system, diminished by the resistance to the flow of the air, unless
a fan is used. The same pressure is available in the case of the
gas, plus the pressure in the gas main, which is more or less under
control through the steam blower on the producer. In order to
determine the chimney effect, it is necessary to obtain the height
of the regenerator.
In a previous chapter several empirical rules were given for the
amount of checkerwork required. According to Gruner, from
50 to 70 kg (50 to 70 Ib) of checker brick are required per kilogram
(pound) of coal burned per reversal. In the case considered,
5 m3 32 (188 cu ft) of gas is to be used each second, each kilogram
of coal producing 4 rn3 39 of gas (70 cu ft of gas per pound).
The coal consumption, therefore, is 1 kg 212 (2.686 Ib) per second.
The weight of checker brick for this amount of coal would be from
60 to 85 kg (135 to 188 Ib). According to this rule, the amount of
checker brick would be:
TABLE 14

	50 to 1 	70 tol 	
For 15-min  (900-sec.) reversals    .             > 	54,540 kg 	76,360 kg 	
For 20-min. (12 0-sec.) reversals 	 s 	120,220 Ib
72,720 kg 	168,320 Ib
101,810 kg 	
For 25-rnin  (1500-sec.) reversals ....         \ 	160,300 Ib
90,910 kg 	224,430 Ib
127,250 kg 	
	200,410 Ib 	280,550 Ib 	
Told suggests 6 m3 00 (212 cu ft) or 2850 kg (6283 Ib) of brick
per cubic meter (35.3 cu ft) of air per second per 100° C. (180° F.)
rise in temperature. According to this rule, the checker brick
would be
2850X8.51X9=218,250 kg (478,900 Ib)
6X8.51X9 = 459 m3 55 (16,228 cu ft)

DESIGN OF OPEN-HEARTH FURNACES

261

This last is reasonably close to the quantities arrived at,
providing Told referred to the chambers at one end only.
The weight of the checker brick will be determined upon the
basis of a temperature change of 100° C. (180° F.), 70 per cent
of the brick being considered effective. The average specific heat
of firebrick is about 0.25; its weight is about 1800 kg. per m3
(112 Ib per cubic foot).
The regenerator computations are made as follows:
TABLE 15

	Gas
Checker
on
Gas 	Air
Checker
on
Air 	Gas
Checker
on Waste
Gases 	Air
Checker
on Waste
Gase 	
Temp, top of checkerwork, C. . . .
F 	
Temp, bottom of checker,   C. . . .
F 	
Average temperature, C 	1200°
2192°
500°
932°
850° 	1200°
2192°
300°
572°
750° 	1600°
2912°
800°
1472°
1200° 	1600°
2912°
600°
1112°
1100° 	
F      	 	1562° 	1382° 	2192° 	2012° 	
Temperature increase or decrease
in checker, C   . . . 	700° 	900° 	800° 	1000° 	
F ..    .   	 	 	1260° 	1620° 	1440° 	1800° 	
Heat capacity in calories per cubic
meter from curve (Fig. 184) :
Waste gases at 1600° 	 			16,32 	1632 	
Air or gas at     1200° .- 	 	445 	646 			
Waste gases at    800° 	 			711 		
Waste gases at   600° 	 				518 	
Gas at                 500° 	 	166 				
Air at                   300° 	 		148 			
Calories absorbed by gas and air or
given up by waste gases 	
Assuming 2 m3 00 (70.6 cu ft) of
gas are burned: 279X2= . . . 	279
558 	492 	921 	1114 	
492X2= 	 		984 			
Total: Required   558+ 984 =
Available 921 + 1114 =
Percentage required for gas:
558-^-1542 = 	 	15
36.19 	42 	20 	35 	
Percentage required for air:
984-4-1542= 	 		63.81 			

262

APPENDIX VII
TABLE 16

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Calories available for gas checker
2035X0.3619=     	 			736 		
Calories available for air checker
2035X0 6381 = 				1299 	
Percentages for air and gas:
736-f- 921 = 			79 91 		
1299-f-1114 = 				116 61 	
Correction to make sum 200 	 			1 41 	2 07 	
Corrected values 			81 32 	118 68 	
Reducing to 100% basis 	 			40 66 	59 34 	
Calories per cubic meter of gas
burned-    921X0 4066=   . 			374 		
1114X0.5934= 	 				661 	
Calories required by preheat 	 	279 	492 			
Volumes of gas, air supply and
products of combustion:
Gas at 0° 760 mm 	 	5 m332 				
Air at 0° 760mm 	 		8m3 51 			
Products of combustion:
12.77X0.4066= 	 			5m3 19 		
12.77X0.5934= 	 				7 m358 	
Calories per second required:
5.32X279= 	 	(188 cu ft
' 1484 	(300 cu ft) 	(181 cuft) 	(270 cuft) 	
5.32X492= 	 		2618 			
5.32X374= 	 			1990 		
5.32X661 = 	 				3516 	
Calories per cycle:
15 minute = 900 seconds 	1,335,COO 		1,791 000 		
20 minute = 1200 seconds 	 	1,781,000 	2,356,000 	2,388,000 	3,164,000 	
25 minute = 1500 seconds 	 	2,226,000 	3,141,000 	2 985 000 	4,219,000 	
		3,627,000 		4,974,000 	

DESIGN OF OPEN-HEARTH FURNACES
TABLE 16—Continued

263

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Weight of checker brick required to
store up heat   in waste gas
(100° change in brick temper-
ature 70% effective):
15-minute cycle:
Gas
[1 791 000 ~(100XO 25)] -7-0 7 = 			102,350kg 		
Air:
[3,164,000 -r (100X0.25)] -v-0.7 = 				180,800kg 	
20-minute cycle:
Gas:
[2,388,000 -5- (100X 0.25)] -s-0.7 = 			136,460kg 		
Air:
[4 219 000 -r (100X0.25)] -^0.7 = 				241,100kg 	
25-minute cycle:
Gas
[2 985 000 — (100X0 25)] -5-07 = 			170,600kg 		
Air:
[4 974 000 -r (100X 0 25)] -5-0.7 = 				284,300kg 	
					
Any change in the base assumptions made will alter these
values in a corresponding manner. The change in temperature
of the gas, air and waste gases will vary the quantity of heat
available. The cyclic change in temperature may be varied;
this will change the volume of brick required to store up the heat,
and the surface required for heat interchange. The heat-storage
capacity must be sufficient to supply the desired preheat, as well
as the loss through the chamber walls, when on air or gas. Too
much checker adds to the first cost; too small a checker increases
the operating cost. The conditions will be changed by the use of
other fuels, as well as by changes in the ratio of the air supply.

264

APPENDIX VII

TABLE 16—Continued

	Gas on
Gas 	Air on
Air 	Gas on
Waste Gas 	Air on
WasfceGas 	
The   volume   occupied    by    the
checker brick will be = weight
Xy-gVo~:
15-minute cycle = . . . 			56 m3 86
75 m3 82
94 m3 78
5m3 19
1200°
5.4040
28 m3 05
-S00°
4.00 	100 m3 90
133 m3 94
157 m3 38
7m3 58
1100°
5.0370
38 m3 18
-1000°
5.00 	
20-minute cyclic ==.... 			

25~minute cycle = . . . . 			

Pass volume in choekerwork :
Qn of gan, air, waste gases . 	5m3 32
850°
4.1195
21 m3 92
+700°
3.50
76 m3 72 	8m3 51
750°
3.7525
31 m3 93
-1-900°
4.50
143 m3 68 	

t° average in checker. . . . 	

	
	
1-Kd for average /° 	
QoX(l +<*/) = 	 	

	
	
Temperature change. . 	

	
	
Average; lim ! in checker seconds,
200° per second change in L . .
Basing pass volume on gas and air
heating time, the pass volume =
Average time in checkers of waste
ga,seH, revised to pass volume,
seconds 	 	

	

	
	
	2.735
4775 cu ft
5372 cu ft
6040 cu ft 	3.763
8613 cu ft
9778 cu ft
10600 cu ft 	
Total checker volume:
15-minute cycle 	 	133 m3 58
152 m3 54
171 m3 50
42.57
57.43
49.70
50.29
55.26
44.74
0.6689 	244 m3 58
277 m3 62
301m 3 06
41.26
58.74
48.25
51.75
52.28
47.72 	

20-ininute cycle. 	 	 	

	
	
25-mirmte cycle 	 	

	
	
Percentage of Hpaec occupied by
Brick, lf)-miuute cycle 	
PasB 	      .   . 	

	

	

Brick, 2Q-tninute cycle 	 	

Pass 	 	

Brick, 25~minuto cycle 	 	

Pans 	 	 	 	

In order to provide a margin for all
possible  contingencies,   the 25
minute, cycle will bo used
lining square paHHCH, the diameter
of unit piiHH = \/() 4474 ~ 	 	

= v'o "4772 = 	 	
	0.6808 			
Brick = 1 0000 — 0 0080= 	 	0.3311 	
			
1  000') — 0 0808= 	 	
	0.3192
7. 5 in.
2. 5 in
5.0 in 			
Make both alike tmHedongas, using
a 2.f> in. (f».'J mm.) briek:
Dim<insion of unit  pass = 63-=-
0   ,'W = h =r                                  	 	190mm
63mm
127mm 	
			
Brick thiekncKH    , . . 	 	 	

Diameter square pa«B 	 	

DESIGN OF OPEN-HEARTH FURNACES

265

The pass unit will be different for a different wall thickness,
and it may be desirable to try several variations, in order to secure
the most desirable arrangement. An old rule is that the active
heat-storage capacity of brickwork is comprised in the depth of
1.25 in from the surface, giving a wall thickness for maximum
results of 2.5 in (63 mm). When the brickwork is laid up to
secure stability, 9-in straights give very good results. With
thicker walls the time of the cycle must be increased, to develop
the full weight of the brickwork. With the time cycle assumed,
which agrees fairly closely with practical working, a wall thickness
of 2.5 in (63 mm) utilizes its full heat-storage capacity. With a
fifteen-minute cycle a 2-in wall would be desirable, but is probably
a little too thin to give the best operating results.
TABLE 16—Continued

	Gas
on
Gas 	*Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
By using a 2-in (50 mm) brick, the
size of the pass and the space
occupied will be reduced :
50-7-0.33=?;= 	 	150 mm 	6 0 in 			
Brick thickness 	 	50 mm 	2 0 in 			
Diamet r square pass 	 	100 rnm 	4.0 in 			
Wall thickness around pass ..... 	63 rnm 	2 5 in 	50 rnrn 	2 0 in 	
Area unit pass = 62 = 	 	0 m2 0361 		0 m2 0225 		
Area of pass opening = 	 	0 m2 0162 		0 m2 0100 		
Area occupied by brick = 	 	0 rn2 0199 		0 m2 0125 		
As the unit pass was made the same,
the volume of brick and pass
in  the   air   checker  will  be
changed to
Brick = 301. 06X0. 5526= 	 	166 m3 37 				
Pass =301.06X0.4474= 	 	134 m3 69 				
The lineal amount of pass and brickwork is found by dividing
the brick and pass volumes by the area of the brick and pass in
the pass unit. It will generally be found that there is a slight
disagreement between the lengths determined for the pass and the
brickwork. It is preferable to take the highest of the values so
found for determining the size of the space to be occupied by the

266

APPENDIX VII

cheekerwork. Another variant which will affect the actual
checkerwork lies in the number of pass units making up the
length and width of the chamber.
TABLE 17

	Gas
Checker 	Air
Checker 	
The lineal amount of pass and brickwork required
will be determined:
For 63 mm (2.5 in) walls:
Brick for gas= 94 78-^0 0199=      	 	4,763 m 00 		
air =166 37 -=-0 0199 = 		8,361 m 00 	
Pass for gas      = 76 72-7-0 0162=        	 	4,736 m 00 		
air       = 134 69 -r 0.0162 = 	 		8,314m 00 	
For 50 mm (2.0 in) walls:
Brick for gas = 94 78-?-0 0125 = 	7,830m 00 		
air =166 37 -~0 0125=        	 		13,309 m 00 	
Pass for gas = 76 72-7-0 0100 = 	7 672 m 00 		
air   =134 69-r-O 0100=          ..   . 		13 469 m 00 	
The heating surface available in these checkers
will be:
For 63 mm (2.5 in) wall:
4763.00X4X0 127= 	 	2,419 m2 00 		
8361.00X4X0.127= 	 		4 247 m2 00 	
For 50 mm (2.0 in) wall:
7,830.00X4X0.100= 	 	26,028 sq ft
3,132m2 00 	45,680 sq ft 	
13,469.00X4X0.100= 	 		5 388 m2 00 	
The corrected volume of checkerwork will be:
For 63 mm (2.5 in) wall:
4763.00X0.0361 = 	 	33,715 sq ft
171 m3 95 	58,000 sq ft 	
8362.00X0.0361 = 	 		301 m3 82 	
For 50 mm (2.0 in) wall:
7,830.00X0.0225 = 	 	6,073 cu ft
176 m3 18 	10,657 cu ft 	
13,469.00X0.0225= 	 		303 m3 02 	
	6,225 cu ft 	10,703 cu ft 	

DESIGN OF OPEN-HEARTH FURNACES
TABLE 18

267

	Gas
Checker 	Air
Checker 	
A checkerwork height has been assumed, in order
to illustrate the effect of a high checkerwork.
On this basis:
The number of passes required will be determined
by dividing the lineal amount of pass required
by the height of checkerwork:
n for gas =4763 -f-7 . 00 = 	 	681 		
n for air =8361 -=-7. 00= 	 		1195 	
Any desired length or width of chamber that will
contain the number of passes may be selected.
When a square pass is used, it is necessary
that the chamber dimensions should be mul-
tiples of the pass dimension, plus one wall.
The length of both chambers will be alike.
Let n = number of passes in length of chamber,
then Z = 190n+63.
Assume n =40, then the length of the chamber
will be: 190X40+63=             	 	7 m 663 	25 14 ft 	
For the width of the chambers, n may be assumed
as some number which will give a number of
passes slightly in excess of that computed
above.    For the case in hand, let n = 18 for
gas and 30 for air.    The corrected number of
passes will be, therefore:
40X 18 for gas = 	 	720 		
40X 30 for air == 	 		1200 	
The width of the chambers required will be :
For gas- 190X18+63 = 	3 m 483 		
For air:  190X30+63 = 	 		5m 763 	
The area occupied by the checkerwork will be:
For gas: 7.663X3.483= 	 	11.425ft
26 m2 69 	18.90ft 	
For air: 7.663X5.763= 	 		44 m2 16 	
The corrected checkerwork volume will be:
For gas: 26.69X7 00= 	 	287. 4 sq ft
186 m3 83 	475. 4 sq ft 	
For air: 44.16X7.00= 	 		309 m3 12 	
	6602 cu ft 	10,916 cu ft 	

268

APPENDIX VII

TABLE IS—Continued

	Gas
Checker 	Air
Checker 	
The heat surface per pass was computed as 	
The corrected value for total heating surface will be :
For gas- 3 556X720 = 	3 m2 556
2560 m2 00 	3 m2 556 	
For air* 3 556X 1200 =    	 		4267 m2 20 	
The corrected total area of the passes will be:
For gas* 0 0162X 720 = 	27,558 sq ft
11 m2 664 	45,935 sq ft 	
For air- 0 0162X1200=       	 		19 m244 	
The corrected average velocity per second of the
gases will be :
For gas: 21 92-r-ll 664= 	 	125. 58 sq ft
1 m 879 	209.32sq ft 	
For air* 31 93-f-19 44 = 		1 m 642 	
For waste gases: 28 05 -r- 11 . 664 	 	6.17ft
2 m 405 	5.38ft 	
38 18-^19 44  = 		1 m 964 	
	6.71ft 	6.44ft 	
TABLE 19

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
The heat transfer, total per second, 					
in calories is. . 	1484 	2,618 	1990 	3,516 	
in B.t.u. is   	 	5900 	10,400 	7900 	13,900 	
Calories per sq m per second 	 	0.5797 	0.6135 	0.7773 	0.8239 	
B.t.u. per sq ft per second 	 	0.214 	0.226 	0.287 	0.306 	
Average temp, differential brick to 					
gas or gas to brick, C 	175° 	175° 	175° 	175° 	
F. . 	315° 	315° 	315° 	315° 	
Convection factor to still air, ac- 	f 				
cording to curve plotted from 					
Langmuir's   experiments   (Fig. 					
164) is calories per m2 per second 	0.294 				
Correction factor for velocity == 					
/35+u 	2.516 	2.384 	2.803 	9  ^RQ 	
\   35       	 				u . O\J*j 	
v — velocity in cm per second. 					
Convection corrected for velocity: 					
in calories per m2 per second . . . 	0.7397 	0.7009 	0.8241 	0.7553 	
in B.t.u. per sq ft per second . . . 	0.273 	0.258 	0.304 	0.278 	

work
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Convection in Gramme Calories per cm 2/sec.—Still Air at 27°
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velocity of flow equals K =
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270

APPENDIX VII

at 27° C. (80° F.).    Whether these assumptions are correct cannot
be determined without further research.
In the foregoing, a checker work of square passes has been
assumed. The method of arriving at the heating surface of the
usual checker construction is somewhat similar to the above.
B. t. u. per sq. ft. per second
naao	o        0.1       Q.9      0.3      0.4      O.S     0.6     0.7     0.8     0.9       1.0    1.1       1.2     1.3
752    400
572    300"
392    200
212    100

F       C

0.5	1.0	1.5	2.0	2.5
Calories per m2 per second

3.0

3.5

fig. 165.—Curve of Heat Loss from Exterior Walls of Furnaces According
to Experiments of Charles R. Darling.
The bricks occupy 0.5526 of the volume and the pass 0.4474;
hence the number of rows per meter will be
nb=552.6 -^63 ==8.771 rows
or	0.5526-^0.21 = 2.63 rows per foot.
The gauge or space between the rows of brick will be
b0=447.4 -f-8.771 = 51 mm (about 2 in)
or	0.4474+2.63 = 0.17 ft (about 2 in).
From these figures the heating surface per square meter, or
per square foot, may be readily computed, as well as all of the
other data necessary to determine the sizes of the checker cham-

DESIGN OF OPEN-HEARTH FURNACES

271

bers for gas and air. When properly laid to secure stability, the
9-in straight makes a checker with the maximum heat storage
utilization of the volume occupied.

All of the computations are based upon an assumed rate of
fuel consumption, and will vary as that rate changes. Other
variations will be introduced by the use of different fuels and
different working conditions, than those which were fixed initially
as a basis for the computa-
tions. However, there is no
basic reason why the design
of a furnace cannot be reduced
to rational methods. When
the method of operation and
the design are fixed, it is
possible to   predict   the fuel ^       __      -- xu  ,    ,   _    .
^	. , .	fig.    166. — Method   of    Laying   Up
consumption within a reason-     Checker   Brick  to   Form   Vertical
able margin,   as well  as  the     Passes.
performance of the furnace as
a  heat-transfer  apparatus.    The  main  difficulty  in  obtaining
accurate  results  with  these  computations—results  which  will
check with practice—lies not in the computations, but in the

Waste 	1 	— p.
1
I 		M 	
Heat 		 				
Boiler 	1 				
	i 				

"Damper
Fan

fig. 167.—Schematic Arrangement of Flues and Dampers with
Waste-heat Boiler.
initial assumptions, for unless the foundation is. true the entire
superstructure will be wrong. For instance, in computing the
heat losses from the exterior walls of the furnace and chambers,

272	APPENDIX VII
the exposure to stray air currents and variations in the cycle of
operation introduce complex variables which are difficult to
consider. When the cycle is fixed and proper allowance made for
the exposure, these losses may be reduced to mathematical
analysis.
The frictional resistance in the checkers and flues may be
approximated by the formula of Mojarow.    This formula is
SL
in which 7 = the frictional resistance expressed in inches of water
or, if the metric system is used, millimeters of
water or kilograms per square meter;
m = coefficient of friction, as determined by Mojarow =
0.003076 for English units or 0.016 for metric
units. This coefficient was determined by obser-
vations on a Cowper hot-blast stove. Murge
fixed a coefficient for mine galleries of one-third
these values — namely, 0.001026 for English and
0.0053 for metric units;
S = perimeter of passage or summation of the perimeters
of passages through which the gases flow;
L — length of the passage or flue;
SL = total surface  of passage or flue in contact with
flowing gases;
co = cross-sectional area of the passage; or, where this
varies, the mean sectional area; or, where the
stream of gas does not fill the flue, the area of the
flowing stream;
vt = average velocity of flow per second at t°;
p* = specific weight of a unit volume of gas at t°;
t = average temperature of the flowing gas in the section
examined.

DESIGN OF OPEN-HEARTH FURNACES

273

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Frictional resistance in checkers:
SL = heating surface = m2 == 	 	2560 	4267 5 			
co = total area of passes m2 	 	11.664 	19 440 			
$ L ~i~ w == 	219 5 	219 5      t 			
vt = velocity m per sec 	1 879 	1 642 	2 405 	1 964 	
ao = specific weigh *"< gases 	1  125 	1 293 	1 320 	1 320 	
t° =s average temperature . 	850° 	750° 	1200° 	1100° 	
1 -\-<xt ==gas factor for t° = . 	4 1195 	3 7525 	5 4040 	5 0370 	
Aj = Ao-J-(l+aO = 	 	0.2731 	0 3445 	0 2443 	0 2621 	
y=kg per m2 friction loss
X =0.016X219.5X 1.879X0.273 = 	1 kg 802 				
0.016X219.5X1.642X0.3445 = 		1 kg 987 			
0.016X219.5X2.405X0.244  = 			2 kg 064 		
0.016X219.5XL964X0.2621 = 				1 kg 808 	
					
As the gases enter and leave the checkerwork they make a 90°
change in their direction of flow, which is equivalent to a total
absorption of their velocity head. The pressure necessary to
impress upon the flowing gases their velocity in the checkers will be:

	Gas 	Air 	Gas on 	Air on 	
	on 	on 	Waste 	Waste 	
	Gas 	Air 	Gas 	Ga 	
h =vt-r- 2g~ meters of gas   olumn. 	0.180 	0.137 	0.295 	0.197 	
5 == h&t — kg per m2 = 	 	0. 49 	0.047 	0.072 	0 052 	

274

APPENDIX VII

	Gas
Checker 	Aii-
Checker 	
Flues below checkerwork and walls :
Chamber width . 	3 m 483 	5 m 763 	
Number of 115-mm walls                             .       	 	5 	9 	
Number of 465-mm flues 	 	6 	10 	

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Fractional resistance in flues below
checker work:
t° = temp. below checkerwork. . .
l-\-cd = 	500°
2 835 	300°
2 101 	800°
3 936 	600°
3 202 	
Qo 	5m3   32 	8 m3   51 	5 m3   19 	7m3   58 	
	15m3   08 	17m3   88 	20m3   43 	24m3  27 	
B — width of flues total 	2 m 790 	4m 650 	2 m 790 	4m 650 	
H = height of flues 	1 m 000 				
Total length of chamber 	7m 663 				
The resistance to flow is about
equivalent to the full volume
for one-third of the length L = 	2.554 				
S= perimeter of flues, total. . . 	17.580 	29.300 			
65 = area of flues, total 	 	2.790 	4 650 			
SL = exposed surface m2 	 	44.90 	74.83 			
	16.09 	16 09 			
aq = specific weight gas 	1 125 	1 293 	1 32 	1 32 	
At=AQ~(l+at) =kg per m3. . . 	0.397
5 404 	0.615
3 84 	0.335
7 324 	0.412
5 22 	
Y/= friction loss in kg per m2 =
0.016X16.09X5.404X0.397 = 	0 kg 553 				
0.016X16.09X3.840X0.615 = 		0 kg 548 			
0 016X16 09X7 324X0 335 = 			0 kg 632 		
0.016X16.09X5.220X0 412 = 				0 kg 554 	
The pressures requisite to impress
their velocity on the gases in
the flues below the checker-
work:
d=At(vt2+2g) =kg per m2= . . . 	0.590 	0.460 	0.916 	0.570 	

DESIGN OF OPEN-HEARTH FURNACES

27-5

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Space required in chamber above
checkerwork   by   Yesmann's
formula, which was used in
obtaining the height  of the
heating chamber
For the case in hand:
qq — volume of gases per second
1° = temperature 	 	5m3   32
1200° 	8m3   51
1200° 	5m3   19
1600° 	7m3  58
1600° 	
1 -{-at = gas temperature factor ....
Qi=Qo(H-«£) = ... 	5.404
28 m3   75 	5.404
45 m3   99 	6.872
35 m3  66 	6.872
52 m3  08 	
0,2=       	 	827 	2115 	1272 	2712 	
B — width of chamber = 	3m 483 	5 m 763 	3 m 483 	5 m 763 	
B2= 	 	12.13 	33.21 	12.13 	33 21 	
BH=-                         	 	14,543 	39,852 	19408 	53 135 	
Q?-i-Bn=      .        	 	0 05686 	0 05306 	0 06555 	0 05104 	
					
<\/Qt* + BH = X= 	
A ~~ coefficient 	0.3845
3 40 	0.3758
3 53 	0.4032
3 40 	0.3710
3 53 	
ht = AX   . 	1 m 306 	1 m 327 	1 m 372 	1 m 310 	
Rise of arch over chamber 	 	0 m 420 	0 m 700 			
Checker to skewback 	 	1 m LSO 	0 m 900 			
Chamber above checkerwork:
The  frictional  resistance  to  the
flow of the gases will be about
equivalent to the full volume
for one-third the length
m = coefficient of friction = . , .
• S = perimeter = (2X3. 483) +
(2X1 250)== 	0.016 		9 466 		
L — length        	 			2 554 		
8 = perimeter = (2 X 5 . 763) +
(2X1 250) = 				14 026 	
w = area = 3. 483X1. 250=... 			4 354 		
co = area = 5. 763X1. 250 = ... 				7 203 	
SL+u= 9.466-^-4.354 = 	 			2 174 		
£L-r-co = 14 026-T-7 203= 	 				1 947 	
^ = Qjj -t- co = m per sec 	 	6.60 	6 39 	8 19 	7 23 	
ao — specific weight gas .       . . 	1 125 	1 293 	1 32 	1 32 	
A;=A0-KH-<*0 kg per m3. . . 	0.2082 	0.2393 	0.1921 	0.1921 	

276

APPENDIX VII

	Gas 	Air 	Gas on 	Air on 	
	on 	on 	Waste 	Waste 	
	Gas 	Air 	Gas 	Gas 	
-y=frictional resistance in kg per 					
0.016X2.174X6.60X0.208 = 	0 kg 048 				
0 016X1 947X6 39X0 239 = 		0 kg 048 			
0.016X2.174X8 19X0 192 = 			0 kg 055 		
0 016X1 947X7 23X0 192 = 				0 kg 043 	
7 may be considered as kg per 					
m2 or as mm of water 					
The pressure required to create the 					
air and gas velocity above the 					
checkerwork = 					
5 = (vf ~s-20) Aj kg per m2 	 	0 kg 462 	0 kg 498 	0 kg 657 	0 kg 512 	
The height from the bottom of the checker chambers to the
port sill or bridge of the furnace can now be fixed from dimensions
that have been determined. This permits the approximation of
the chimney effect of the checkers and uptakes. The height will
be found as follows:

Flues below checker chamber 	 	1 m 000 	3 280 ft 	
Checkerwork height 	 	7m 000 	22.963ft 	
Checker to arch at center 	1 600 	5 249 	
			
J^rom bottom of arch to port sill 	9 m600
3m 000 	31.492ft
9 844 	
			
H — total height to port sill 	 	12 m 600 	41.336ft 	

Chimney Effect of Checkers
and "Uptakes 	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
5 ^^(Aair — Agas t°) 	 					
£ ° = average temperature 	850° 	750° 	1200° 	1100° 	
1 -^.(xt = gas factor 	 	4 1195 	3 7525 	5 4040 	5 0370 	
Ao = specific weight of gases ....
Afgass=Ao-s"(l"r'**0 kg perm3 	 	1.125
0.273 	1.293
0 345 	1.32
0 244 	1.32
0 262 	
a&it = specific weight of air 	 	1.293 				
Aair — Ajgag = kg per m3 	1 020 	0 848 	1 049 	1 031 	
$1 = 12.60X1.02  =kgperm2.. 	12 kg 851 				
52 = 12 60X 0.848= kg per m2 		10 kg 683 			
53 = 12. 60X1. 049=kg per rn2. . 			13 kg 217 		
54 = 12. 60X1. 031 =kg perm2. . 				12 kg 990 	

DESIGN OF OPEN-HEARTH FURNACES

277

The gas and air necks, the cinder pockets and the uptakes are
next in order. The efficiency of the cinder pocket depends upon
the change in the direction of the flow, as well as upon the reduc-
tion in the velocity of flow. The width of the pockets fixes the
taper of the necks. Both pockets will be made the same width,
say, 2 m 00 (6.56 ft) with a space of 1 m 250 (4.10 ft) between
them. The gas neck will be 3 m 00 (9.84 ft) wide where it leaves
the chamber, tapering to 2 m 00 in a distance of about 3 m 750
(12.3 ft). The air neck will taper from a width of 5 m 00 (16.47 ft)
to 2 m 00 (6.56 ft) in the same distance. These figures have been
fixed arbitrarily and the assumption made that the same or
greater areas will exist than above the checkerwork.

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Air and gas necks: 					
The frictional resistance will be 					
based on the following: 					
Z/= length of neck    . . 	3 m  750 	4m 000 			
S= perimeter average. .  .   . 	9 m 000 	11 m 000 			
SL = surface 	 	33.75 	44.00 			
co = area in square meters 	5m2   00 	7m2   00 			
OJL/ ~f- CO = . .                .                  .                   .... 	6.75 	6 28 			
Qt — volume of gases flowing . . 	28m3   75 	45m3   99 	35m3   66 	52m3   08 	
vt = Qt -:- co = m per sec 	5m    75 	6m    57 	7m    13 	7m    44 	
Aj = kg per m3 gas 	 	0.208 	0.239 	0.192 	0.192 	
7= frictional resistance in kg per 					
0.016X6 75X5.75X0.208 = 	0 kg 129 				
0 016X6 28X6 57X0 239 = 		0 kg 144 			
0 016X6 75X6 57X0 192 = 			0 kg 147 		
0 016X6 28X7 44X0 192 = 				0 kg 144 	
The gas velocity in the necks is 					
slightly less than in the cham- 					
ber above  the  checkerwork 					
and is assumed the same as in 					
the cinder pockets.   The pres- 					
sure in kilograms per m2 re- 					
quired to impress these veloci- 					
ties on the waste gases will be : 					
5=Aj(w/2-7-20) —kg per m2= . . . 	0.354 	0.525 	0.495 	0.543 	

278

APPENDIX VII

The frictional resistances met with in the cinder pockets will
be assumed as equal to those computed for the neck.
The uptakes will be proportioned as follows, and their frictional
resistances computed:

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Qt — volume of gases flowing . .
Vi ~~ velocities assumed 	 	28 m3 75
15 m/sec 	45 m3 99
10 m/sec 	35 m3 66 	52 m3 08 	
co = area of uptake, total .... 	2m2 00 	4m2 60 			
N ~~ number of uptakes 	1 	2 			
2^ — velocity, actual          .... 	14m    4 	10m  00 	17 m  83 	11 m 32 	
$ = perimeter (assumed) .... 	5 m  00 	12 m    0 			
L ~~ height = 	3 m  00 				
$£ _•_ w —                                        .... 	7 50 	7.83 			
7 — frictional resistance in kg per
m2 =
0 016X7 50X14 40X0 208 = 	0 kg 360 				
0 016X7 83X10 00X0 239 = 		0 kg 300 			
0 016X7 50X17 83X0 192 = 			0 kg 411 		
0 016X7 83X11 32X0 192 = 				0 kg 274 	
The pressure necessary to impress
their velocity upon the flow-
ing gases will be*        	 					
— A<(i)2 — '2(]} — Irgr t\qt rn~ 	2 kg 199 	1 kg 219 	3 kg 111 	1 kg 254 	
					
The assumption is made that the turn into the uptakes for the
incoming gas and air absorbs the velocity in the necks and cinder
pockets.

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Frictional resistance of f antails for 					
air and gas : 					
$= perimeter (assumed) .... 	6 m 00 	10 m  00 			
L =length 	 	5 m 00 	6 m  00 			
C4 = area         	 	3 m2 00 	5 m225 			
t = average temperature. . . . 	500° 	150° 	800° 	600° 	
i _r_ ,y __ ffo s factor 	 	2.835 	1 . 5505 	3.936 	3.202 	

DESIGN  OF OPEN-HEARTH FURNACES

279

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Air 	
Frictional resistance of fantails for
air and gas:
Q0 = volume of gases 	 	5 m332 	8 m3 51 	5 m3 19 	7 ms 58 	
Qt = QQ(l-}~oit) = .   .   . 	15 m3 08 	13 m3 19 	20 m3 43 	24 m3 27 	
i}t = Qt -r- a? = m per sec 	5 m 03 	2 m  51 	6 m 81 	4 m  62 	
A0 = specific weight gases ....
At = Ao -r- ( 1 -\-ctt) = kg per m3. .
£L^co =   . 	1.125
0.397
10 00 	1.293
0.834
11 43 	1.32
0.335
10 00 	1.32
0.412
11 43 	
y = frictional resistance il. kg per
m'- =
0.016X10.00X5.03X0.397 = 	0 kg 320 				
0.016X11.43X2.51X0.834 = 		0 kg 383 			
0 016X10 00X6 81X0 335 = 			0 kg 338 		
0 016X11.43X4.62X0 412 = 				0 kg 359 	
The pressure necessary to impress
their velocity upon the flowing
gases will be:
8 = A/?;/2 -r- Id] = ker ner m2 	 	0.512 	0.268 	0.795 	0.454 	

	Stack
Flue to
Boiler or
Chimney 	Stack
Flue
from Air
Valve 	Stack
Flue
from Gas
Valve 	
Frictional resistance of flues:
L = length in meters 	 	5 m  00 	4m  00 	8 m  00 	
$ s= perimeter in meters 	 	8 m  00 	8 m 00 	7 m  00 	
co = area in square meters 	4m200 	4m2 00 	3 m2 00 	
SL — co =                                  	 	10 00 	8 00 	18 67 	
Qo = volume of gases flowing per sec . . .
t° = average temperature 	 	12 m3 77
630° 	7m3 58
550° 	5m3 19
750° 	
1 ~\~a.t — gas factor      	 	3.312 	3.0185 	3 7525 	
Qf = Qo(l -\-otC) average volume gas 	42 m3 29 	22 m3 89 	19 m3 48 	
vi = Qt-z-(Jl) = velocity m per sec 	10 m  58 	5m 72 	6 m  50 	
ao ^ specific weight of flue gases 	 	1 kg 32 			
ai = ao -r- ( 1 -\-ott} — kg per m3 gas 	 	0 399 	0.437 	0 352 	
7=frictional resistance in kg per m2 =
0 016X10 00X10.58X0.399 = 	0 kg 676 			
0 016X 8 OOX 5 72X0 437 = 		0 kg 320 		
0 016X18 67X 6 50X0 352 = 			0 kg 684 	
The pressure necessary to impress the veloc-
ity upon the gases in these flues will be :
5 = A,(?;,2-~20> =ke t>er m2 = 	 	2.250 	0.730 	0.760 	

280

APPENDIX VII

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Valve resistances : 					
qq= volume flowing  . 	5m3 32 	8m3 51 	5 m3 19 	7 m358 	
t° = average temperature' 	 	500° 	50° 	750° 	550° 	
1 -\-at = gas factor 	 	2.835 	1 . 1835 	3.7525 	3.0185 	
Q/ = Q0(l+aO = . . 	15 m3 08 	10 m3 07 	19 m3 48 	22 m3 89 	
Valve size in inches 	54 in. 	66 in. 	54 in. 	66 in 	
w= valve area 	1m2 48 	2m2 21 	1 m248 	2 m221 	
vt — velocity  through  valve = 					
Qj -t- to = m per sec 	10m 19 	4m 56 	13 m  16 	10 m 36 	
h=vz+2g=. 	5 m 291 	1 m  06 	8 m 83 	5 m 47 	
A0 = specific weight gases . 	1.125 	1.293 	1.32 	1 32 	
Ai = A0-5-(l+aO=kg perm3.. . 	0.397 	1.093 	0.352 	0.437 	
As the gases make a 180° bend in 					
passing through the valve, the 					
velocity   must    be    created 					
twice; therefors, the pressure 					
required will be: 					
5=2/iAz = kgper m2 	 	4 kg 201 	2 kg 317 	6 kg 216 	4 kg 781 	
					
Where changes of direction of flow occur, there is a loss of
pressure, or, more exactly, additional pressure is required to
impress the necessary velocity in the new direction of flow. In
addition, where the gases flow from a larger passage into a smaller,
their velocity of flow increases and additional pressure must be
provided to impress this change in velocity upon the gases. The
pressures necessary for this purpose must be approximated in the
following manner:

DESIGN OF OPEN-HEARTH  FURNACES

281

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Pressures required for impressing velocity
and velocity changes upon flowing gases
in kg per m2 or mm of water:  8 =
Uptakes 	 	2 199 	1 319 	3 111 	1 254 	
Cinder pockets 	            .... 			0 495 	0 543 	
Necks 0.525-0.498= 	 		0 027 			
Chamber above checkerwork 	 	0 462 	0 498 			
0.657-0.495= 	 			0.162 		
Checkerwork 	            .   . 	0 049 	0 047 	0 072 	0 052 	
Flues below checkerwork 	 			0 916 	0.570 	
0 590-0 512 = 	0 078 				
0.460-0.268= 	 		0.192 			
Fantails 	              .... 	0 512 	0 268 			
					
8 total between valves and ports, kg per
m2 or nun of water. . .        .              .   . 	3 300 	2 351 	4 756 	2 419 	
The friction losses = 7 in kg per in2 between
the valves and the ports are:
Uptakes    	              .   . 	0 360 	0 300 	0 411 	0 274 	
Cinder pockets 	0 129 	0 144 	0 147 	0 144 	
Necks 	0 129 	0 144 	0 147 	0 144 	
Chamber above checkerwork 	0 048 	0 048 	0 055 	0 043 	
Checkerwork 	 	1 802 	1 987 	2 064 	1 808 	
Flues below checkerwork 	 	0.553 	0 548 	0 632 	0 554 	
Fantaiis 	 	0.320 	0 383 	0.338 	0 359 	
					
7 total between valves and ports, kg per m2
or mm of water 	 	3 341 	3 554 	3 794 	3 326 	
Valve resistance 5 = kg per m2 	 	4.201 	2 317 	6.216 	4.781 	
5 = velocity pressures between valves and
ports         	 	3 300 	2 351 	'4 756 	2 419 	
7 = friction losses between valves and ports 	3.341 	3.554 	3.794 	3.326 	
Summation, kg per m2 or mm of water . .
Chimney effect of checkerwork, uptakes, etc. 	10.842
12.851 	8.222
10.683 	14.766
13.217 	10.526
12.990 	
Chimney effect available for port velocity,
kg per rn2 or rnm of water 	2 009 	2 461 			
Draft   depression   required   at   reversing
valves, kg per in2 or rnm of water  .... 			27.983 	23.516 	

APPENDIX VII

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Draft depression in kg per m2 or mm of
water B>t reversing valves                .   .... 			27.983 	23.516 	
7= fractional resistance in flue from valve,
kg per rn2                   	 			0.684 	0.320 	
•S— velocity pressure in flue from valves,
kg per m2  	 			0.760 	0.730 	
					
Total draft depression required at point of
junction of flues             	 			29.427 	24.566 	
y = f rictional resistance in flue to stack or
boiler in kg per m2 or mm of water . . 			0.676 		
5 = velocity pressure required for stack flue
— 2 250 — 0 730— kg perm2     .   . 			1 520 		
					
Total draft depression at base of stack or
inlet to boiler kg per m2 or mm of water 			31 623 		

In the foregoing, Mojarow's value for the coefficient of friction
(m = 0.016) was used. This coefficient was derived from observa-
tions made on Massick and Crook and Cowper hot-blast stoves.
.It is probably correct where a considerable portion of the flue
system consists of checkerwork. Murge, however, has deter-
mined the coefficients of friction of air at low temperatures in
mine galleries. The work was done very carefully. The coefficient
is one-third of that obtained by Mojarow, and is probably a closer
approximation when the flues are large and open. A further
confirmation of the fact that Mojarow's value is too high lies in
the fact that, in several cases where furnaces in service have
been analyzed, the computations showed the necessity for forced
draft. These furnaces were in operation without forced draft,
but in a more or less defective manner, giving operating troubles
and having a shorter campaign than normal. Applying Murge's
value for the coefficient of friction, the friction losses are reduced,
as is also the total draft depression required. The revised values
follow:

DESIGN OF OPEN-HEARTH FURNACES

283

	Gas
on
Gas 	Air
on
Air 	Gas on
Waste
Gas 	Air on
Waste
Gas 	
7= friction loss between port and valves,
revised, kg per m2 or mm of water. . . .
d— pressure to impress velocities between
port and valves, kg per m2 or mm of
water ... 	1.114
3 300 	1.185
2 351 	1.265
4 756 	1.109
2 419 	
Valve resistance, 5= kg per m2 	 	4 201 	2 317 	6 216 	4 781 	
					
Summation, kg per m2 or mm of water . .
Chimney effect of checkerwork, etc., kg per
m2 or mm of water . . 	8.615
12 851 	6.853
10 683 	12.237
13 217 	8.309
12 990 	
					
Chimney effect available for port velocity. 	4 236 	3 830 			
Draft depression required at reversing valve 			25.454 	21.299 	

	Gas on
Waste
Gas 	Air on
Waste
Gas 	
Revised figure for draft depression required at reversing
valve, kg per m2 or mm. of water 	       	 	25.454 	21.299 	
7= re vised frictional resistance in flue from valve, kg per m2
or mm of water 	0 228 	0 107 	
5= velocity pressure required in flues from valves 	 	0.760 	0.730 	
Revised total draft depression required at point of junction of
flues kg per m.2 or mm of water 	26 442 	22 136 	
T= revised frictional resistance in flue to stack or boiler,
kg per m2 or mrn of water              	 	0 226 		
8= velocity pressure required in stack flue, kg per rn2 or rnm
of water 	 	1 . 520 		
			
Total draft depression required at base of stack or boiler
inlet, kg per m2 or mrn of water          	 	28 . 188 		
			
The port areas and velocities may now be fixed. In so doing, it
should be borne in mind that the waste gases must pass out
through the gas- and air-ports in proper proportions to supply the
required amount of preheat. This is very rarely accomplished
when chimney draft is depended upon, particularly when the gas

284	APPENDIX VII
is given a high velocity as compared to the air. The angle neces-
sary for the jet of flame to sinter in the bottom will be fixed by the
resultant of the air and gas angles and velocities. That is, either
the air or the gas may be given a maximum velocity; but any
change in air velocity will entail a corresponding change in gas
velocity, and vice versa, as well as a change in port angles, in order
to produce the fixed resultant velocity and angle.
For instance, if the gas-port is lined on the resultant angle,
the gas velocity will be maximum and the air velocity a minimum.
The desirable condition is a velocity which will make the furnace
hot throughout its full length. Frequently the trouble with over-
heated port blocks at the outgoing end is due to the high velocity
of the incoming gases. With a high velocity at the incoming end
a portion of the jet is practically shot into the outgoing port.
In most American furnaces, the air-port forms a segment over
the gas-port; it is claimed that this construction forms a blanket
of cooler air between the jet of flame and the roof. As the entering
air is several hundred degrees cooler than the flame itself or the
hot products of combustion, it is probable that this blanketing
action is largely a matter of the imagination. Cooler gases have
a tendency to sink below hotter gases; but any swift-moving jet
has a tendency to hang together and will cany a layer of colder
gases on top of it; these colder gases will have a tendency to move
diagonally to the edges of the jet, while they are absorbing heat.
The hottest gases, as soon as they escape from the influence of the
jet, lose their velocity and tend to seek the roof of the furnace.
The air pressure available for creating velocity in the port is
3 mm 830 of water (0.15 in water column) due to the stack effect
of the checkers and flues; it is not, however, advisable to utilize
the full pressure available. In the case of the gas, 4 kg 236
(0.166 in of water) are due to the stack effect of the checkers and
flues, but in addition there is the pressure created in the producer,
which may be varied, amounting to one-half inch to one inch of
water (12 to 25 kg per square meter). However, for every unit of
pressure expended in creating velocity in the gas-port, a unit of
pressure must be available at the outgoing port in order to pull a
proportional part of the waste gases through the port. If this
is not the case, the quantity of waste gases passing through the
gas regenerator will be reduced and the amount of heat available
for preheating the gas will be reduced.

DESIGN OF OPEN-HEARTH FURNACES	285
Allowing 2 kg 50 for impressing velocity upon the air, the
formula d = (vt2 -r-20)At can be transposed, as follows:
For the case in hand, <5 = 2 kg 50
A*=0.239
20=19.62
and	v = 14 m 325 per second (47.00 ft per second)
The air and gas velocities have to be corrected by a coefficient,
according to their relative masses and volumes. These coefficients
are derived as follows:
5.32X1.125 = 5.9855 = 0.3523 for gas
8.51X1.293~11.003~0.6477 for air
Therefore, the value of the air component will be
14.325X0.6477 = 9.28.
The area of the air-port will be
45.99-^-14.325 = 3 m2 21 = 34.55 sq ft.
Considerable latitude may be allowed in proportioning the gas-
and air-port velocities and angles, to obtain the necessary resultant
angle and velocity. Theoretically, the entire velocity may be
supplied by either the gas or the air, or it may be divided between
them. The ports may both be given the resultant angle, or the
port angles may differ, provided the angular velocity components
of the air and the gas give the angle and velocity necessary for the
resultant. In practice there are certain structural limitations in
regard to the location of the ports. These limits must be con-
sidered. In this case it will be assumed that the port angles are
the same, being the resultant angle. The resultant velocity is
20 m 00 (65.62 ft) per second. Under these conditions the
velocity component for the gas will be
20.00-9.28 = 10.72;
from which the gas-port velocity will be
10.72 •*- 0.3523 = 30 m 43 per second (99.84 ft per second).

286	APPENDIX VII
The gas-port area will be
28.75-^30.43 = 0 m2 945=10. 17 sq ft.
The gas velocity arrived at is the minimum for the assumed air
velocity. If a higher gas velocity is used, the port angles will be
changed; if a lower gas velocity is desired, it will entail a corre-
sponding increase in the air velocity. There are an infinite number
of combinations which will satisfy the resultant velocity and angle;
but any change in one component will react upon the other. An
apparently slight change, made without analyzing the conditions,
is liable to lead to unexpected results. As there are, necessarily,
certain angles and velocities which will give the best results, as
well as others which give unreasonable results, the designer must
use a certain amoun to fjudgment in coping with the problem.
The pressure required to impress this velocity upon the gas will be
d = (30 . 432 -*• 19 . 62)0 . 208 = 9 kg 817 per m2
9 mm 817 of water
0.387 in of water
The velocity of the waste gases passing through the gas-port,
based upon the proportional division between the ports, will be
v~Qt~-u
^ = 35.66^-0.945= 37 m 74 per second
124 ft per second
The draft required will be
5 = (37. 742 -19.62)0. 192 =13 kg 94
0 . 55 in of water
The velocity of the waste gases, through the air-port, will be
v = 52.08-J-3.21 = 16 m 25 per second
53 . 06 ft per second
The draft pressure required will be
5 = (16.252-^19. 62)0. 192 = 2 kg 577
0.101 in of water
The chimney effect of the gas checkers available for impressing
velocity upon the entering gas was 4 kg 236 (0.166 in of water).
The gas velocity requires a pressure of 9 mm 817 (0.304 in) of

DESIGN OF OPEN-HEARTH FURNACES	287
water), therefore the pressure to be supplied from the gas main
will be
9.817-4.236 = 5kg581
0.22 in of water
The chimney draft required for removing the waste gases from
the heating chamber will be

	Gas on
Waste
Gas 	
Draft required at flue junction    	 	26 kg 442 	
Draft required for port velocity 	 	13 kg 940 	
		
Draft in inches of water column 	40 kg 382
1 60 	
		
The total draft at the base of stack or waste-heat boiler inlet will be
40.382+0.228 + 1.520 = 42 kg 130 per m2
42 mm 413 of water
1.67 in of water
The height of the chimney will be based upon the assumption
that the furnace will be workable by natural draft with the waste-
heat boiler out of service. The temperature of the waste gases
at the base of the stack will be 630° C. (1166° F.) and the volume
of the waste gases 42 m3 29 (1494 cu ft) per second at this tempera-
ture. The area of the chimney may be fixed by assuming a
desired velocity of 10 m 00 (32.7 ft) per second. A velocity head
of 5 m 10 (16.7 ft) will be required to impress this velocity upon
the gases. The area of the stack may be approximated by the
following formula:		
Qt =
in which Q* = the volume of gases flowing per second; for the case
in hand, this is 42 m3 29;
H = the head at the base of the stack, assumed as 5 m 10;
2g = gravitational constant = 2X9.81 = 19.62;

288	APPENDIX VII
co = the area of the stack in square meters, to be deter-
mined;
ki and *2 = coefficients for velocity at contracted vein and the
ratio of the area of the contracted vein to to;
for the case in hand these may be assumed as unity;
Aair = weight per cubic meter of air; for the case in hand
Z = 30° C. (86° R), 1+0^ = 1.110, 1.293-M.110 =
1 kg 165;
Agaa = weight per cubic meter of gases, Ao = l kg 320,
* = 630° C. (1166° R), 1+^=3.3121, 1.320-
3.312 = 0.399.
The formula may now be written with numerical values, as follows :
42.29 = 1X^/19.62X5.10 1'165
0.399
from which w = 3.07, say, 3 m2 14 (33.10 sq ft), giving a stack
diameter of 2 m 00 (6.5 ft).
t = average temperature of gases in chimney	'600° (1112° F.)
Qo = volume of waste gases at 0° (32° F.)	    12 m3 77
451 cu ft
l-j-orf = gas factor for t°	      3.202
A0 = specific weight of waste gases per cubic meter	  1 kg 32
Pounds per cubic foot	  0.0821
Q« = Qo(l+oO -12.77X3.202=	 40 m3 89
1440 cu ft
Ai = A0* (1+ofl =1.32-5-3.202 = weight per m3	  0 kg 412
Pounds per cubic foot	  0.0257
co =area of chimney bore	  3 m2 14
33.10 sq ft
Diameter of chimney bore =	 2 m 00
6.5ft
vt — average velocity of gases in chimney = 40.89 -?• 3.14= 13 rn 00 per sec
42.8 ft per sec
£air=temperature of external air, assumed to be	 30° (86° F.)
Aair = weight per cu m of air at 30° (preceding operation)..  1.165 kg
Pounds per cubic foot	 0.0725
Aair-Agas = l. 165-0.412 = differential per m	  0 kg 753
Draft depression required at base of stack =	 42 kg 130
Entry pressure=5.10X0.399 =	    2 kg 040
Velocity pressure = 5=A^z;2^20) =0.412(132-*-19.62) =	    3 kg 550
47 kg 720
First approximation of height of stack=47.720 ^-0.753 =... 63 m 50
208ft

DESIGN OF OPEN-HEARTH FURNACES	289
Additional stack height will be required to cover the friction in the
stack; this additional height may be approximated as follows:
Assume about 5 m 00 in height required for this purpose; then
0.0053X6-283X1^-5°X13.00X0.412
h=	l__	_ = 5 m 15.
The total height of the chimney will be
63 m 50+5 m 15 = 68 m 65 = 225 ft.
Additional chimney height might be desirable in order to pro-
vide a larger margin for increased draft resistance toward the end
of a campaign, due to blocking up of the checkerwork. A dif-
ferent fuel, a different method of operation, or a reduction or
increase in fuel consumption will modify these figures, but this
method of analysis may be applied^ not only to such cases, but
likewise to the design of other types of regenerative furnaces.
In connection with the reversing valves, a factor of importance
is the depth of the water seal. In the case of the gas valve, this
seal is exposed upon one side to the pressure within the gas main,
while the other is influenced by the draft depression at the valve.
The air-valve seal is influenced by the stack depression. In the
case of the gas valve, the gas pressure will be approximately 0.50 in
of water and the draft depression about 1.50 in of water, making
a total differential of 2.00 in of water. Gases, when their flow is
interrupted, have a tendency to produce a rise in pressure, as
water does. Therefore, with a 3-in water seal, only 1 in. of which
is effective, there is the possibility of a blow-through.
Practically all reversing valves present more or less of a direct
connection between the gas main and the stack flue or the air,
during reversal, unless special dampers or other means are pro-
vided to prevent this. Some of the devices designed to operate
dampers for this purpose are so arranged that the water seal on
the valve is broken before the dampers have cut off either the gas
main or the chimney flue. There is, however, no particular
difficulty in arranging a mechanism or a valve which will com-
pletely cut the furnace and flues off from the stack and the air
during reversal.
One of the main reasons why open-hearth progress has been
very slow is that space around the valves is limited, and it is

290	APPENDIX VII
practically impossible to secure the necessary clearances to
install different equipment or to provide the necessary rearrange-
ment of the flues. This obstacle is somewhat difficult to over-
come. The first installation is always difficult to secure, and in
many cases it is the only one made.
A certain amount of producer gas will be lost every time the
furnace is reversed. The gas regenerator and certain other parts
of the furnace are full of gas prior to reversal. A portion of this
trapped gas passes into the furnace and burns, but part of it will
be drawn backward into the chimney ^flue. This loss cannot be
eliminated. The more frequently the furnace is reversed, the
greater the loss.
Wind exposure has a certain effect upon furnace operation. It
affects the chimney draft appreciably. At the same time, it will
have an effect upon the velocity with which the air enters the
reversing valve, according to^its exposure. Mr. Allyn Reynolds
stated, at the 1913 meeting of the British Iron and Steel Institute,
that a wind blowing at the rate of 20 miles an hour caused a
variation in the rate of flow of air into the reversing valve of
70 to 350 ft per minute. The entry rate desired was 180 ft per
minute. As variations of this kind are sudden and extremely
irregular, it is difficult to compensate for them.
The use of a fan for introducing the air will not eliminate such
variations entirely; the fan merely causes a motion of the air
within itself, taking the air from the low-pressure side and deliver-
ing it to the high-pressure side. Any increase in the suction pres-
sure will increase the delivery rate of the fan. A great advantage
of a fan, in delivering the air, lies in the fact that it renders the
furnace independent of the stack effect of the regenerators and
uptakes in impressing the air velocity at the port, bringing this
variable more thoroughly under control. If stove-type regenera-
tors extending above the platform are used, a fan will be neces-
sary to force the air through them.
Considerable heat is dissipated from the wall and roof surface
of the regenerator chambers, the amount depending upon their
exposed surface and the air or wind currents to which they are
exposed. The proposal to insulate this surface has been actively
considered. The problem is similar to that of the insulation of the
hot-blast stove, except for the fact that the regenerator usually
works at much higher temperatures than the hot-blast stove.

DESIGN OF OPEN-HEARTH FURNACES	291
The heat loss takes place continually during both the heating
and cooling cycles. This has suggested the possibility of recover-
ing a portion of this heat by enclosing the chambers, with an air
space all around them, in a sheet-iron housing arranged in such a
manner that the air supply for the furnace is drawn from the
highest and hottest portion of the enclosure. This housing should
provide sufficient room to permit the inspection of the chamber
walls.
All regenerative furnaces are more or less subject to explosions
at reversal. These explosions crack and otherwise damage the
brickwork, producing air leakage which reduces the temperature
of the waste gases and increases their volume. The effect of this
leakage is intensified when a strong draft must be used to pull the
waste gases out of the furnace. The intensity of the draft depres-
sion increases progressively from the port to the base of the stack;
and the seriousness of the air infiltration necessarily increases
as the draft depression increases, the greatest amount of air
entering the system through the walls of the flues leading to the
chimney. Leakage outward undoubtedly occurs with both the
air and the gas; but, as the pressure within the flues is extremely
low, the volume lost is much less than the infiltration through the
same wall. The only way of preventing air from leaking into the
flues is to provide them with a covering of sheet steel of suitable
thickness. This will, at the same time, necessitate a consideration
of the fact that an explosion within a tight casing may be much
more violent than one occurring in a brick flue. Such a casing
and the heat insulation of these flues will increase considerably
the amount of heat available for the generation of steam.
One of the factors brought out in the preceding computation
was the draft depression necessary to pull a proportionate amount
of the waste gases through the gas-port of the furnace. This
indicates that a better-working furnace would result from having
large uptakes through which the waste gases would pass with a
low velocity down to the cinder pockets. A further advantage	«
resulting from this increase in uptake area on the outgoing end
will be a greatly increased efficiency of the cinder pocket in	t
catching cinder and other material which is carried out of the
furnace and thus increasing the life of the regenerators. The
carrying power of a flowing stream varies as the sixth power of
its velocity. That is, when the velocity is doubled, the weight of

292	APPENDIX VII
the particle carried will increase sixty-four-fold. When the waste
gases pass down the uptakes with a high velocity they will not
make a sharp turn at the cinder pocket, but will impinge upon its
bottom, unless a considerable depth is provided. The formula of
Yesmann, giving the trajectory of the jet of flame in the furnace,
may be modified to give the distance vertically downward a flowing
jet of gas will penetrate a cooler medium, as follows:
ix/r * •
Metric:
-.
2g    tn-
English units:	H^f-
The temperature of the gases leaving the heating chamber, tm,
is 1600° (2912° F.) and U, the temperature of the gases in the
cinder pocket, is assumed as 1400° (2552° F.). The velocity of
the waste gases in the gas and air uptakes has already been
determined as 17 m 83 (58.5 ft) and 11 m 32 (37.14 ft) per second,
respectively. When these values are substituted in the above
formula, the following values of H will be found:
in gas cinder pocket ff=16 m 94 (55.58 ft)
in air cinder pocket #= 6 m 83 (22.41 ft)
Naturally, if the temperature of the immobile gases in the
cinder pocket is lower than it is assumed to be, the penetration
of the jet will be less as the difference in temperature increases.
But reducing the velocity of the waste gases will decrease the
value of Hj according to the ratio of the squares of the velocity.
Both McKune and Egler have attacked this problem and
produced head constructions which bring the air and the gas
together in a rational manner at the incoming end and provide
for an increased area of uptake at the outgoing end. Both of
these methods are radical departures from previous head con-
struction. The writer has devised a method of obtaining a
similar result and at the same time presenting the possibility of
adjusting the angle of the flame.
A large segmental air-port over a smaller gas-port is a con-
struction much favored in American furnaces. The high gas
velocity and the low air velocity result in a long flame. It was also
considered that this form of port produced a blanket of cooler

DESIGN OP OPEN-HEARTH FURNACES	293
air on top of the jet of flame, and in this manner protected the
roof. As the coldest gases tend to seek the lowest portion of the
chamber, it is somewhat difficult to see just how this argument
is tenable. At the same time the waste gases reaching this large
port should be somewhat hotter than those reaching the smaller
gas-port at a lower level. This difference in temperature might
not be very great, as the vertical distance between the ports is not
great.
However, a much larger proportion of the waste gases would be
drawn off through this port, and, as a result, the air would be
preheated to a higher temperature than the gas. With this con-
struction the gas regenerator is strangled; that is, it cannot
obtain the proportion of the waste gases necessary to preheat the
incoming gas to the same temperature as the air supply, unless a
considerable draft differential is available to force a correct
division of the waste gases. A further disadvantage of this type
of head is the tendency of the bath to chill at the incoming end
with irregular reversals.
Port erosion, increasing the area of the gas-port and reducing
the jet velocity, has been very troublesome, as a point is speedily
reached at which the proper sintering of the bottom becomes
impossible. This entails shutting down the furnace for repairs
with consequent loss of production. Water-cooled ports are a
partial cure for the trouble; they increase the time between port
repairs, but they do not contribute to the correct division of the
waste gases between the regenerators.
Another result of the improper division of the waste gases
between the regenerators is a tendency for the furnace to work cold;
that is, the time per melt is increased, owing to the improper com-
bustion conditions produced. At the same time, the wear upon
the furnace is greater, particularly upon the roof, gas ports, cinder
line, etc.
The durability of any material exposed to heat is dependent
upon its ability to conduct this heat away from the heated end
and emit a sufficient amount of heat from its cool end to prevent
the hot end from overheating. When the hot end commences to
absorb heat faster than the cool end can emit heat, the temperature
of the hot end will commence to rise until it fails.
Water cooling supplies a more rapid method of removing heat
than air currents; it is particularly valuable in those cases where

294	APPENDIX VII
the refractory is subject to erosion or chemical action, as both of
these forms of attack are more rapid at high temperatures. Reduc-
ing their temperature increases their resistance to such attack.
Another function of water cooling is in reinforcing the rigidity of
the binding of the furnace. Metal work exposed to heat will
warp; cooling the metal prevents warping and holds the furnace
to line. It is possible, however, to overdo the cooling; it, there-
fore, requires careful consideration, and the apparatus must be
designed in such a manner that all steam and air pockets are
avoided. With an open-hearth furnace, as with a blast furnace,
cooling should only be used to hold vital points which cannot
be held in any other way.
Thermal insulation for the conservation of heat will only be
successful where the maximum temperature to which the refrac-
tories are exposed is less than their yielding temperature and
where a sufficient thickness of the refractory is interposed to
protect the insulation from temperatures above its yield point.
In some cases the insulation will replace a certain amount of
refractory brick, which serves to reduce the cost of the insulation;
in other cases the insulation will be an addition to the cost of the
refractories. The whole question must be settled on the basis of
"Will it pay?" The balance between the cost of the thermal
insulation and the value of the heat which it makes available for
other purposes must not only pay the interest upon the investment,
and supply funds for maintenance, etc., but must replace the
capital invested. It is needless to say that the output of the
waste-heat boiler will be increased by the delivery of high-tem-
perature gases.
Waste-heat boilers are an indirect means of heat recovery.
The main purpose of the furnace is the production of steel, and
auxiliary apparatus cannot be permitted to interfere with this.
Considerable diversity of opinion exists in regard to waste-heat
boiler design and installation, the type of boiler and the method
of baffling.
High gas velocities have been considered necessary for rapid
heat transfer from gas to water. Such velocities mean a con-
siderable draft differential through the boiler and are based upon
the idea that, at high velocities, stream-line flow of the gases is
replaced by confused eddies. Stream-line flow cannot occur with
gases which are in contact with surfaces hotter or cooler than

DESIGN OF OPEN-HEARTH FURNACES	295
themselves. The difference in density created by temperature
changes creates local recirculating loops which eliminate stream-
line flow.
A good idea of these confused currents may be gained by
observing any current of hot air rising alongside of a hot furnace.
These currents may be rendered visible by using a bright light
which will be partially polarized by the eddies created, causing
them to cast a shadow. A light which contains an appreciable
proportion of the blue end of the spectrum will render visible the
heat waves beyond the visible red of the spectrum.
In a gas-to-fluid heat transfer through a metal partition,
there are two very important factors, either one of which will
limit the value of the test. The heat transmission of the metal
will be limited by the manner in which the fluid circulates past
the wet surface, to a much greater degree than it will be limited
by the manner in which the hot gases circulate past the dry sur-
face. Practically all the recent experiments regarding gas-to-
fluid heat transfer through metal have entirely neglected the
part played by the fluid in carrying off the heat. Until the fact
is recognized that the gases cannot transfer heat to the metal any
faster than the water, in turning to steam, is able to carry it away
from the metal, very little progress will be made in boiler design.
In metallurgical furnace work it has long been recognized that
there are limitations upon the rate of temperature drop. In this
work there is frequently only a small temperature differential
between the gas giving up heat and the material to which heat is
imparted. In the steam boiler the temperature differential
between the hot gases and the water turning into steam is very
large, and the main obstacle to a high rate of heat transfer is the
poor arrangement of the water circulation.
Table 20 gives the quantity of heat available for a waste-heat
boiler at various initial and final temperatures, together with the
drop in temperature, initial and final gas volumes and the change
in the gas volume due to the drop in temperature. These values
clearly illustrate the large amount of heat lost by the drop in
temperature between the regenerator and the boiler and carried
away from the boiler by high waste-gas temperatures. With
leaky gas flues there is not only the drop in gas temperature, but
the added volume of air, which may increase the volumes to be
dealt with by 30 to 40 per cent, or more.

296	APPENDIX VII
The question of waste-heat utilization must be considered
upon an economic basis. A further factor to be taken into
account is the question of dividing the heat, which leaves the
laboratory of the furnace, between the regenerators and the waste-
heat steam generator. The higher the temperature at which the
gases are passed to the boiler, the greater its steam-generating
capacity; there is thus a possibility of reducing the cost of the
regenerator. The whole question of the design of the open-hearth
shop and its equipment is a matter of compromise and of balancing
one thing with another in order to secure a desired result—ingot
tonnage of the desired quality, at a profit.
In the foregoing discussion, producer gas has been the only
fuel considered. The fuel question depends largely upon local
conditions for the particular plant. Natural gas and coke-oven
gas eliminate the producer plant; but in many localities natural
gas is becoming scarce and coke-oven gas is not available at a
price and in a quantity which will permit its use. Tar is used in a
few plants, in order to get rid of the enormous quantities produced
by the by-product coking plants. Water gas has been used, as
well as blast-furnace gas mixed with producer or some other gas;
but the use of these last was more or less forced by war conditions.
Pulverized coals are used, as is also oil, which may be atomized by
steam or compressed air, or by mechanical means. Pulverized
coal adds a certain proportion of its ash to the normal cinder,
while finer portions are carried further and about 25 per cent of
ash passes out of the stack suspended in the gases. With most
of these fuels, only the air is preheated.
One of the most important elements in the fuel for an open-
hearth is. sulphur. The less sulphur present the better; it has a
tendency to pass into the cinder and metal, under certain condi-
tions, adding to the expense and time of the melt.

DESIGN OF  OPEN-HEARTH FURNACES

297

TABLE 20

Temperature,
Degrees C. 	Volume of Waste Gas,
Cubic Meters 	Heat Available,
Calorics per Second 	
Initial 	Final 	Drop 	Initial 	Final 	Change 	Initial 	Final 	in
Boiler
2490 	
900 	400 	500 	54.91 	31.54 	23 . 37 	4330 	1846 	
	
	350 	550 		29.11 	25 . 80 		1622 	2714 	
	300 	600 		20.82 	28.09 		1383 	2953 	
	250 	650 		24.52 	30.39 		1144 	3192 	
800 	400 	400 	50.31 	31.54 	18 . 77 	3814 	1846 	1968 	
	350 	450 		29.1.1 	22.20 		1622 	2192 	
	300 	500 		26.82 	23 . 40 		1383 	2-131 	
	250 	550 		24.52 	25 . 79 		1144 	2070 	
700 	400 	300 	45 . 59 	31 . 54 	14.05 	3400 	1840 	1554 	
	350 	350 		29.11 	10.48 		1622 	1778 	
	300 	400 		26.82 	18.77 		1383 	2017 	
	250 	450 		24.52 	21.07 		1 144 	2256 	
600 	400 	200 	40.87 	31 . 54 	9 . 33 	2814 	1846 	008 	
	350 	250 		29.11 	1 1 . 76 		1622 	111)2 	
	300 	300 		26.82 	14.05 		1383 	143! 	
	250 	350 		24.52 	10.35 		1M4 	1670 	

298

APPENDIX VII

TABLE 20—Continued

Temperature, 	Volume of Waste Gas, 	Heat Available, 	
Degrees F. 	Cubic Feet per Second 	B.t.u. per Second 	
Initial 	Final 	Drop 	Initial 	Final 	Change 	Initial 	Final 	in
Boiler 	
1652 	752 	900 	1939 	1114 	825 	17,206 	7326 	9,880 	
	662 	990 		1028 	911 		6337 	10,869 	
	572 	1080 		947 	992 		5488 	11,718 	
	482 	1170 		866 	1073 		5450 	12,666 	
1472 	752 	720 	1777 	1114 	663 	15,134 	7326 	7,808 	
	662 	810 		1028 	749 		6337 	8,797 	
	572 	900 		947 	830 		5488 	9,646 	
	482 	990 		866 	911 		4540 	10,594 	
1292 	752 	540 	1610 	1114 	496 	13,492 	7326 	6,166 	
	662 	630 		1028 	582 		6337 	7,155 	
	572 	720 		947 	663 		5488 	8,004 	
	482 	810 		866 	744 		4540 	8,952 	
1112 	752 	360 	1443 	1114 	329 	11,168 	7326 	3,842 	
	662 	450 		1028 	415 		6337 	4,831 	
	572 	540 		947 	496 		5448 	5,680 	
	482 	630 		866 	577 		4540 	6,628 	

DESIGN  OF OPEN-HEARTH FURNACES

299

TABLE 20—Continued
Base Data:
Qog = volume of gas burned per second = 5 m3 32 = 188 cu ft.
Qowg = volume of products of combustion with 40 per cent excess air
= 12m3 77 =451 cu ft.

Temperatures, initial, 	C 	 	600° 	700° 	800° 	900° 	
	F 	1112° 	1292° 	1472° 	1652° 	
Gas factor 1-f-ai 		3 20 	3 57 	3 94 	4 30 	
Temperatures, final, 	C 	250° 	300° 	350° 	400° 	
Gas factor, 1-j-ai. . . . 	F 	 	482°
1 92 	572°
2 10 	662°
2 28 	752°
2 47 	
						
Heat capacity of products of combustion from curve for producer gas,
SC-DSW, Fig. 184:

Calories initial 	2 814 	3400 	3814 	4336 	
B t u 	11,168 	13492 	15,134 	17206 	
Calories final 	       	 	1,144 	1,383 	1,622 	1846 	
Btu                	 	4,540 	5,488 	6,337 	7326 	
Volumes initial, m3    . . . 	 	 	40 87 	45 59 	50 31 	54 911 	
cubic feet 	1 443 	1 610 	1 777 	1 939 	
Volumes final   m3 	24 52 	26 82 	29 11 	31 54 	
cubic feet 	 	866 	947 	1,028 	1,114 	

APPENDIX VIII
DESIGN OF HOT-BLAST STOVES
By A. D. WILLIAMS
A. E. maccoun, in his paper before the American Iron and
Steel Institute, May 28, 1915, showed the temperature distribution
and the approximate isotherms for a Cowper stove at the Edgar
Thomson Furnaces. The isotherms, being those taken imme-
diately after the stove went on gas and just before going on blast,
indicate that the hot gases, in cooling, tend to flow through those
passes which lose the most heat, those closest to the shell of the
stove, and that the blast, in heating, tends to pass through the
hottest passes, those in the central portion of the stove. This
distribution follows natural laws and cannot be changed except
by the application of sufficient insulation around the outside of
the brickwork to reduce the amount of heat lost through the shell
of the stove. Changing the height of the bridge wall or the dome
of the stove, or increasing the number of chimney valves, will not
affect this distribution, provided, of course, that the one chimney
valve has sufficient area. Strangulation by insufficient valve area
is a common fault, not only in hot-blast stoves, but in many other
types of furnaces.
In a paper before the American Iron and Steel Institute in
October, 1916, Arthur J. Boynton gave a number of illustrations
of current designs in hot-blast stoves, the number of passes varying
from two to four. This paper and its discussion seemed to indicate
that the laws governing the subdivision of streams of heating and
cooling gases were not clearly understood, and this was also shown
in the stove designs illustrated. The laws governing the flow of
heat and the relationship between the thickness of the wall of the
checker openings and the time required to saturate the heat-
storage capacity of the brickwork are not understood. The
checker wall thickness ranged from 1.5 inches (38 mm) to 3 inches
(75 mm), with variations in pass diameter.
ano

DESIGN OF HOT-BLAST STOVES	301
Tables No. 1 and No. 2 were approximated from a curve
showing the temperature on the central line of a wall of firebrick,
in percentage value of the temperature of the surface of the brick,
which was given on page 222, Appendix VII. The curve is based
upon a flat wall. In applying this to brickwork built up to
form square passes it is necessary to allow for the effect of the
corners where a square column of brick is formed. As the ratio
between the diagonal and the side of a square =1.41 = -\/2, the
existence of such columns will double the heating time. These
times are only approximate and would not apply to large passes
with thin walls between, nor to small passes with thick walls.
Table No. 3 shows the relationship between the brick and the
free area for different ratios of pass and wall thickness. As a
general rule the stove is on gas from two to three times as long
as it is on air. Therefore the cooling period Vvill determine the
volume of the brickwork and the checker-pass volume required.
Tests made by the Bureau of Mines (Bulletin No. 8, " The Flow
of Heat Through Furnace Walls "); indicate a transfer drop in
temperature from a hot gas to a brick wall of less than 150°.
Numerous other data indicate a temperature drop in a gas-to-gas
transfer of heat through checkerwork of 300°. This latter drop
is less than that shown in the Cowpcr stove tested by Mr. Mac-
coun, where the blast temperature was 650° and the gas tempera-
ture around 1200°, a drop of 550.°
Table No. 4 consists of data abstracted from the test of a
two-pass Cowper stove at the Edgar Thomson Furnaces in 1913
and contained in Mr. A. E. Maccoun's paper before the American
Iron and Steel Institute on May 28, 1915, and the computations
based upon these data.
The. combustion chamber has an area of 3 m2 79 and a height
above the burner of 23 m 10, giving a volume of 87 m3 54. The
gases in this chamber have a very high temperature, about 1220°.
Assuming their specific weight to be equal to that of air, this
temperature would be sufficient to give them an ascensional
velocity of
1.29-1'29
^1200 =   / 2gII	—^r—— = 44 m 70 per second,

302	APPENDIX VIII
which would carry the gas to the dome in half a second. The
average time the gases remain in this chamber as computed from
their average temperature in the stove will be about five seconds.
The volume of gases formed each second in the combustion
chamber is
4.31X5.404 = 23 m3 29 with 40 per cent excess air,
4.75X5.404 = 25 m3 67 with 80 per cent excess air,
which would make the average area of the ascending column less
than 0 m2 70 or less than 20 per cent of the combustion chamber
area. The gas shoots across the short diameter of the chamber
and strikes the wall with considerable force. As a result of these
conditions, the flame in the combustion chamber may take on a
resonant vibration similar to that of the " singing flame " of the
physical laboratory.
The mushrooming of the burner jet is one of the causes for
the flame coming out around the burner. The hot column of
blazing gas will rise through the stagnant gases in the combustion
chamber and, since convection currents for gas are readily set up
there will be considerable recirculation. Noisy burning is a
well-known feature of stove operation. The mushrooming of the
gas jet assists in the mixing, and further mixing is effected when
the gases reach the dome. Mr. Maccoun's test proved that
unburned gases reached the dome but did not pass down into the
checkerwork.
The draft conditions existing in a stove are peculiar, inasmuch
as there may happen to be a greater draft depression at the
chimney valve than at the foot of the stack. This arises from the
fact that upward pressure exists in the combustion chamber and
likewise, to a lesser extent, in the checker, and these pressures
counterbalance each other. Assuming for the sake of simplicity
that the waste gases, etc., have the same specific weight as air,
the upward pressure in the combustion chamber will be
Ai2 oo = 23.101.29---   =+26.20 mm of water.
V	1+at/
In the checker this upward pressure will be
= 26.10/1.29
2X273

DESIGN OF HOT-BLAST STOVES	303
Mm. of
Water
Column
Upward pressure in combustion chamber	 +26.20
Upward pressure in checkerwork	 -f 24.60
Difference or positive pressure acting at chimney valve	  -f- 1.60
Draft depression at chimney valve	   —38.00
Draft depression at chimney valve due to stack will therefore be. . .   —36.40
Upward pressure in checker	   -f-24.60
Draft depression in dome of stove due to chimney	   —11.80
Upward pressure in combustion chamber	  +26.20
Making a draft depression at the burner available to draw in the air
required for combustion	   — 38.00
Professor Groume-Grjimailo has suggested that combustion
conditions in the two-pass Cowper stove may be improved by
springing an arch across the chamber with an opening proportioned
to retard the flow of the gases to such an extent that combustion
occurs in the chamber. The location of the arch will be fixed
by the amount of gas burned and the time required for combustion.
Two seconds may be allowed for combustion, which will be very
rapid under incandescent chamber conditions, with good mixing.
The size of the chamber and the port may be arrived at as follows:
Chamber volume = 25.67 X 2 = 51 m3 34,
Height of chamber = 51.34 -r- 3.79 = 13 m 60.
It is necessary to provide an opening in the arch over the top of
the combustion chamber which will permit the waste gases to
escape and yet restrict their flow sufficiently to supply time for
the completion of combustion. The area of this opening may be
determined by the use of Yesmann's formula, as follows:
in which Q = the quantity of gas flowing, in cubic meters per
second; for the case in hand, Qi2oo= 25 m3 67;
H=the head at the orifice or the vertical distance from
the orifice to the lower free surface of the gases;
for the case in hand 77 = 13 m 60;
2g = gravitational constant = 2 X9.81 = 19.62;

304	APPENDIX VIII
Aair = specific weight of air=l kg 29 per cubic meter;
Agaa = weight of gases at combustion-chamber temperature;
in this case 2=1200 and 1.29^-l+a* = 0 kg 239;
K<o = area of orifice in square meters;
ki = coefficient of contraction of the jet, or the ratio
between the area of the contracted vein and
o> (in hydraulics, the contracted vein for a circular
orifice is about 0.67co);
K2=velocity coefficient, or the ratio between the actual
velocity in the contracted vein and the theoretical
velocity (in hydraulics, the velocity in the con-
tracted vein is about 0.970).
ki and /C2 have not been accurately determined for gases.
For the case in hand they may be assumed as equal to unity, and
the formula becomes, for the particular case,

/	i   OQ _ 0   93
25. 67=lXlXcoA/19. 62X13. 60X*	= 0m2749.
\	^
U .
The velocity through the orifice will be
25 . 67 -t- 0 . 749 = 34 m 27 per second.
A combustion chamber of this kind might be constructed in an
old stove, but it would be difficult to maintain with dirty gas.
The furnace dust has a fluxing tendency upon the brickwork and
in many cases forms a heavy deposit. Mr. R. J. Wysor, in his
discussion of Mr. Boynton's paper, presented some interesting
photographs showing the fluxing action experienced in certain
furnaces at South Bethlehem. The fume at these furnaces is high
in alkali.
The stove tested was provided with three chimney valves,
being operated in some runs with all three and in others with
only two. The valves were 20.5 inches in diameter, giving an
area of 0 m2 212 each. The average temperature at the chimney
valve was about 280°. The volume of gas flowing per second,
$280=4.75X1+0^ = 9 ni3 63; therefore the velocities would be
9 63
with 3 valves, v = ^    ' 212 = 15 m 10 Per second,
9 63
with 2 valves, v=      '        = 23 m ^ per seconc*-

DESIGN OF HOT-BLAST STOVES	305
The pressure, in millimeters of water or kilograms per square
meter, required to impress this velocity upon the gases would be:
With 3 valves:
52==_L:—X .,,••-, = 7 kg 392 per square meter;
JjQ	L ~\~(X.t
= 7 mm 392 of water.
With two valves:
23.702    1.29     1Q1     00
<j2 = —— X1 , •   = lo kg 22 per square meter;
Zi(j         1 ~\~cx.t
= 18 mm 22 of water.
The draft depression at the chimney valves was — 38 mm of water.
Therefore, from 20 to 48 per cent of the draft at these points was
required to supply a sufficient velocity to remove the waste gases.
This would seem to indicate insufficient valve area. Two valves
tend to strangulate the stove, but with three the strangulation is
lessened. The chimney valve is a weak point; any leakage of
blast at this point is effectually concealed. A multiplicity of
valves increases the opportunity for valve defects, but at the
same time permits blanking a valve, if necessary, without shutting
down the stove for any length of time. Large valves are costly,
but one large valve reduces the number of potential leakage points.
The lowered velocity reduces the draft required in proportion to
the square of the velocity, and the friction and other losses are
likewise reduced.
The distribution of the gases through the checkerwork will not
be affected by the number of chimney valves, clampers and
partitions, but by the friction, heat loss, etc. The rapidity with
which the current of gas gives up its heat in any particular checker-
pass will determine the quantity of gas flowing in that pass. A
mathematical demonstration of this is given in Groume-Grjimailo's
work, and the distributions of the isotherms, as shown in Fig. 6 of
Mr. Maccoun's paper, confirm this. The natural velocity of con-
vection currents is higher than is generally realized. Table No. 8,
Appendix VI, gives the convection velocities for various average
temperature differentials acting through heights of 0.10, 1.00 and
10.00 meters. The checkerwork is 24 meters high; the velocity
average for the blast and the hot gases is 2 m 63 and 2 m 41 per
second, which is less than the convection velocity for an average
temperature differential of 10° acting for 10 m 00. The tempera-

306	APPENDIX VIII
ture differential for the blast in the checker is about 580° and of
the gases about 940°. Through the checkerwork the convection
currents act in the same direction as the flow of the blast and the
gases. Therefore the convection circulation tends to make every
particle of the gases brush every unit of surface. This fact was
demonstrated many years ago by Peclet at the Institut des Arts et
Metiers, at Paris, but is still ignored by many.
In the combustion chamber the convection currents will be in
the reverse direction to the flow of the blast and the gases. For
that reason, it is probable that temperatures taken slightly below
the top of the dome would show a higher blast temperature than
would be found at the hot-blast valve, lower down.
The study of Table No. 4 reveals several interesting facts in
regard to the two-pass stove which was tested. Hot-blast stove
temperatures are comparatively low, both as regards the tempera-
tures realized from the burning of the gas and the hot-blast tem-
perature. In this stove the gas-to-gas differential was about 600°,
which is nearly double that for other types of regenerators. The
rate of heating and cooling, that is, the average temperature
change per second in the blast heating and the gases cooling is low.
The checker contains 28 m2 32 of heating surface per cubic meter
of free air per second, or, if the average volume of the blast in the
checker is considered, this ratio becomes 24 m2 35. The rate of
heat absorption by the blast averages 0.659 calories per square
meter of heating surface per second. The fact that the isotherms
at the upper end of the checker are much closer together than those
lower down may be interpreted as indicating that this end of the
checker worked too cold, due, possibly, to the greater heat loss
through the walls and shell of the stove.
The usual thickness of the outer walls of stoves is 18 inches of
brick, 450 mm, with an air space of from 1 to 2 inches. A cyclic
change in temperature occurs in the inner portion of this wall
while the outer portion will give a temperature gradient toward
the air space. Due to the fact that the heating and cooling periods
are not equal and there is a constant heat or temperature loss
through the wall, the analysis of this cycle is not simple. The
central portion of the wall has a small temperature change. There
is a constant flow of heat to the outer surface and a periodic flow
from and to the inner wall surface, according to whether the stove
is at the beginning or end of the heating or cooling period. The

DESIGN OF HOT-BLAST STOVES

307

heat loss at the top of the checkerwork will naturally be several
times as rapid as at the cooler end. Hence, if heat insulation is
applied, it is necessary to use a greater thickness at the top. In
determining the amount of insulation required, a study of the
temperature cycle of the wall should be made, as it will throw an
important light upon the subject.
The frictional loss through the checkerwork may be approx-
imated by the formula developed by W. A. Mojarow and given
in the Revue de Metallurgie for May, 1914, page 320.(*> This
formula is as follows:
SL
y = m—vtpt.
0)
Applying this formula to the conditions existing when the stove
is on air, the values of the quantities are as follows:
m — coefficient of friction determined by Mojarow as =0.016 per1
meter, by observations made upon Cowper stoves;
SL = the heating surface, 8, being the perimeter of the passes and
L their length, for this case =4738 m2 00;
co = the area of the passes = 7 m2 40;
vt = average velocity of gas =2 m 63 per second;
pt = weight of the gas at temperature and pressure = 1 kg 115 per
cubic rneter for air at 1 atmosphere and an average tem-
perature of 360°.
Substituting these numerical values in the formula, the fric-
tional resistance to the passage of the blast is found to be equal
to 30 mm of water.
The following computations have been made with a view to
the possibility of obtaining higher blast temperatures, say, 900°
(1650° F.), with the same volume of blast as the stove tested
(16 m3 78 of free air per second).
Blast temperatures: Maximum of hot blast.... 900°
Cold-blast main.	    70°
Rise in temperature	 830°
Average temperature	 485°
(l) Refer to Appendix IV.

308	APPENDIX VIII
The heat capacity of the blast, per 100 molecular volumes, is
obtained from data in Table No. 8, Appendix X.
Heat capacity of hot blast t = 900°	660 calories
Cold blast	£=70°	    50
Absorbed by blast in an increase of 830°. 610       "
The total amount of heat absorbed by the air in heating,
during each second the stove is on air, will be
(16.78X44.80-:-100) X 610 = 4586 calories per second.
(The value 44*80 is the number of molecular volumes of 22.32
liters in 1 m3.)
With a cycle of one hour upon air, the total amount of heat
carried away from the stove by the blast will be
4586X3600-16,590,000 calories.
In making the following computations, no allowance has been
made to cover the heat lost through the walls of the stove or the
necessary volume of gas to be burned to supply this heat. The
amount of gas required will depend in part upon the heat loss
and the insulation applied to prevent such loss, upon whether the
gas and air from its combustion are preheated or not, upon the
design of the combustion chamber, etc. The possibilities of hot-
blast stove design have not been as well appreciated as they might
be. Detail improvements in burners and valves, with their
comparatively slight opportunity for improving the results
obtained in producing hot blast, have obscured the greater possi-
bilities of increasing the temperature of the blast by rational
construction. Multiple-pass stoves have comparatively little
excuse for existence. The main advantage of an even number of
passes is the location of valves, etc., near the bottom of the stove.
Three-pass stoves are not only irrational in design but require that
valves be located near the top of the stove, where trouble is not
only difficult to detect but hard to remedy.
Assuming that a temperature change of 100° in the checker
brick is permissible, the weight and volume of brick required will be

DESIGN OF HOT-BLAST STOVES

309

These values do not allow for heat loss; that is, this
volume of brickwork, when heating, would have a temperature
change from 20° to 50° greater than when on blast, as the
100° change is the change covering the heat transferred to the
blast.
The temperature of the blast increases 830° in the checker.
The average rate of increase assumed will determine the time
allowed for heating and, with the blast volume, the space required
in the checkerwork. Assuming a heating rate of 100° per second,
the time necessary will be 8.3 seconds. Slower or faster rates of
heating will correspondingly affect the time as well as the apuoo
required to contain the blast while heating. The volume of froo
air blown per second is 16 m3 78, its average temperature in tho
checker is 485°, and it is under a pressure of one atmosphere, tho
volume under these conditions being 23 m3 33, which, multiplied
by 8.3, the heating time, fixes the space required as 193 m;j 70.
The total checker volume will be, therefore, 193.70+368.80 =
562 m3 50.
The brick coefficient = 368.80 -*• 562.50 = 0.6557.
The pass coefficient = 193.70-4- 562.80 = 0.3443.
The side of the square for the pass unit = V0.3443 = 0.5868.
The portion of the unit square occupied by the brickwork will
be 1.0000-0.5868 = 0.4132.
As the cooling time of the stove is one hour, it is not desirable
to make the wall thickness between the passes greater than 75 mm;
therefore the side of the unit square will be 75 — 0.4132= 181.5 mm
or, say, 180 mm. The diameter of the square pass will be
180-75 = 105 mm = 4.125 ins.
The area occupied by a checker unit = 0. ISO2 = 0 rn2 0324
The area occupied by the pass	= 0.1052 = 0 rn2 0110
The area occupied by brick	=	Om2 0214
The lineal amount of checker required, based upon the pass
= 193.70-0.0110=17,609 m, or, if based on tho brick = 368.80-f-
0.0214 = 17,230 m. Using the largest of these values arid assuming
a checker height of 25 m, the number of passes = 17,609-r-25.00
= 704.

310	APPENDIX VIII
The total area occupied by the
passes                                        =0.0110X    704=	7m2	75
The total area occupied by brick    =0.0214X    704=	15m2	07
Checker area                                  = 7.75    +15.07 =	22 m2	82
The perimeter of one pass             =0.105 X       4=	Om	42
The total perimeter                       =0.420 X    704=	295m	68
The heating surface                       =295.68X    25  = 7392m2	00
Heating surface per cubic meter of
free air per second                      =7392    --16.78=	44m2	05
Heating surface per cubic meter at
pressure and average tempera-
ture                                           - 7392    -^ 23.33 =	31m2	68
The average heat transfer rate will be 4586-^7392 = 0.6204
calories per square meter per second for the existing differential.
The average velocity of flow of the air through the checker will
be 23.33-^7.75 = 3 m 01 per second.
The frictional resistance in the checkers by Mojarow's formula
will be 42 mm 80 of water, while there will be a hydrostatic pressure
upward of 9 mm of water, so that the drop through the checker
will be 33 mm 80 of water.
The possibility of increase in blast temperatures is limited
by the possible temperature which may be realized from the
combustion of blast-furnace gas. Mallard and Le Chatelier, in
the course of their work for the Commission de Grisou, determined
the heat capacity of various gases. Working with these data,
it is possible to approximate the instantaneous calorific intensity
of combustion of various fuels under athermal chamber conditions,
as well as the effect of preheating the air or the gas, or both.
Such a curve has been computed for a blast-furnace gas having a
volumetric composition of H2 = 3.92, CO = 23.95, 02 = 0.39,
C02 = 12.96, H20 = 1.65 and N2 = 57.13. This gas has a thermal
value of 1861 calories per 100 molecular volumes (2 m3 232)
equivalent to 835 calories per cubic meter and 93 B.t.u. per cubic
foot. This curve (Pig. 181) shows intersection points which may
be read to approximate the temperature which may be realized
from the combustion of this gas with various air supplies and
preheating conditions.
Table No. 5 gives computations, which are believed to be
self-explanatory, for the plotting of the curve. In making them,
however, it has been assumed that the air is composed of 1 volume

DESIGN  OF HOT-BLAST  STOVES

311

of 62 and 4 volumes of N2- While this is not absolutely accurate,
it is sufficiently close for the purpose and saves considerable time
in computing. Table No. 6 summarizes the instantaneous
calorific intensities as read from the curves for different conditions.
Tables 6 and 8, Appendix X, give the data used in the computa-
tions of Table No. 5, both being abstracted from Les Sources
de UEnergie Calorifique by Damour, Carnot and Rengade.
TABLE 1
tempeka.ture on centeb linhe op checker. wall laid up in" straight
passes in" pee cent value of the surface temper attire op the
brick. allowing for the corner effect

Heating Period in Minutes,
Wall Thickness 	15 	30 	45 	CO 	
Indies 	Millimeters 	Temperature on Center Line in Per Cent of
Surface Temperature 	
2.0 	50 	99.0 	99.9 	99.99 		
2.5 	63 	94.0 	99.5 	99.9 	.... 	
3.0 	75 	91.0 	99.0 	99.5 	.... 	
3.5 	90 	80.0 	97.0 	98.5 	99.8 	
4.0 	100 	70.0 	93.0 	98.0 	99. /> 	
4.5 	113 	59.5 	87.0 	-    96.0 	99.0 	
TABLE 2
time in* minutes required for the center linu of a wall to
given percentage values or^ the surface temperature, a&lo-wing
FOR THE   CORNTER EFFECT

Center Line Temperature 						
in Per Cent of Surface 						
Temperature 	95 	90 	SO 	70 	(>() 	
Wall Thickness 						
Inclies 	Millimeters 	Time In Minutes 	
2.0 	50 	32 	26 	18 	14 	12 	
2.5 	63 	54 	42 	30 	24 	20 	
3.0 	75 	76 	56 	44 	32 	27 	
3.5 	90 	106 	82 	62 	50 	38 	
4.0 	100 	130 	104 	76 	62 	48 	
4.5 	113 	170 	134 	98 	78 	60 	

312

APPENDIX VIII

TABLE 3
relationship between the wall volume and area and the free
volume and area within the checker work, for various
ratios of wall thickness and checker opening, based upon
square checker passes

Ratio of Wall Thickness to Checker Opening 	Brick Area 	Free Area 	
Diameter of Square Pass 	or Volume 	or Volume 	
	per Unit of 	per "Unit of 	
				Area or 	Area or 	
Wall 	Pass 	Wall 	Pass 	Space 	Space 	
1.00 	0.33 	3.00 	1.00 	93.75 	6.25 	
1.00 	0.40 	2.50 	1.00 	91.84 	8.16 	
1.00 	0.50 	2.00 	1.00 	88.88 	11.12 	
1.00 	0.67 	1.50 	1.00 	84.00 	16.00 	
1.00 	1.00 	1.00 	1.00 	75.00 	25.00 	
1.00 	1.50 	0.67 	1.00 	64.00 	36.00 	
1.00 	2.00 	0.50 	1.00 	55.56 	44.44 	
1.00 	2.50 	0.40 	1.00 	48.98 	51.02 	
1.00 	3.00 	0.33 	1.00 	43.75 	56.25 	
1.00 	3.50 	0.28 	1.00 	39.51 	60.49 	
1.00 	4.00 	0.25 	1.00 	36.00 	64.00 	
1.00 	4.50 	0.22 	1.00 	33.06 	66.94 	
1.00 	5.00 	0.20 	1.00 	30.56 	69.44 	
1.00 	6.00 	0.17 	1.00 	26.53 	73.47 	
The values for the last two columns of this table were obtained
from a table contained in Mr. Boynton's paper.

DESIGN  OF HOT-BLAST STOVES

313

TABLE 4
data abstracted from "blast furnace advancement/' by A. E.
maccoun, presented before the american iron and steel insti-
tute meeting op may 28, 1915
Test of a 22' 0"X 100' 0"—Two-pass Cowper Hot-blast Stove

Heatin0* surface of checkers . 	51 192 ft2 	4764 m2 	
Total of stove 	 	55 866 ft2 	5202 m2 	
Combustion chamber, area 	       .   . .   . 	40 8   ft2 	3 m2 79 	
Height to burner 	 	10 62 ft 	3 m  50 	
Above burner 	 	76 75 ft 	23 m  10 	
Total  .... 	87 38 ft 	26 m 60 	
Volume, below burner ... 	468 ft3 	13 m3 26 	
Above burner 	             .   . 	3092 ft3 	87 m3 54 	
Total 	 	3560 ft3 	100 m3 80 	
Dome volume 	1381 ft3 	39 m3 10 	
Checker Number of passes 	329 		
Dimensions of passes. ... 	6"X6" 	150X 150 mm 	
Total area of passes 	 	82 25 ft2 	7 m2 64 	
Perimeter of one pass 	 	2 0 ft 	0 m 60 	
329 passes 	658 ft 	197 m 40 	
Height of 	 	77 75 ft 	24 m 00 	
Heating surface = 197 . 40X 24 . 0 = 	 	51.160 ft2 	4738 m2 	
(Difference due to use of approximate metric value)

Wall thickness 	 	0 25 ft 	75 mm 	
Area per pass = (150X75)2 = 		0 m2 050625 	
Of pass = 1502. 		0 m2 02250 	
Brickwork per pass (difference)  . .      	 		0 m2 028125 	
Percentage of in brick (Table 3) 	 		55 56 	
In pass (Table 3) 		44 44 	
Total Checker = 0 050625X329 = 		16 m2 655 	
Passes          = 0 . 022500X329 = 	 		7 m2 403 	
(Difference due to use of approximate metric value?)

Brick = 16 655-7.403= 	 		9 m2 252 	
Volume, Total brick and passes 16.655X24= 	 		400 m3   30 	
Passes = 7 403X24 = 		177 m3   64 	
Brick 	 		222 m3   66 	
(Difference due to use of approximate metric value)

Weight (as given) 251.85X1800 =.
(metric)    222.66 X1800 = .

453,350 kg
400,800 kg

314

APPENDIX VIII

TABLE 4—Continued

	Blast 	Air Supply for Com-
bustion of Gas 	

	40 Per Cent
Excess 	80 Per Cent
Excess 	
Volumes at 0° 760 mm per second 	 	16 m3 78
8m3 39
650°
70°
360°
4-580°
2.32 	2m3 26
1220°
280°
750°
-940°
3.75
95.0
2 m3 15
182.0
4m3 31
16 m3 16
5.42
3.45
11.00
19.87
47.3°
85.5°
2m 182
1950
375
1575
1595 	2m3 26
1220°
280°
750°
-940°
3.75
123.0
2m8 78
210.0
4m8 75
17 m8 81
4.94
2.21
9.98
17.13
54.9°
94.2°
2m 405
2220
433
1787
1809
18,232,000 	
0° 1 atmosphere 	

	
Temperatures, maximum                       . . 	

	
Minimum 	        	 	

	
Average 	

	
Change 	

	
Gas factors for average temperature . .   . 	

	
Air supply, per cent of gas volume 	 	

	
Volume 0° -760 mm 	 	 		

Products of combustion per cent gas 		

Volume 0° —760 mm 	 		

Volumes   at   average  temperature  and
pressure 	        .   . 	19 m3 46
4.50
2.02
9.14
15.66
37.1°
63.5°
2m 626 	

Time, average, in seconds to pass through
Combustion chamber  . 	

	
Dome 	 	

	
Checker 	 	

	
Total 	 	

	
Temperature change, average per second
Based on total volume 	 	

	
Based on checker only 	

	
Velocity, average in checker 	

	
Heat capacities per 100 molecular volumes
from Curves.    Calories
Gases at 1220° 	 	

	
Blast at 650° 	 	465 	

Gases at 280° 	 	

	
Blast at 70° 	    • 	50
415 	

Difference 	 	

	
Calories released or absorbed per second
(2. 26X44. SO -^ 100) X 1575 = .... 	

	
1787= 	 		

(16. 78X44. 80- 100) X 415=. 	3120
11,232,000 	16,078,000 	
	
Calories absorbed in one hour on blast =
3120X3600= 	 	

	
Calories released from gases in 2 . 8 hour =
10,080 seconds
1575X10.080=... . 	

	
1809X10,080=... 		

Assuming specific heat of brick =0.250
at 1 ° change in its temperature will =
	 400,800X0.250 = 100,200 calories 		

DESIGN OF HOT-BLAST STOVES

315

TABLE 4r-Continued

	t»i    , 	Air Suppb
bustion 	t for Com-
of Gas 	
	Blast 	40 Per Cent
Excess 	80 Per Cent
Excess 	
The total average temperature change in
brickwork of checker will be on above
basis 	 	112.3° 	160.7° 	182.2° 	

The difference between the heat in the blast of the gases will be
16,078,000-11,232,000 =4,846,000 = 30.4% loss
18,232,000-11,232,000 =7,000,000 = 38.8% loss
This covers merely the interchange loss in stove checker.    If the total heat
released by the gases is considered, down to 0°, the following will govern:
Der second
)= 	 	 	1974 	
 	 	 	
 	 	19,520 000 	
 	 	 	
Calories released by gases:  Per
(2.26X44.80 -f-100) X1950= .
2248
22$
Per cycle: 1974X10,080 =
2248X 10,080=	       22,485,000

19,520,000-11,232,000
22,485,000 = 11,232,000

= 8,288,000 = 42.46% loss
= 11,253,000 = 50.04% loss

316

APPENDIX VIII

TABLE 5
combustion of blast furnace gas—computation sheet

Compo-                     n ,
- , •       r                    v^ai—
sition of
Gas 	Products of Combustion 	

	O2 	C02 	H2O 		
H2
CO
02
C02
H20
N2 	3.92X5
23.95XC
0.39
12.96
1.65
57.13 	8.2= 228
.8.2 = 1633 	1.96
11.98 	23.95 		3.92 		

	

	

	
			12.96 	

	

	1.65 	

	

	

	

		

	
	1861 	13.94
0.39 	36.91 		5.57 	1 	

	

		

	
	
	13.55 	36.91 	5.57 	1 	
Air 	Supply 	Excess
Air 	Products of Combustion in Molecular Vo 	
Per
Cent 	Mol.
Vols. 	
	02        C02       H2O 	N2 	Excess
N2 	
100
120
140
180 	67.75
81.30
94.85
121.95 	0.0
13.55
27.10
54.20 	0.0      36.91      5.57
2.71    36.91      5.57
5.42    36.91      5.57
10.84    36.91      5.57 	111.33
122.17
133.01
154.69 	0.0
10.84
21.68
43.36 	
Expressed upon a Percentage Basis these Values are

100 			0.0 	24.00 	3.62 	72.38 		
120 			1.62 	22.05 	3.33 	73.00 		
140 			2.99 	20.40 	3.08 	73.53 		
180 			5.21 	17.74 	2.68 	74.37 		

DESIGN OF HOT BLAST STOVES

317

TABLE 5—Continued
combustion of blast furnace gas—computation sheet 2
Points for heat capacity curves.    Products of combustion, air and gas
volumes from Appendix X are multiplied by values in Table 8, Appendix X.

Vol. 	200° 	400° 	600° 	800° 	1000° 	1200° 	1400° 	1600° 	1800° 	
N2  111.33
CO2 36.91
H20  5.57 	155
68
10 	314
147
20 	480
238
33 	048
445
46 	827
458
61 	1008
574
77 	1195
708
95 	1386
853
113 	1582
1004
133 	
2 100% air 	233 	481 	751 	1139 	1346 	1659 	199S 	2352 	2719 	
+20% 13.55 	19 	38 	58 	79 	101 	123 	145 	169 	193 	
S 120% air 	252 	519 	809 	1218 	1447 	1782 	2143 	2521 	2912 	
C+40%27.10 	38 	76 	116 	158 	202 	246 	290 	338 	386 	
S 140% air 	271 	557 	867 	1297 	1548 	1905 	2288 	2690 	3105 	
H-80% 54.20 	76 	152 	032 	316 	404 	492 	580 	676 	772 	
2 180% air 	300 	633 	983 	1455 	1750 	2151 	2578 	3028 	3491 	
Pleat Capacity Air Supply

100% 67.75 	94 	191 	292 	394 	
120% 81.30 	113 	229 	350 	473 	
140% 94.85 	132 	267 	409 	552 	
180% 121.95 	170 	344 	526 	710 	
Heat Capacity of the Gas

N2+     85.39 	117 	238 	364 	491 	
CO2      12.96 	24 	52 	83 	118 	
H20        1.65 	3 	6 	9 	13 	
S        	 	144 	296 	456 	622 	
N2 57.13+02 0.39+H2 3.92+CO 23.95 = 85.39

318

APPENDIX VIII

TABLE ^—Continued
combustion of blast furnace gas—computation sheet 3
Computation for curves showing the effects of preheat upon calorific in-
tensity.   Values from Sheets 1 and 2.

Temperature of Preheat 	0° 	200° 	400° 	600° 	800° 	
Calories released by gas at 0° 	 (A) 	1861 					
Added to gas by preheat                (I?) 		144 	296 	456 	622 	
Preheated gas (A -j- J5) 	 S 		2005 	2157 	2317 	2483 	
Added by air preheat 100% 	 (C) 		94 	191 	292 	394 	
Preheated air (A-\-C) 	 (D} 		1955 	2052 	2153 	2257 	
Preheat gas and air (D-h-S) 	  £ 		2099 	2348 	2609 	2879 	
Added by air preheat 120% 	 (J?) 		113 	229 	350 	473 	
Preheated air (A-+E] 	 (F) 		1974 	2090 	2211 	2334 	
Preheated gas and air (.F-KB) . . . .  S 		 	2118 	2384 	2667 	2956 	
Added by air preheat 140 % 	 ((?) 		132 	267 	409 	552 	
Preheated air (A+G) 	 (//) 		1993 	2128 	2270 	2413 	
Preheated air and gas f/7-f j?) 	 2 		2137 	.2424 	2726 	3035 	
Added by air preheat 180%   .      (K) 		170 	344 	526 	710 	
Preheated air (A+K) 	 (L) 		2031 	2205 	2387 	2571 	
Preheated air and gas (L-f B) . . . . 2 		2175 	2501 	2843 	3193 	
The values marked S, D, F, H, L are spotted upon the heat capacity
curves for their corresponding air supplies, and curves are drawn through
these points which enable certain approximations to be made in. regard to
other air supplies and temperatures of preheat.

DESIGN OF HOT BLAST  STOVES

319

TABLE 6
instantaneous calorific intensity of blast furnace gas with various
air supplies and showing the effect of preheat of both the
air and the gas (approximate). (read from curve, fig. 181.)

Temperature of
Preheat

Air Supply in Per Cent of Theoretical
Requirements

Gas 	Air 	100% 	120% 	140% 	180% 	
0° 	0° 	1330° 	1240° 	1175° 	1050° 	
0° 	200° 	1380° 	1310° 	1250° 	1140° 	
200° 	0° 	1425° 	1330° 	1250° 	1170° 	
200° 	200° 	1475° 	1390° 	1325° 	1210° 	
0° 	400° 	1440° 	1370° 	1310° 	1225° 	
400° 	0° 	1500° 	1410° 	1330° 	1200° 	
400° 	400° 	1610° 	1530° 	1470° 	1350° 	
0° 	600° 	1490C 	1435° 	1390° 	1300° 	
600° 	0° 	1590° 	1500° 	1420° 	1280° 	
600° 	600° 	1740° 	1675° 	1625° 	1525° 	
0° 	800° 	1550° 	1500° 	1460° 	1390° 	
800° 	0° 	1675° 	1580° 	1490° 	1340° 	
800° 	800° 	1880° 	1825° 	1730° 	1650° 	

APPENDIX IX
COMBUSTION AND BOILER SETTINGS
A. D. WILLIAMS
when coal or other commercial solid combustibles are burned
directly in the firebox it is difficult and in some cases impossible
to obtain a temperature around 1600° C.; though the theoretical
combustion temperature of a good grade of coal in an athermal
enclosure is about 2050° C. This temperature limitation for a
long time hampered the development of many lines of metal-
lurgical and industrial work as the cost of obtaining the required
temperatures was too great for commercial use. The limitation
arises from the fact that it is practically impossible to force
sufficient air for complete combustion through the incandescent
bed of fuel; in other words, the bed of burning fuel acts as a
producer of combustible gases which in turn must be burned by
an additional air supply. The rate at which the air is forced
through the fuel bed directly affects the rate at which the fuel is
burned, but the mass of air per unit mass of combustible is prac-
tically constant under all conditions.
A very interesting series of tests on " Combustion in the Fuel
Bed of Hand-fired Furnaces " (Bureau of Mines, Tech. Paper 137)
has been made by Kreisinger, Ovitz and Augustine. One of the
features of this paper that attracted the writer's attention was the
statement that the mass of air per unit of combustible, computed
from the analysis of the gases in the upper layers of the fuel bed
was, in all cases, less than the mass of air per unit of combustible,
as measured by an orifice meter, introduced into the ash pit. The
quantity of air forced into the ash pit was also less than the
theoretical air supply required for the fuel.
In endeavoring to obtain an explanation of this difference it

COMBUSTION AND BOILER SETTINGS	321
was found that the computed combustion temperatures derived
from the heat capacity of the gases in the fuel bed agreed very
closely with the observed temperatures. This would appear to
indicate that a portion of the air supply, instead of passing up
through the fuel, passed up the walls of the firebox. This con-
clusion was borne out by the writer's recollections of fires which
seemed to burn faster close to the wall than they did in the center
of the grate and of clinkers occurring along the walls, and fused
to them, when the central portion of the fuel bed was free from
clinkers. This last would seem to indicate a sort of an air-blast
or oxidizing-zone effect close to the walls, strong enough to solidify
the viscous ashes.
Another indication of the possibility of the air passing up
between the wall and the fuel bed lies in the fact that the CC>2
in a number of the tests had a curve with two peaks. One was a
high peak with low CO, after which came a steady decrease with
an increase in CO, this valley being followed by an increase in
C02 (and a decrease in CO) to a low peak; then there was another
drop in the C02. The last drop in C02 only showed in a few
cases, and might be an error as it was very slight.
The tabulations on p. 322, of the results with a 12-inch fuel
bed summarize the combustion results attained:
The total weight of air required for the burning of 1 Ib of com-
bustible will vary from 11.5 to 15 Ib and will have a volume at
ordinary temperatures of from 144 to 187 cu ft. But the amount
of air that can be forced up through the fuel bed is much less.
The specific gravity of coal will average about 1.20 and a cubic
foot of coal as fired will weigh from 40 to 50 Ib. From this it will
be seen that the volume of the voids will be between 33 and 45
per cent of the mass and this will also give the proportion of the
fuel bed area through which the air must be forced. The tempera-
ture of the fuel bed and of the gases leaving it will be about
1400° C. and the gases will have an impressed velocity. A formula
might be devised to give the ash pit pressure required for burning
a given weight of fuel per unit of area, but there are so many
variables that it would be of comparatively little use. The limit
of the ash pit pressure is reached when the ascending volume of air
forced through the fuel is sufficient to keep it floating. Such an
intense draft pressure, however, would tend to carry unburned
fuel away from the grate.

322

APPENDIX IX

	Pittsburgh Coal, .
7 Tests 	Anthracite Coal,
7 Tests 	Coke,
7 Tests 	

	Av. 	Min. 	Max. 	Av. 	Min. 	Max. 	Av. 	Min. 	Max. 	
Carbon in ash, per
cent of total car-
bon 	 	7.98
92.02
17.00
76.00
4.00 	3.95
82.10
11.00
65.00
1.00
0.13
21.00
4.10
5.00
5.20 	17.90
96.05
25.00
85.00
10.00
1.33
131.00
6.10
8.20
7.20 	10.76
89.24
16.95
82.53
0.52 	2.96
75.20
7.90
68.00
0.30
0.20
20.00
5.70
7.30
5.90 	24.80
97.04
31.50
91.50
1.00
2.36
99.50
7.50
10.70
6.60 	7.32
92.68
22.00
77.70
0.30
...... 	3.80
90.45
14.90
71.00
0.10
0.05
15.00
6.10
8.10
6.60 	9.55
96.20
29.00
84.90
0.60
1.67
118.60
7.30
10.60
7.60 	
Carbon burned, per
cent of total car-
bon 	 	

	

	

	
Per cent of carbon
burned to C02.. .
burned to CO. . .
burned to CH4. .
Pressure in ash pit,
inches of water. .
Pounds of coal per
sq ft per hr 	

	

	

	

	

	

	
	
Pounds of air per Ib
of fuel 		

	

	

Pounds of air per Ib
of combustible . .
Pounds of air per
lb of combustible
from gases 	 		

	

	

		

	

	

		

	

	

When the burning gases leave the fuel bed they have an ascen-
sional force, due to their temperature alone, of between 30 and 80
ft per second and are at least 1000° C. hotter than the heating
surface of the boiler. As a result the ascending stream of hot gas
will be very much smaller than the area of the pass and the firebox,
the balance of this area being occupied by cooler eddies of gases
chilled by their contact with the heating surface of the boiler and
the walls of the settings.
A very interesting illustration of the way gas may flow through
a setting was shown on page 709 of Power, Nov. 17, 1914. Mr.
Morgan B. Sniith, however, has his arrows indicating the course
of the gases pointing in the wrong direction. Fig. 169 shows the
correct pointing of the arrows. The hot gases from the fire rise
straight up to the coking arch, and just below this arch the gases
are forced to flow horizontally to the end of the arch where their

COMBUSTION AND BOILER SETTINGS	323
velocity carries them through the bank of tubes and the hole in
the baffle. In fact it is very probable that the failure of the
baffle at this point was due to the continual impinging upon it of
the hot gases. The chilled current of gas flowing down around
the tubes of the boiler would also tend to force the hot gases,
flowing out from below the arch, against the baffle. After passing
through the break in the baffle a portion of the hot gases will
tend to rise into the upper portion of the first and second pass,
while the balance will be carried down by the current of cooler
gases flowing down the second bank of tubes and will pass under
the second baffle. They will then immediately rise to the outlet,
passing up the space between the second baffle and the third bank
of tubes, then crossing the tube bank near the top, under the rear
drum.
The explanation of this action is very simple. Anyone who
has sat by a window on a cold day knows that the air chilled by
contact with the window drops to the floor, and that the velocity
of the air current is appreciable, although the difference in tem-
perature between the inside of the room and outside of the building
is comparatively small, say, from 20° to 40° C. The same
phenomenon, except that the current of air rises, may be witnessed
in the vicinity of any radiator in a steam-heated building, while
the hot-air furnace installed in many homes depends upon con-
vection currents. If currents can be established at such low
temperature heads in a room at ordinary living temperature, it is
only logical that similar currents will be established where tem-
perature differences of several hundreds of degrees exist.
A phenomenon similar to the deflection of the current of heated
gases flowing through the broken baffle by cooler downward
currents can be observed by using an electric fan to break up and
distribute the current of hot air rising fronra radiator. The mere
fact that a certain amount of gas is being drawn off at one point
of the setting and a corresponding quantity of gas or air admitted
at another part will not affect the local convection currents any
more than the drawing off and admission of air into a room affects
the current of cold air at the windows and of the heated air at the
radiators.
Unfortunately we have all been hypontized by the idea that
any current of gas passing through a series of enclosures sweeps
uniformly through the full cross-section of all the passages or

324

APPENDIX IX

flues open before it, entirely forgetful of the fact that in gases, by
reason of their high coefficient of expansion due to temperature
changes, great variations of density occur. At a temperature of
1638° C. a cubic meter of air weighs 0.171 kg, while at 0° C. the
same volume of air will weigh 1.293 kg or 7.5 times as much.
The relative densities may be compared by likening the high-
temperature air to water, weighing 62.5 Ib per cubic foot, while

^^^$^^^

3 Hot Gases Rising:
[^[Gases Chilled by Contact
•iiiil     with water cooled
jjJEddy Areas of Partially Surfaces fallins
chilled Gases

fig. 168.—Diagram of Gas Flow in Stirling Type Boiler.
the low-temperature air may be likened to molten iron, which
weighs 430 Ib per cubic foot or nearly 7 times the weight of water.
One thing that has tended to obscure this great difference in
density that occurs in gases is the fact that most engineering
works, in considering the gases passing through a boiler, supply
the information as weight of gases, allowing the investigator to lose
sight of the fact that a unit weight of gas in the firebox will
occupy approximately three times the volume it does when it

COMBUSTION AND BOILER SETTINGS

325

reaches the smoke flue connection. The relative difference in the
density of the gases at these two points is as great as the difference
in density of wood and granite, and it is a matter of common
knowledge that granite will sink in water while wood will float.
In the same manner the hottest gases will tend to float above
cooler gases. Convection currents and conduction will naturally

-*—*»— Chilled Gases	•<	Hottest Gases
fig. 169.—Diagram of Gas Flow in Stirling Boiler with Broken Baffle.
tend to equalize the extreme temperature differences, if the
supply, of heated gases is not maintained, but equalization in this
manner would be comparatively slow.
Fig. 168 shows the type of boiler with the broken baffle,
baffled according to the builder's catalogue with arrows to show
the circulation of the gases. The heated gases rising from the

326	APPENDIX IX
fuel bed impinge upon the arch where the direction of flow changes
to horizontal. These gases when they reach the end of the arch
will have a certain velocity of flow which will carry them beyond
the end of the arch, possibly a portion of them into the first bank
of tubes, before they start rising again. The upper portion of
the first and second pass acts as an inverted pocket into which the
hottest gases flow, the section under the front drum being much
hotter than that under the second drum. The tube banks act as
refrigerating surface for the gases and heating surface for the
water.
The current of hot gases in front of the first bank of tubes is at
least 700° C. hotter than the tubes. Their ascensional velocity,
due to temperature, is sufficient to carry them the height of the
setting in a very small fraction of a second. A part of the gases
will be chilled below the ignition temperature and below the
temperature which would permit them to float over the top of the
first baffle. These gases will circulate down in the spaces between
the tubes, depositing soot on them, until they reach the back of the
firebox, where they absorb heat and tend to rise again.
The gases in the top portion of the second pass will have a
temperature in excess of 600° C. which is about 350° C. hotter
than the second bank of tubes, a temperature sufficiently low to
permit 75 per cent of the CO present to be dissociate into CC>2
with an accompanying deposit of soot. The refrigerating surface
of the second bank of tubes will chill these gases still further so
that they will tend to drop into the lower part of the setting
where a portion of them will pass under the second baffle. This
portion of the gases will be hot enough to float up to the top of
the third pass after mixing with some of the chilled gases that
have flowed down the third bank of tubes. Some of the gas will
be carried downward by the cooling action of the third bank of
tubes but the temperature difference between the water-cooled
refrigerating surface and the gases is not very great at this point,
and the hottest portion of these gases will tend to rise further into
the smoke flue.
A number of attempts have been made to distribute the draft
loss between the ash pit and the stack damper, on a percentage
basis, between the different passes. All of these are apparently
based upon the static pressure. In the boiler shown in Fig. 168
there are three vertical columns of gases. These columns exert

COMBUSTION AND  BOILKH   SIOTTIN'CJS	.'&/
a pressure against the top of the setting proportional to their
vertical height and their average temperatures in Ilio same manner
asa chimney. The gases in the first pass, being lighter Ifinn those
in the second pass, exert more pressure and therefore tend (o foree
the gases in the second pass down and under the second Imflle.
In the third pass this uplift tends to accelerate the movement of
the gases to the smoke flue. The greater the height of I ik* set! in«
the greater the upward pressure. These pressures will nntumlly
affect the reading of any draft gage attaehod to the boiler. The
dynamic pressure due to velocity of flow nuiy have nn additive
or subtractive effect on the reading of the dniff. pi^e^depeiidinK
upon its location or, more correctly, upon the. lonilion of the*
connections to the setting.
In connection with baffles designed ostensibly to inerea.sc Hie
velocity of flow of the off gases of combustion Ihe following fable
gives the volumetric air supply and the resulting off #iseH from
an exceptionally good grade of coal having a very low nsh content.

	Volume at 0° C. und 	
	Air Supply 	Waste Gas 	
	CubicMeter 	Cubic Meter 	
	per Kilo- 	per Kilo- 	
	gram Coal 	gram Con I 	
Air supply 100 per cent . 	8.71 	9 . 04 	
"        110 per cent. 	9.58 	0.91 	
' '        120 per cent . 	10.45 	10.78 	
' '        140 per cent . 	12.19 	12.52 	
' l        150 per cent . 	13.06 	13.31) 	
' '        175 per cent . 	15.24 	15 . 57 	
"        200 per cent. 	17.42 	17.75 	

Air Supply 	WnHf.<* C jiim 	
pc*r Pound 	jmt Pound 	
C'cml 	C "i ml 	
	 1:w 	 '" 	i in 	
1 53 	i /in 	
HiK 	17-1 	
HI5 	2CII 	
2(1!) 	215 	
21 f 	25(1 	
27H        !        2HI 	

As the composition of the coal varie.s, those* volumes will vary.
The coal consumption per boiler horsepower will vnry from two
pounds per hour upward and the total amount of roal hnnml cm it
grate will depend upon the size of the boiler ami (he amount if in
forced above its nominal rating. As largo hiwh nn* the incwt
interesting an 875 horsepower Sterling type* boiler ojrntfed ni
several loads will be considered. The volume* inside the net ting J«

328

APPENDIX IX

about 5100 cu ft; about 30 per cent of this space will be occupied by
tubes, etc., so that the net volume will be about 3570 cu ft, or a
trifle over 100 cu m. A boiler of this size should operate on a coal
consumption of about 2.5 Ib per horsepower with 20 per cent excess
air. The gases of combustion will have the following volume:

	Volume of Waste Gases per Second 	

	120 Per Cent Air Supply 	140 Per Cent Air Supply 	

	Cubic Feet 	Cubic Meter 	Cubic Feet 	Cubic Meter 	
Normal ratin
150 per cent
200 per cent
300 per cent 	2! 	106
159
212
318 	3.001
4.501
6.003
9.005 	123
185
246
369 	3.483
5.225
6.966
10.449 	

	of rating . . .
of rating. . .
of rating . . . 	

	
	
The average temperature of the gases within the setting will be
about 800° C., for which the value of the factor 1+0.003672 will be
3.936. This gives the average minimum and maximum gas
volumes of 417 and 1455 cu ft, from which the average time of the
gas inside the setting will be 8.56 seconds for the minimum amount
of gas and 2.46 seconds for the maximum amount of gas. This
gives a temperature drop of from 117° to 407° C. per second.
The distance from the grate to the smoke-flue outlet is about 60 ft,
which gives an apparent average velocity of flow ranging from
7 to 24.5 ft per second.
Assuming that the combustion arch is about 6 ft above the
grate and the gases leave the fuel at a temperature of 1400° C.,
they will have an upward pressure against the arch slightly less
than 0.10 in of water, and their velocity will be about 42 ft per
second. At 200 per cent of rating the volume of gases rising from
the fuel bed will be about 212 cu ft per second, which at 1400° C.
will give a volume of 1300 cu ft. The firebox of the boiler has a
width of 15 ft and the arch will be about 12 ft deep from the front
wall, giving an area of 180 sq ft. From Bazin's formula for the
flow of water over weirs, Professor Yesmann, of the Polytechnic
Institute of Petrograd, has developed a formula which makes it
possible to approximate the depth to which the space below this
arch will be occupied by the hot gases. In reaching this arch,

COMBUSTION AND BOILER SETTINGS	329
which forces them to turn, horizontally, the gases lose their vertical
velocity.
Applying this formula to the case in hand, it is found that the
depth ht will be 1.27 m or 4.17 ft. The horizontal velocity of the
gases flowing out at the end of this arch, will be about 15.25 ft
per second and their mean velocity will be about 10.20 ft per
second. As soon as they pass beyond the end of the arch the hot
gases "will have an ascensional component, due to their density, of
zero at the end of the arch but increasing so that their rise "will be
on an arc of a parabola unless interfered with by other forces. In
the boiler setting these other forces are a current of colder gases
descending among the tubes and the tubes themselves, and while a
portion of the gases flowing out from under the arch will penetrate
the colder layer of gases and possibly reach the baffle behind the
tubes, this action will occur intermittently according as the current
of hot or cold gas is stronger in its surges. Naturally these sudden
changes in. the temperature of the gases at the baffle "will cause
cracks and ultimately failure of the baffle as shown in Mr. Smith's
article. When this occurs the hot gases will pass through the
break as indicated in. Fig. 169.
At 226 Ib pressure absolute, the steam temperature is 200° C.
The temperature of the outside of the iron tube should not exceed
220°, allowing a liberal drop between the "wet surface and the
emulsion of steam and water, and assuming that the tube is clean,
and free from both scale and soot. The temperature in the firebox
is around 1400° C., and it has "been customary to assume that the
curve representing the drop in temperature from the fire to the
smoke-flue outlet is a regular logarithmic curve, this curve being
based upon assumptions which violate the simplest principles of
elementary physics. The difference of 1200° between the hot
gases and the water tube is nearly five times the difference in tem-
perature between that of the workroom and the temperature
of liquid hydrogen, —259°. The refrigerating effect of the cold
tube on the hot gases is almost equivalent to that of dipping
a red-hot bar of steel into liquid hydrogen. The ignition tem-
perature of the gases varies between 350° and 800°; any portion
of the unburned gases coming in close contact with the tubes will
be chilled belo^y the ignition point. In the case of CO this may

330	APPENDIX IX
result in its decomposition, the formation of carbon and CO2,
which is an exothermic reaction releasing 38.8 calories per molecular
volume of CC>2 formed, and the deposition of soot on the tubes.
Another source of soot lies in the hydrocarbons. The high firebox
temperature has a tendency to break these up, forming soot, CO
and hydrogen (Efo). The luminosity of the flame in the firebox
is due to the heating of this soot to incandescence, and unless this
floating carbon is burned in a properly designed combustion
chamber a considerable portion of it will be carried to and deposited
on the tubes.
Combustion, like all chemical reactions, follows the law of
mass action and the laws of chemical equilibrium. The velocity
of the reaction is affected by the temperature of the reacting
masses, by the mixing of the combustibles and the comburent
and by the dilution with inert gas. The velocity of the reaction
increases very rapidly with the temperature. Tor example, a
mixture of hydrogen and oxygen at 200° will require months to
combine, while at 2200° the explosion wave indicates that combina-
tion occurs in one ten-millionth of a second. The ratio between
the two velocities of the reaction is that of 1 to 1014. Increases
of pressure increase the velocity of the reaction. This factor,
while important in internal combustion motors, does not amount
to very much at the slight differences of pressure that exist in
furnace fireboxes used in industrial heating. Dilution with inert
gases slows down the reaction velocity by reason of the increase
of the mass. The mixing has a considerable effect on the velocity
of the reaction as may be readily verified by observing the flame
of a Bunsen burner while altering the air supply. The slower the
reaction velocity the longer the flame length and the distance
the gases travel in burning. The temperature will be lower with
a long flame than ifc will be with a short flame.
In a boiler it is absolutely necessary that combustion should
be completed before the water-cooled surfaces are reached, as
complete combustion will result in the practical elimination of the
soot trouble, with a resultant increase in the efficiency of the heat-
ing surface. Most boilers and settings, however, are so designed
that the incandescent gases are shot up against a refrigerating
surface before combustion can be completed. The so-called
combustion arches and the baffling being so arranged that this
refrigeration will be promoted, instead of combustion.

COMBUSTION AND BOILER SETTINGS	331
WATER CIRCULATION IN BOILERS
by A. D. WILLIAMS
owing to the fact that water may be converted into vapor at
rather low temperatures, there is no particular difficulty in con-
structing a boiler that will produce steam when heat is applied
to it. The earliest boilers were modeled upon the familiar kitchen
kettle. To-day there are so many different designs of boilers
that it would be difficult to enumerate them. A few years ago
boilers were operated and rated at the nominal figure of 10 sq ft
of heating surface per boiler horsepower. To-day the nominal
rating remains the same, but in practice the boiler is operated at
from 150 to 300 per cent of rating. The water-tube boiler was
devised to increase boiler efficiency by securing improved water
circulation and breaking the circulating water up into multiple
streams surrounded by hot gases. In this it has met a certain
degree of success, as is proved by the modern method of boiler
forcing.
The most widely used design of the water-tube boiler consists
of one or more steam drums and an assemblage of inclined tubes,
the pitch or slope varying from 8 per cent to 30 per cent. The
tubes are generally arranged in multiple, but there are designs
tha?t employ series operation of a number of multiple banks of
tubes. Circulation generally depends upon the thermal syphon
principle, that is, upon the hydrostatic head developed by the
difference in weight of two columns of water of slightly different
temperatures. Additional circulating velocity is supposed to be
due to the fact that one of these columns of water is solid and the
other partially displaced by steam bubbles.
The accompanying table shows the weights of water and
steam at different temperatures, by 20° C. increments, together
with the corresponding pressures. At the boiling temperature,
100° C., the ratio between the weights of equal volumes of steam
and water is about 1 to 1600, which is sufficient to supply an
•ascensional velocity to the steam of about 177 m (580 ft) per
second. At 200° C. the ratio drops to 1 to 110 and the ascensional
velocity to 46.5 m (153 ft) per second. The coefficient of friction
between the bubble of steam and the surrounding water is un-
known, but even if an extremely liberal allowance is made for this

332	APPENDIX IX
weight of water and steam at various temperatures

	Steam Pressure 	Weights of 		
				Water, 				
Temper-
ature,
Degrees
C. 	Kilo-
grams
per
Square
Centi-
meters 	Pounds
per
Square
Inch 	Water
Pounds
per
Cubic
Feet. 	Kilo-
grams
per
Cubic
Meter.
Ounces
per Cubic 	Steam,
Kilo-
grams
per
Cubic
Meter 	Steam,
Pounds
per
Cubic
Feet 	Ratio
of
Weights,
W+S. 	
				Feet 				
0 	0.00623 	0.0886 	62.492 	999.87 	0.00485 	0.000303 	206,158 	
4 		.... 	62.500 	1000.00 				
20 	0.0238 	0.338 	62.389 	998.23 	0.0173 	0.00108 	57,701 	
40 	0.0749 	1.066 	62.016 	992.25 	0.0511 	0.00319 	19,517 	
60 	0.2028 	2.885 	61.453 	983.24 	0.1305 	0.00815 	7,534 	
80 	0.4828 	6.867 	60.739 	971.83 	0.2938 	0.0183 	3,307 	
100 	1.0330 	14.690 	59.899 	958.38 	0.5980 	0.0373 	1,602 	
120 	2.0240 	28.790 	58.963 	943.40 	1.1220 	0.0700 	841 	
140 	3.6840 	52.390 	57.900 	926.40 	1.9680 	0.123 	471 	
160 	6.3000 	89.590 	56.719 	907.50 	3.2650 	0.204 	278 	
180 	10.2160 	145.30 	55.413 	886.60 	5.1500 	0.322 	173 	
200 	15.8400 	225.20 	53.925 	862.80 	7.8400 	0.489 	110 	
coefficient and for the viscosity of the hot water the steam bubble
will rise above any moving stream of water circulating through a
tube before it can be carried any great distance horizontally. A
simple experiment will permit the verification of this. A glass
test-tube is nearly filled with water and a smaller tube is used to
blow air so it will bubble up through the water. A cork with a
vent on one side and a hole for the smaller tube permits the test-
tube to be inclined at various degrees. The ratio between the
weights of equal volumes of air and water is 1 to 774. (When the
tube is inclined the vent should be at the upper side, otherwise
the apparatus will " backfire.73) Upon blowing through the small
tube it will be found that at the vertical position and at slight,
inclinations from the vertical, the air will rise in bubbles. This
action is utilized in the air lift used in raising water from deep
driven wells. When the degree of inclination approaches the
horizontal there will be a tendency for the stream of bubbles to

COMBUSTION AND  BOILER SETTINGS	333
follow the high side of the tube, and a stream of air can be formed.
The less the pitch of the test-tube the easier it is to maintain this
stream of air. This would lead to the conclusion that in the
inclined-tube design of water-tube boiler the lowest portion of the
tube would be filled with water for its full area while at its highest
portion the tube would have the lower part of its area filled with
water and the upper part filled with steam.
In the boiler, however, the action is complicated by the
bafftmg and the portion of the tube exposed to the hottest gases.
With the ordinary method of baffling, used with the B. & W. type
of boiler, the high end of the tubes is exposed to the hottest gases
and this end, therefore, will be filled partly with steam and partly
with water. When the lowest portion of the tube is exposed to
the hottest gases there is a tendency for a portion of the steam
generated to pass from the tube to the rear header and up to the
steam drum. This action may be avoided by bushing down the
rear end of the tube and in this manner increasing the velocity of
the water entering to an extent that will enable it to carry the
steam with it to the front header.
An experimental single-tube boiler may be extemporized from
a gage glass, a wooden clamp arranged to hold the tube at various
degrees of inclinations, two pieces of rubber tubing fitted to the
ends of the gage glass and connecting with nozzles on the bottom
of a tin pail, and a Bunsen burner or a blow torch. The pail
should be partially filled with water and supported so that there is
space below it to permit the gage glass to be brought nearly ver-
tical. The heat can be applied to different parts of the water
tube and held there until steam commences to form. The evi-
dence of convection currents may be obtained by dropping a few
crystals of potassium permanganate into the water near the down
leg. As these crystals slowly dissolve a stream of pink will show
the direction of the current. If the water is colored a light pink,
it will, in the steaming tests, permit the steam bubbles to have a
higher degree of visibility. When the heat is applied at the lower
end of the slightly inclined tube it will be found that a portion
of the steam goes up the down leg instead of the up leg. As the
inclination of the tube is increased this tendency decreases until
all of the steam tends to flow to the up leg, and this greatly
increases the velocity of circulation. (Note: A neat modification
of this one-tube boiler has glass up legs and down legs of various

334

APPENDIX IX

lengths, with only short rubber connections between the tubes
and to the pail.) A number of very interesting experiments may
be conducted with this simple apparatus, and in this way a better
idea of the conditions governing water circulation will be obtained.
The specific heat of water and its heat capacity are unity.
The heat capacity of steam has a fractional value, but in contact
with water, under the conditions existing in a boiler tube, it has
reached the limits of its heat-absorbing capacity for the existing
temperature; that is, any additional heat imparted to the steam
in the tube will be immediately absorbed by the vaporization of a
corresponding amount of the water present. When the water is
converted into steam its volume increases from 110 to 1600 times
and it displaces from 109 to 1599 additional volumes of water.
The 4-in or 100-mm boiler tube has a sectional area of 78 cm2
54 (12.56 sq in). Its length is about 5 m 50 (18 ft) and its heating
surface 1 m2 73 (18.6 sq ft). When a boiler is driven at 200 per
cent rating it is evaporating water at the average rate of 8.1 grams
per square meter per second. On this basis each tube will evap-
orate 14 grams of water per second on the average. However, it
is not unreasonable to suppose that the lower tubes, directly
exposed to the hot gases and radiant heat from the fuel, will have
an evaporation rate of, say, ten times the average, or 140 grams
of water per tube per second. At a steam temperature of 200° C.
this would give a volume of 15,400 cm3 of steam per second. The
internal volume of the boiler tube is 43,200 cm3. This would
mean that about 35 per cent of the internal volume of the tube was
occupied by steam. At lower steam temperatures the volume of
the steam released will be much greater and fill a larger per-
centage of the tube volume. It is probable that the lower end of
the tube will be occupied by solid water, and if this is the case and
the steam is generated uniformly the full length of the tube, 70 per
cent of the area of the highest end, will be occupied by steam.
Assuming that the pitch of the tube is 30 per cent, this is suf-
ficient to give a head that will impress a velocity of 5 m 69 per
second on the steam. Friction against the water surface may be
either negative or positive, depending upon their relative veloci-
ties. Friction against the tube surface will reduce the steam
velocity.
The steam in the upper section of the tube will not be able to
absorb heat as rapidly as the water in the lower section, but as

COMBUSTION AND BOILER SETTINGS	335
long as a portion of the perimeter of the tube is covered with
water there is no danger of the tube becoming overheated. The
hydrostatic head causing the flow of water into the tube will be
due to any difference of temperature between the front and rear
tube headers and the height of the water column above the tube.
Some experiments have indicated that this velocity decreases as
.the boiler is forced above rating. Should the flow of water be
interrupted it will only require a few seconds for the tube to
become full of dry steam, it would then rapidly heat until it burst.
This would throw full boiler pressure against any slight obstruc-
tion and immediately remove all evidence of the cause of the
trouble. With tube pitches of less than that assumed, the liability
to interruption in the water circulation increases. The slight
differential head that exists through a tube might readily oe
sufficient to hold a piece of loose scale over the end of a tube and
be insufficient to break it; that is, a very slight obstacle would
suffice to stop the flow of water or so reduce it that a considerable
portion of the tube surface would become dry. Another possible
cause of burst tubes is the forcing of the boiler to such an extent
that the water inflow into a tube becomes insufficient to provide
for the evaporation taking place. This last condition would be
more likely to occur in a clean tube, free from scale internally and
from dust externally, than in a dirty tube.
When the boiler tubes are vertical or nearly vertical the
water circulation is enhanced by the " air-lift effect " of the steam
bubbles. Like the air lift, this is a problem that involves so
many uncontrollable variables that it is doubtful whether any
rational expression for this circulation will ever be worked out.
The investigation of this circulation, however, will throw con-
siderable light upon the rational design of steam boilers. It is
very possible that a modification of the design of the Niclausse
boiler, having the field tubes set vertically with the manifold at
the top, will offer almost unlimited forcing possibilities, greatly
exceeding the evaporative capacity of existing designs. To secure
increased circulation in any design it is rather important that the
course of the water and the steam bubbles should be arranged in
such a manner that they do not impede each other. Theoretically,
there should be no limitation to the amount of forcing which a
vertical-tube boiler can stand except the heat-absorption capacity
of its heating surface. With inclined tubes the boiler can be

336	APPENDIX IX
forced only to the extent of turning a sufficient amount of water
into steam to occupy the full area of the hottest tubes at their
highest point. Any further forcing with this type of boiler will
cause it to destroy itself.
Exactly what the last word in boiler design will be is hard to
say. Present designs leave much to be desired, not only in the
circulation of the water, but in the manner in which the hot gases
pass through the setting and come in contact with the heating
surface. The ruling temperature of boilers is very low. Con-
vection currents in water are set up with very low-temperature
differences, and as the temperature of the mass increases the
convection head caused by one degree difference in temperature
increases. These physical principles do not cause design dif-
ficulties and it is probably for this reason that boiler engineering
has settled into a rut and the mechanical details of the connections
entirely overshadow the importance of increasing the heat-
absorbing capacity.
SUGGESTIONS FOR CORRECT BOILER BAFFLING
by A. D. WILLIAMS
heating or the application of heat to industrial and domestic
processes is an engineering problem of importance. A study of
existing installations reveals many interesting discrepancies in
practice. In writing about heating furnace a great deal has
been said regarding the importance of permitting the heat to
soak in. It is well known that a time factor is necessary. The
velocity of gas travel is very low in many furnaces. But when
boiler settings are considered, a great deal is said regarding the
importance of high gas velocities as contributing to efficient
operation.
The ideal condition is found between these two extremes.
In boiler practice the problem is to pass the gases by the recipient
surface at a velocity which will permit them to give up or transfer
all of the heat they carry between two temperature limits. Their
initial or high temperature limit is fixed by the firebox or com-
bustion temperature. Their final or low temperature limit is
fixed by the ruling temperature, or temperature of regime, of the
boiler plus the temperature required to supply a temperature head
necessary for the transfer of heat. This final temperature of the

COMBUSTION AND  BOILER SETTINGS

337

gases should be somewhere between 200° and  300° C.   Fre-
quently it is much higher.
Another point to be considered in connection with gas velocities
arises from the fact that the carrying power of the flowing stream
varies with the sixth power of its velocity. The heavier particles

Diagram showing the flow of gases in a B. & W. type boiler with special setting.
This boiler is gas fired. Temperature observations made in this setting by the Bureau of
Mines are shown in Figs. 171, 172 and 173. The observations of temperatures made by
the bureau indicate that the flow of the gases follows the laws of hydraulics. The hot gases
behaving in the same manner as an inverted stream of water. By looking at this cut
from the top instead of the bottom of the page this analogy may be clearly seen.
are more readily thrown out of the stream into the eddies where
changes of direction occur. Soot blowers and the steam lance
are employed to rid the heating surface of this dirt, soot, etc.,
instead of attacking the root of the trouble and thereby eliminating
it, or at least reducing it to a minimum. The usual methods of

338

APPENDIX IX

setting and baffling boilers coupled with the design of the boilers
themselves. is well calculated to intensify combustion and soot
difficulties. At the same time the troubles with existing plant

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Length of Path of Gases from
Position of Tiernoocouple A, Feet
FlG. 171.
Curve showing temperature of the gases flowing through the B. <fe W. type boiler setting
shown in Fig. 170. The letters on the curve refer to pyrometer locations as indicated in
Fig. 170. Solid curves show temperatures indicated by pyrometer couples. Dotted
curve shows the computed temperatures from experimental data. Dash curve shows
computed velocity of gases. This curve is probably based on the assumption that the
flowing gases entirely fill the full area of the passage. As the basic assumption does not
agree with the action of the gases in this matter, the true velocity curve will be much
higher at certain points. Upper and lower diagrams show similar data for two different
initial temperatures.
may be considerably reduced by consideration of the laws govern-
ing the flow of hot gases.
In April, 1919, the Bureau of Mines issued their Bulletin
No. 145 on " Measuring the Temperature of Gases in Boiler

COMBUSTION  AND BOILER SETTINGS

339

0	I	2
Distance from Central Position, Feet
fig. 172.
Curve showing variation in temperature at points E and G at different distances from
the center line of the boiler shown in Fig. 170. Upper pair of curves shows the tempera-
tures indicated by moving twin couple E 1-in steps away from center line. Lower pair
of curves show indications of twin couple G when moved by 6-in steps away from the
center.

1300
1200
1100
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fig. 173.—Curves Showing the Fluctuations of Temperature at Points A
and C in the Boiler Shown in Fig. 170.
The fluctuations were obtained by reading the small couple at two-second intervals.
These fluctuations are a beautiful illustration of the analogy between the flow of water and
the flow of hot gases. Couple C is located near the bottom of the steam drum where it is
immersed in a comparatively quiet body of gas. Couple A is located immediately below
the tubes at a point where it would show the effects of all the surges in the stream of flowing
gas. Anyone who has watched water flowing, from the top of a dam or the spout of a
pump, has noticed that the flow is broken up by numerous small surges. This pyrometer
shows the effect of the gas surges. Another factor contributing to these surges is the
refrigerating action of the water-cooled tubes on the gases. Chilled gases will be held
among the tubes in the same manner as a ball is supported by^a stream of water or air,
until the weight of chilled gases becomes sufficient to permit it to break its way down
through the up-flowing current of hot gases. Conditions similar .to this exist with all
the usual forms of boiler baffling, as they are well arranged to promote this condition.
One of the effects of this condition is the formation of soot and COz by the dissociation of
CO instead of its combustion. Considerable heat loss results.

340

APPENDIX IX

Settings." The temperature curves plotted in this bulletin con-
firm in a very interesting manner the hydraulic laws governing the
flow of hot gases. The illustrations in this article are taken from
this bulletin and the only additional feature is that in three of the
figures lines have been added to show the flow of the hot gases
and soot pockets and the flow of the chilled gas in Figs. 170, 174
and 177 of this article (Figs. 2,4 and 6 of Bulletin 145).
Fig. 170 shows a gas fired type boiler installed at the Carnegie

fig. 174.
Diagram showing flow of gases in single pass horizontally baffled boiler. Underfeed
stoker coal firing. Temperature measurements made in this boiler setting are shown in
curves, Figs. 175 and 176. By looking at this figure upside down the analogy to the flow
of water will be clearly observed. This type of baffling is particularly well adapted for
the formation of cool gas and soot pockets.
Institute of Technology. By turning this figure upside down it
will appear that the flow from the firebox falls on the inclined
baffle on the lower tubes and cascades over the end of the baffle
into and among the tubes, flowing under the top of the baffle.
This flow continues until the last baffle is overflowed and a cascade
is formed to the breeching. The hot gases being very much lighter
than the air have a tendency to rise. Relatively cooler gases will
have tendency to fall below hotter gases or stratify above colder
air or gas. Portions of the setting have been indicated as forming
cold or cool gas pockets while other portions are indicated as the

COMBUSTION AND BOILER SETTINGS

341

location of eddies. Arrows indicate approximately the flow of the
cold and the hot gases. The pockets of relatively cold, chilled
gases form banks of soot and dirt. Letters on this figure designate
the points where the pyrometer couples were located.

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0 	5       10 	15 		20 	25       30 	35 		i 	
	
Length of Path of Gasee from
Position of Thermocouple A, Feet
fig. 175.
Curve showing temperature of gases flowing through single pass horizontally baffled
boiler. Positions of thermo-couple are indicated by letters in Fig. 174. Solid lines curve
show temperatures indicated by couples. Dotted" curve shows approximate computed
true temperatures, dash curve computed velocity of gases at different points. The velocity
curve, being probably based on the sectional area of the pass, is erroneous. Upper and
ower diagrams show similar data for two different initial temperatures.
Fig. 171 shows the curve of temperature drop through the
setting. One of the interesting features of this curve is the dif-
ference between the indications of the large and the small couples.
It is rather important that the pyrometer couple be suited to the

342

APPENDIX IX

work. The large couples are better suited to obtain the average
temperature as they have an inertia that prevents their responding
to sudden differences due to the continual surging of the gas
currents. This surging is very much the same as that of water
falling over a dam. Fig. 173 illustrates these surges at points
A and C. The surges at C have an amplitude of slightly over
50°, while those at A have an amplitude of about 300°. Anyone

1000 			•— 	—»•" 	_
— - 	.— - 	^-* 	^ 	-V
B 	S 	N 		— 	— 	— 	-_ 	— 	— 		— 	- 	1832 	
900 						— 	- 	_ 	— 	- 		\ 	\ 	_ 	__ 	~ 	__ 	— 	__ 	— 	-- 	1CG2 	
8UO 														\ 								1472 	
															X 								
ri "7 A(l 																\ 							
emperature, "< 	_ 	— 	... 	._ 		_ 	_- 	_. 		C 		__.. 	.._ 	— C 	"~ 	__ 	\ 	s 	V 	— 	— 	: i-« >•
1 S c^
naperature, J? 	
										x^ 	K-— 												
a on 							^ 															rrrt 	
					X 																		
300 				x 																		f Hrt 	
																							
200 																						392 	
123
Distance jfrom Inside of Water Leg, Feet
fk;. 176.

Curve showing variation in tr-mporuturc at
wat<T U'K of a Hinglo. pann horizontally baffled b
loci
curvcH were obtained by uiovinjr, the (
a point (> in inside the water lep; to a point 48 ii
Hfferent distjuieoH from the insides of the
iler, Holid fuel, underfeed Btoker. These
ted at point.s B and f' by (>-in steps from
from the water lep;. These curves ilhiB-
ilng a stream of hi^h temperature gases
trate the "hydraulie" flow of the hot Kasen for r
below the lower surface of each baffle and etutcadiiiK <>vur the end of the baffle to the next
higher level. The location of the high temperature poiritw and the drop in these curves
indicates the trajectory of the stream of gases due to its horizontal velocity in flowing off
the end of the baffles.
who has watched a bonfire located where the flames were sheltered
from the wind, has noticed that there were continual flame surges.
In fact a fairly good idea of flame surges may be obtained by
watching a match burn -when the flame is sheltered from all
drafts. Another illustration of the surging of flames is the
" singing flame " mentioned in all works on elementary physics.
Any flame burning in an enclosure will be subjected to certain
periodic vibration.

COMBUSTION and boiler settings'

343

The slight amplitude of the temperature surges at C is due to
The fact that this couple is located at a point where a pocket of
hot gas occurs      This would hold the temperature within rather
close limits and it is fairly probable that these surges are due in part, to the infiltration of cold air, as those couples were located
fairly close lo the center line of the boiler. This location would
bring them between the two drums at a point where cold air might
drop them thorn from leakage. The air leaking in at this point would
be heated by the* brickwork. Stratification would not be likely

fkj. 177.
Diagram showing the flow of gases in two pass horizontally baffled boiler. Temperature measurements made in this setting are shown in curves, Figs. 178 and 179. This boiler is the same size and make as the single pass shown in Fig 174. Presumably the steam was generated at about the same rate in both boilers. The location of cool gas pockets is indicated in the same manner as in Figs. 170 and 179.
at this locution tin the tubes have a tendency to mix the gases
very completely uh they pans upward.
The large* amplitude of the temperature surges at A is probably
due* to the fact that this couple was at times immersed in the jet
of ascending hot. gases and at other times in the eddy of com-
paratively cool gases at this point. Another factor that is men-
tioned in the caption of the curve is the formation of balls of
chilled gases among the tubes. These balls of cool gas will have a
tendency to drop into the lower portion of the setting, but will be
sustained by the up flowing current of hot gases. An analogy
in found in the submerged bubbles of air caused by a stream of
water falling into a body of water.

344

APPENDIX IX

Another fact that is shown in Fig. 173 is that the temperatures
at points A and C are those between which the dissociation cf
2 CO to C and C02 will occur as shown in the curve in Fig. 180.

						I 															2102
3012
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1472 °S
1292 |
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1832
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			Tcmpfrntur 	e of Steam at 35G°F, a 	nd 	111 Po 	UtH 	» 					
	
Telocity of Cases, Feet Per Second
3 SI g^ a o* £ $ e
7 i Temperature, Cj ^,1 »- 1 *. i
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				Tcmpetatuie of Steam at 35C F, and 131 Pounds 					

		i 	1                     1              "    	 1 "•     1          I 					
	
0-4         8        12       16        20       24       M       32       30     40
Length of Pitk at Gaees from ToBiUoa oIThetmooouple 4. Feefc
fig. 178.
Curve showing the temperature of gases flowing through double pass horizontally
baffled boiler in Fig. 177. Positions of thermo couples indicated by letters. Solid line
curves show temperatures indicated by pyrometer couples. Dotted line curve shows
computed approximate true gas temperatures. Dash curve shows computed gas velocities,
probably based on gases occupying full area, of pass. Upper and lower diagrams show
similar data for two different initial temperatures.
A considerable portion of the soot formed in this pass will drop
into the pocket in the setting below the pass, other portions will
pass on and out of the stack.

COMBUSTION AND  BOILER SETTINGS

345

Fig. 174 shows the stream of hot gases passing through a
single pass horizontally baffled boiler. The location of pyrometer
couples is indicated by letters and the curves in Figs. 175 and 176
have been plotted from the readings made. The point B on
curve in Fig. 175 is 125° lower than the peak of the curve in Fig.
176. In commenting upon Fig. 176 (Fig. 14, Bulletin 145) the
bureau says: " Couple B showed a considerable range of tem-
perature variation. The maximum temperature, which was at a
point about 2 ft from the inside of the water leg, was 430° C.

200
392
1234
Distan.ce from Inside of Water Leg, Feet
fig. 179.

Curves showing the temperature at points at different distances inside of the water
legs of the boiler as indicated in Fig. 177, showing two pass horizontally baffled boiler.
The flatness or lack of variation in curves B and E indicates that one of these was located
in a chilled gas pocket and the other in a stream of hot gases. Curve C indicates that
the points furthest from the water leg were just on the edge of the stream of hot gas flowing
below the baffle. The drop toward the water leg shows an eddy of cooler gas at this point.
The drop in D furthest from the water leg shows the cool gas pocket formed above the
baffle.

higher than that at a point 4 ft from the water leg. This wide
variation was undoubtedly caused by the position of the end of the
lower baffle and the sudden turn of the gases. It seems that
immediately above the lower baffle there was a layer of comparatively
inert gas which had a temperature much lower than that of the stream
of moving gases." The italics are the writer's. It will be noted
that the bureau attributes this correctly as a layer of cool gas is
indicated in Fig. 174 immediately above the lower baffle. The
drop in the curve C (Fig. 176) is likewise due to this eddy of cooler
gases. In this boiler (Fig. 174) the slope of the upper baffle is
such that it will tend to increase the velocity of the stream of hot

346

APPENDIX IX

gases flowing immediately below it, thus decreasing the thickness
of the stream and increasing the thickness of the eddy of cooler
gases below it.
It is to be regretted that the bureau did not make surge
observations in this boiler setting as they would have been par-
ticularly interesting. This particular setting is an extremely good
example of what should not be done. In his book, Fours a Flamme,
Professor Groume-Grjimailo makes the following comment upon
boiler settings: " The builders of boilers very rarely pay any

Combustion of Solid Fuel
32*
2S*
24*
20 %
1C*
12*
s*
4* 							— ^- 	 ' 	^. 		

	E de J
2CO» 	1-Le Chi 	teller 	Exother 	Dic 	/^ 				

	c+o « 	2coC° 	L — 39
L- + 29.1 	Endothe
Exother 	•mic     /
nic / 	_ Curve 	of Disso
of CO 	iation 		

	C+Oo
CO+ 0> 	,C02 	L-+97.6
L-+68.2 	Exothermic/ 3(CO
Exothermic
i/ 	)+5(CO. 	)- i.oci 	x prcscnc
of N«) 		

		— -^ 	^ 		19300 ,L<
T 	g.nep    4CO-o) "1
(1-5 COs)2 	J.Crcoustt 	ut 	

			^ 	V 						

			./ 	/ V- 	-   Curve 	f Dissoci
of COS 	ition 			

			/ 		\ 					

		^ 				^^ 	~— 	 _ 	~ 	 rnl .I-....I.I-- 		
400°
500°
700°
800°
900°
1200°
1000°

fig. 180. — Equilibrium Curves of CO and C02 in the Presence of Nitrogen.
In the combustion of solid fuel the reaction occurs with a rising tempera-
ture CO-2Tl-C = 2CO when the temperature drops, particularly in the
presence of iron oxide the reaction reverses,
attention whatsoever to the rational distribution of the hot gases.
These defects are extremely common in the most recent designs
of water tube boilers; this is the explanation of the numerous
systems of bafflings and obstructions of the gas passages which
are intended to distribute the hot gases in such a manner that they
will bathe regularly and uniformly the tubes of the boiler. In
reality it is not necessary to have any baffling or distributing walls.
The hot gases will rise of their own accord and the heat will be
regularly and uniformly distributed to all parts of the boiler.77
The setting designed by A. Bement is shown in Bureau of Mines

COMBUSTION AND BOILER SETTINGS	347
Bulletin No. 40, Fig. 3, page 15. This setting comes the nearest
to being in agreement with the flow conditions existing in a boiler
set as recommended by the builder. Mr. Bement, however, has
altogether too great an area in his first and last pass.
Fig. 177 shows the gas flow in a two pass horizontally baffled
boiler. This design of baffling is better than the single pass. The
gas velocities computed by the Bureau of Mines are much higher
(see curve, Fig. 178) than those of the single-pass boiler. In
reality the gain in this boiler is due to the longer path of the gases
in contact with the tubes, but it is extremely doubtful whether
the gas velocity is any higher than in the single-pass boiler.
Fig. 179 shows curves of temperatures made by locating the
thermo couples at different distances from the water legs. The
drops in curves D and C indicate the same pockets of cooler gas
which occurred in the single-pass setting. While the regularity
of the curve E would seem to show that this couple had not at
any time come in contact with the stream of hot gases.
The location of the last thermo couple in all of these tests
seems to the writer to cause some doubt as to whether it really
showed the temperature of the stream of hot gases leaving the
boiler. This stream of ascending gas would have a fairly high
velocity due entirely to its temperature and it is extremely unlikely
that it filled the full area of the gas uptake, being surrounded by a
layer of relatively cooler gases.

APPENDIX X
HEAT CAPACITY AND CALORIFIC INTENSITY CURVES
by A. D. WILLIAMS
heat is probably the energy of the moving molecules of a
substance. Its intensity is measured by the thermometric scale,
and its quantity by the Calorie or the British thermal unit. Heat
transfer takes place by conduction, convection or radiation and
will occur whenever a temperature differential exists. Fuel is
merely latent heat energy. The quantity of heat stored in a unit	!
of fuel may be determined by the calorimeter or computed from	\
the chemical composition of the fuel.    But the amount of heat	1
stored up within the fuel does not supply any index of the tern-	j
perature differential which may be established by its combustion.	!
For instance, blue water gas at 300 B.t.u per cubic foot will
produce a higher temperature than natural gas of three times this
thermal value or producer gas of one-half its thermal value, while
all of these fuels may be used in a suitably designed furnace for
the melting of steel or for other high-temperature applications.
Combustion is the oxidation of fuel, releasing the latent heat
and establishing a temperature differential which will permit
utilization of the heat. The losses which occur in combustion are
small and comparatively unimportant in comparison with the
enormous losses which occur in the application and utilization
of the heat released. At the same time fuel costs are continually
advancing. This leads to a consideration of the possibility of
substituting for one fuel another, or of introducing methods of
operation and apparatus, which will accomplish the result at a
lower cost.
Comparison of the relative values of different fuels for any
given purpose involves many factors, any one of which may have a
determinative effect. There are many tables giving the thermal

HEAT CAPACITY AND  CALORIFIC INTENSITY CURVES   349
values of fuels, as determined by the calorimeter or by computa-
tion, but the temperature obtainable by the use of any particular
source of heat energy depends upon so many variables that it
cannot be reduced to tabular form. Experiment and practice
have developed a certain amount of knowledge regarding the tem-
peratures obtainable, but this is an uncertain guide regarding
the temperature effects which may be expected under different
conditions.
The temperature obtainable by the oxidation of a combusti-
ble depends upon:
(a) The quantity of heat released by the oxidation of a unit
of combustible;
(6) The oxygen supply or the amount of air used;
(c)	The temperature of the fuel and air supply at the point
of combination;
(d)	The heat capacity of the products of combustion;
(e)	The velocity of the reaction of combustion;
(/)   The combustion chamber;
(g) The completeness of the reaction.
Each one of these seven important variables has a considerable
effect upon the temperature produced, a is readily obtainable.
b and c are susceptible of control and in turn bring d under control.
The problem may be solved by making certain assumptions regard-
ing the other variables. These assumptions are:
1.	That complete, instantaneous combustion occurs;
2.	That the total amount of heat released is contained in the
products of combustion, i.e., that combustion occurs
in an athermal chamber which does not absorb or
give off heat.
It is impossible to realize either of these assumptions in practice,
but they permit the computation and plotting of curves which
supply a large amount of " relative " information regarding the
temperature possibilities of a combustible under a variety of
conditions. True, the values are only approximate, only relative,
the assumed conditions impossible, but at the same time these
curves permit a very close approximation of the results obtained
in practice and of the effect of variations in operating conditions
upon the temperature realized. There is a time element in the

350	APPENDIX X
combustion of any substance. This time element varies with the
temperature of the combining bodies according to an exponential
law. High-velocity combustion may be extremely desirable in
artillery practice, or in a very high-speed gas engine, but it would
be of doubtful utility in a boiler setting or an industrial furnace.
The velocity of the reaction is dependent upon mixing as well
as temperature; that is, the same amount of gas burned per
unit of time will give a short flame when jetted through numerous
small holes and a long flame when burned in one jet.
The facility with which gaseous fuels may be mixed with their
air supply is one of their inherent advantages over liquid and
solid fuels. The liquid fuels fall into an intermediate class, while
liquids which have a low evaporative temperature are inter-
mediate between those of high boiling point and the gases.
The investigations of Mallard and Le Chatelier determined the
heat capacity and specific heats of several gases, the heat capacity
of any substance being the amount of heat which will be absorbed
by or given up by that substance when heating or cooling between
the absolute temperatures of to and ti. The specific heat of
this substance at any given temperature may be derived from its
heat capacity, or the amount of heat that will be absorbed in
increasing its temperature from tq to ti. In all heating and
cooling operations, the heat capacities of the substances involved
are much more important than their specific heats, as the function
of the operation is heat interchange. The heat capacities fix the
amount of heat that may be given up by one substance as well
as the amount of heat absorbed by the other substance, between
the temperature limits involved.
Therefore these curves, in addition to showing approximately
the temperature that may be realized from the combustion of the
particular combustible, give the amount of heat that will be
available or given off by the products of combustion in cooling
from a high temperature to a lower one.
The utilization of this heat will depend upon:
(a) The ruling temperature of the operation, that is, the
upper and lower temperatures required;
(6) The design of the heating chamber;
(c) The heat capacity of the substance to which the heat is
imparted;

HEAT CAPACITY AND  CALORIFIC INTENSITY CURVES   351
(d)	The thermal receptivity and mass of the substance to
which heat is imparted ;
(e)	The temperature differential established;
(/)  The velocity of flow of the gases;
(g) The pressure in the combustion chamber.
The accompanying curves show the. possibilities, as regards
heat transfer, of the respective combustibles when burned with
various amounts of excess air and various amounts of preheat
for the air and the fuel, when this latter does not contain hydro-
carbons dissociated by preheating. The chemical composition
of these combustibles is given in Table 6. In the case of the
liquid and pulverized fuels the amount of air or steam required
for atomizing purposes is given in the caption of the curve. One
of the interesting facts revealed is that the use of steam instead of
air for atomizing oil results in reducing the temperature obtainable
by 170° C. (306° F.). This is due to the fact that the same
amount of air is required in both cases, and the steam merely
increases the volume and weight of the products of combustion.
At the same time it may be that it is much more economical to use
the steam directly in the atomizing instead of indirectly in com-
pressing the air for atomizing. A steam jet is notoriously inefficient.
In a marine installation where space and weight have to be con-
sidered, a Great Lakes boat would use a steam jet floating in her
boiler feed supply. On salt water, where boiler make-up is
obtained by evaporation, an air compressor would exhaust to the
condenser and evaporator capacity would be saved or the air blast
fans would be run by motors. Steam jets would increase evap-
orator capacity and heat consumption. Mechanical atomizing
will avoid fans or compressors but will necessitate the use of oil
heaters and the pumps necessary to create the oil pressure required
for the spray nozzles. Assuming a 20 per cent excess air supply, the
comparison on p. 352 can be made from the curves. While the
difference in favor of air atomizing is only 1 per cent of the heat
released it is available in producing steam at boiler efficiency, from
1 to 9 per cent of the steam generated will be used in atomizing.
The oil will evaporate from 11 to 14 times its weight of water.
With air atomizing the temperature in the firebox will approxi-
mate 1885° C. (3280° F.) and with steam 1710° C. (3110° F.).
The actual temperature realized will be about 100° C. or 200°

352

APPENDIX X

	Steam Atomizing 	Air Atomizing 	

	Calories
per
Kg- 	B.t.u.
per
Lb. 	Calories
per
Kg. 	B.t.u.
per
Lb. 	
Heat released by oil                    .   .   . 	10,400
1,960 	18,720
3,528 	10,400
1,850 	18,720
3,330 	
Heat carried to stack at 400 ° C . (752° F.)
Difference available in boiler . 	

	

	8,440 	15,192 	8,550
110 	15,390
198 	
Difference in favor of air atomizing . . 	

	
	
F. lower, due to firebox construction. In fact, much lower tem-
peratures may be obtained under unfavorable conditions. Similar
methods to the above make these curves and the volumetric data
in Tables 11 to 21 extremely useful in designing furnaces for a
particular fuel.
Several systems are in use for preheating the air for boilers on
ships and on land. The temperature drop of the waste gases
ranges from 70° C. (126° F.) to 120° C. (216° F.). The tempera-
ture rise in the air ranges from 60° C. (108° F.) to 105° C. (189° F.).
These curves may be utilized to approximate the effect of such
preheat:
Steam or Air Atomizing

	Calories
per Kg. 	B.t.u.
per Lb. 	
Heat in 120 per cent air supply at 120° C.
(184° F )                . .            	 	420 	756 	
			
This will result in an increase in calorific intensity of about 50° C.
(90° F.). This extra heat will be utilized at boiler efficiency in
producing steam. Preheating of the oil supply to secure fluidity
results in a slight addition to the heat available.
The ruling temperature of a heating operation is the tempera-
ture to which the material being heated must be raised in order to

HEAT CAPACITY AND CALORIFIC INTENSITY  CURVES   353
effect a given result. In order to produce this rise in temperature
a heat flow must be established by a temperature differential.
In many cases it is necessary that the products of combustion
leave the heating chamber at a temperature higher than the
ruling temperature. This is the case in the open-hearth furnace,
the steam boiler, etc. One of these is such a high-temperature
operation that it is necessary to preheat the air and frequently
the fuel supply in order to attain the high temperature at which
the waste gases leave the chamber, while waste heat boilers
can be advantageously employed to recover heat leaving the
regenerator chambers. The steam boiler is a low-temperature
heat application and for that reason permits a greater heat
utilization than is possible in a high-temperature process; at
the same time it is frequently found desirable to pass the gases
leaving the boiler through an appliance which recovers heat and
returns it to the boiler in the shape of hot feed-water or preheated
air supply. The foregoing methods of preheating the air and
fuel supply or the waste heat boiler are indirect methods of heat
recovery, while the heating of the feed water or the preheating
of material as it is moved from a low temperature to a higher
temperature zone in the same furnace are direct methods of heat
recovery. The indirect methods involve a greater inherent heat
loss than the direct methods. High-temperature operations and
processes cannot be accomplished without considerable loss of
heat. The lower the temperature required for an operation or
process the greater the possibility of reducing the heat loss to a
minimum by utilizing the maximum amount of the heat released
in the operation itself. At the same time the very ease with
which the low-temperature operation may be accomplished leads
to a very superficial study of its possibilities. Therefore such
operations are notorious for their wasteful utilization of the heat
and fuel.
It is hardly necessary to state that intermediate conditions
between those plotted on the curve may be obtained by proportion.
In the same manner other values for preheat may be established
by the use of dividers and graphical addition; that is, the curves
permit the making of numerous approximations, giving a relative
idea of what may be expected from any fuel, a base for the com-
parison of the results which may be obtained by the substitution
of one fuel for another> However, it is very important to bear

354	APPENDIX X
in mind that the heat appliance which works successfully and
economically with one form of fuel may not be adapted in any
way to the use of another form of fuel, unless extensive alterations
are made. There are great differences, not only in the amount of
heat released by different fuels, but in the temperatures obtained
by the different fuels. For instance, Table 22 compares several
gases, arranged in the order of the temperatures obtained through
their combustion with the theoretical air supply. It is interesting
to note that blue water gas comes first with a thermal value of less
than one-third that of natural gas, which comes third in calorific
intensity. Another interesting fact is that with 80 per cent
excess air, natural gas and a good producer gas are very nearly
on par. This tabulation also shows the number of volumes of air
supply, products of combustion and combustible mixture. The
gas cannot burn unless it has an opportunity to combine with
oxygen and it is the thoroughness of the mixing which governs the
length of the flame and its temperature. With too long a flame
and without good mixing, the temperature realized may be very
much lower than the potential temperature of the gas.
The working base necessary for the computation of any of these
curves is a complete analysis of the fuel, either by weight or by
volume. When the proportions are given by weight, each unit
per cent is taken as 10 grams or 10 ounces and divided by the
molecular weight to obtain the molecular proportions. Volu-
metric values may be considered as gram molecules or ounce
molecules or as cubic feet or cubic meters. As the chemical
equation of any substance fixes the relative weights of the sub-
stances and the relative volume when in the gaseous state as
well as the amount of heat released or absorbed in a reaction,
basing the computations on the molecular composition simplifies
the work of computation by eliminating a number of clumsy
conversion factors.
A further advantage of using molecular units arises from the
following facts:
When the weight is in grams the volume is	22.32 liters
When the weight is in kilograms the volume is	22.32 rn3
When the weight is in ounces the volume is	22.32 cu ft
Another short cut is the assumption that the air consists of
1 volume of oxygen and 4 volumes of nitrogen, making 5 volumes

HEAT CAPACITY AND CALORIFIC  INTENSITY CURVES   355
of air. This assumption is close enough for the purpose and saves
much laborious calculation. In addition it compensates to some
extent for the fact that the air naturally contains a certain amount
of water vapor and that all combustible gases carry water vapor,
being generally saturated at ordinary temperatures.
Table 6 gives the usual combustible elements of fuels, their
molecular weights and the amount of heat released in calories
per gram molecule at constant pressure, water assumed to remain a
vapor. While this last assumption gives lower thermal values it
agrees with practice, inasmuch as water vapor never condenses
within the furnace. The reaction formulas given in this table
do not contain the nitrogen. Table 7 is merely an extension of
this table, giving oxygen required for the hydrogen and carbon
and the total oxygen, the volume of nitrogen and the air volume,
as well as the volume of the products of combustion. This table
is based on the assumption that the air consists of 1 volume of
oxygen and 4 of nitrogen.
The first step in the plotting of. these curves is the computation
on Table 1, in which the volumetric composition of the gas is
considered as giving the number of gram molecules. These are
multiplied by the calories released per molecule at constant
pressure, and the summation of these values gives the total heat
released by the combustion of 100-g molecules of the gas. In
the case of solid or liquid fuels it is necessary to divide the weight
of each element multiplied by 10 by the molecular weight of the
substance or use weight values for the heat released. The prod-
ucts of combustion and the amount of oxygen required are tabu-
lated for the combustible portions of the fuel, and summed with
the inert portions of the fuel. When the fuel contains oxygen
the amount of this oxygen is deducted from the total of the
oxygen column and four times this value is deducted from the
total of the nitrogen column. The summation of these four
columns gives the total amount of oxygen required and the
products of complete combustion in air. If the weight of the
fuel is desired the number of molecules may be multiplied by the
molecular weights. This total weight may be readily converted
to the specific weight of a unit volume.
Should it be desired to note the effect of reducing the air
supply, deficiencies of 20 and 40 per cent are generally assumed
in order to get three points. Hydrocarbons are assumed to dis-

356	APPENDIX X
sociate. It is likewise assumed that 90 and, 80 per cent of the
hydrogen is consumed and the oxygen remaining is combined with
the carbon and carbon monoxide. These assumptions may not be
correct, but they supply a base for the purpose desired and data
covering the case have not been found. Several other assumptions
were made and tried, but the one given seemed to average up with
the others within 4 or 5 per cent; therefore it was used. The
amount of heat released and the products of combustion were
computed in the same manner as for complete combustion,
except that the unconsumed hydrogen and carbon monoxide were
carried into the products of combustion as shown in the computa-
tions on Table 1.
Table 2 is a tabulation of the air supply and the products
of combustion for various percentages of the theoretical air
supply ranging from 60 to 500 per cent. These values are
selected with a view to facility in computation; that is, the
volume of excess air or deficiency in air, in the second and
fourth lines of the table, is the same as the volume of oxygen for
complete combustion, and the other values in this column are
simple multiples of this value. The deficiency or excess of
oxygen is one-fifth of the excess or deficiency in the air supply.
The excess of nitrogen is the difference between the excess air and
PI! '	the excess oxygen. The total nitrogen is obtained by adding the
excess nitrogen to the volume of nitrogen in the products of com-
bustion with 100 per cent air supply. The last column, total
products of combustion, is obtained by adding the excess air to the
total volume of products of combustion with 100 per cent air
supply.
Table 3 is the computation of the points for the heat capacity
curves of the products of combustion resulting from 100-g mole-
cules of the gas. For the case in hand the computation has been
carried to ridiculous limits in order to determine the limiting
combustion conditions both with excess air and with a deficiency
of air. This point is of some importance in connection with the
use of producer and blast furnace gases, and in certain applica-
tions of these gases it has been found necessary to use an auxiliary
coal fire in order to insure ignition. It is well known that with
both of these gases the flame may be extinguished by an excess
of air cooling the products of combustion and the heating chamber
below the ignition temperature of the gases. Similar difficulties

HEAT CAPACITY AND  CALORIFIC  INTENSITY CURVES     357
are experienced in starting up regenerative furnaces where the
operator has been unfamiliar with producer gas.
Table 8 gives the heat capacities of the usual gases found in the
products of combustion as determined by the formulas developed
by Mallard and Le Chatelier. These formulas, given in Table 10,
were used in computing the heat capacities of the gases at intervals
of 200° C. (360° F.) between 0° C. (32° F.) and 2600° C. (4712° P.)
which are given in Table 8.
At the bottom of Table 1 there have been collected and
totalized the numerical values used in the second column of
Table 3 designated by the symbols N2+ and N2. These gases
have the same heat capacity per gram molecule as given in the
second column of Table 8. This procedure simplifies the com-
putation. The other numerical values in the second column of
Table 3 were brought forward from Tables 1 and 2. These
numerical values, designating the number of gram molecules in
the products of combustion, were then multiplied by the heat
capacity values given in Table 8 and the products for steps of
400° C. (720° F.) were tabulated in columns three to nine, inclu-
sive, of Table 3. The points for the curves were obtained by the
summation of these values for the appropriate combustion condi-
tions. These points were then plotted and connected by curved
lines giving a number of diverging parabolas indicated by the
solid black lines, each of which is marked by a percentage value
designating the air supply conditions which influenced the forma-
tion of the products of combustion.
Table 4 shows a similar computation made to obtain the heat
capacity of the gas itself and the air supplies.
The heat capacity of the gas is plotted in dash lines and that
of the air supplies in dot-dash lines, these last being marked with
the percentage values of the air supply.
The next step in the plotting of these curves is the spotting of
the points denoting the amount of heat released by the combustion
of the gas, with 60, 80 and 100 per cent air supply. The values
marked /, F and A in Table 5 give the summations of the number
of calories released by the gas as given in Table 1, where they are
marked with the same reference letters. From this point on, the
plotting may be done graphically or by computing the points as
in Table 5. When the points /, F and A have been spotted, a line
parallel to the temperature scale is drawn downward crossing all

358

APPENDIX X

the heat capacity curves, over 100 per cent air supply, the assump-
tion being made that the total heat released is absorbed in raising
the temperature of the products of combustion. This curve has
a point of flexure at A on the curve of the heat capacity of the
products of combustion formed with 100 per cent or theoretical
air supply.
With this line as a base the points for similar curves may be
located by setting off with a pair of dividers the additional heat
capacities added by the preheating of the gas and the air supply
to any temperature. These heat capacities are given in Table 4
and are plotted on the chart. The dividers may be set from the
air or gas heat capacity curves on the charts and measuring the
quantity of heat added at the temperature of preheat, and this
distance added to the base line A to fix a point upon a curve
showing the effect of preheat. Care should be used in stepping
these distances off to set the dividers parallel with B.t.u. or
calorie scale.
The writer frequently prefers to sum up the preheat points
analytically, as shown, and use reference letters to connect the
corresponding values shown.
TABLE 1
peoducee gas No. 3, clean cold gas.    tae retttened to peodttcer
Liscum, A. C.    Ford Motor, Co., Power, Aug. 31, 1920

Theoretical Air
Supply
(1)    (2)         (3) 	Calories
(4) 	02
(5) 	Products of Combustion 	

	
	C02
(6) 	H2O
(7) 	N2
(8) 	
H2   16.60X 58.2 =
CH4 5.50X195.2 =
CO 27.10X 68.2 =
CO2  3 90    ... 	966
1074
1848 	8.30
11.00
13.55 		16.60
11.00 	33.20
44.00
54.20
46.30 	

	
	5.50
27.10
3.90 	

	

		
	
N2   46.30    	 			

	
H2O 0.60    	 				0.60 	
	
/ 				

	3888 	' 32.85 	36.50 	28.20 	177.70 	

HEAT CAPACITY AND  CALORIFIC  INTENSITY CURVES    359
80 per cent air supply.    Assumed that CH4 dissociates, that 90 per cent
will be burned.    02 available = 32.85X0.8 =26.28.

80% Air Supply 	Calo-
ries 	Products of Combustion 	

	02 	H2 	CO 	C02 	H2O 	N2 	
H2   16.60X0.9 = 14.94X58.2 =
CH3 5.50     Dissociates
H2   11.0 X0.9= 9.90X58.2 =
C       5.50                        X97.6 =
26.28-17.92=8.36
CO 27.10             16.72X68.2 =
C02  3.90
N2   46.30
H20 0.60
F 	870
576
537
1141 	7.47
4.95
5.50 	1.66
1.10 			14.94
9.90 	29.88
19.80
22.00
33.44
46.30 	

	

	

	

		5.50 	

	
	
		10.38 	16.72
3.90 		

	
	17.92
8.36 	

	

					

	

						0.60 	

						

	3124 	26.28 	2.76 	10.38 	26.12 	25.34 	151.42 	
60 per cent air supply.    Assumed that CH3 dissociates, 80 per cent of H2
will be burned.    O2 available = 32.85X0.6 = 19.71.

60% Air Supply 	Calo-
ries 	Products of Combustion 	

	02 	H2 	CO 	CO2 	H2O 	N2 	
H2   16.60X0.8 = 13.28X58.2 =
CH4 5 . 50   Dissociates
H2   11.00X0.8= 8.80X58.2 =
C       5.50                        X97.6 =
CO 27.10
19.71-16.54 = 3.17
6.34X68.20 =
A 	773
512
537 	6.64
4.40
5.50 	3.32
2.20 			13.28
8.80 	26.56
17.60
22.00
12.68
46.30 	

	

	

	

		5 50 	

	
	
		20.76 	6.34
3.90 	0.60 	

		16.54
3.17 	

	

	432 	

	

	

	2254 	19.71 	5.52 	20.76 	15.74 	22.68 	125.14 	
100 per cent air supply, products of combustion: N2 = 177.70
80 per cent air, products of combustion:
N2-fCO-f-H2 = 151. 42+10. 38+2.76 = 164. 56.
60 per cent air, products of combustion :
2 = 125.14+20.76-h5.52 = 151.42.
The assumption is made that air = l volume O2 and 4 volumes of N2;
that 5 volumes of air are required to supply 1 volume O2. This allows for
moisture in fuel and air supply.

APPENDIX X
TABLE 2
volumetric Am supply and volume op pkoducts of combustion per
100 volumes of gas burned.    computed from data in table 1

Per
Cent
(1) 	Air Supply 	Products of Combustion per Unit Volume of Gas
Burned 	

	Vols.
(2) 	Excess
Vols.
(3) 	Excess
02
(4) 	CO
(5) 	H2
(6) 	C02
(7) 	H20
(8) 	Excess
N2
(9) 	Total
N2
.(10) 	Total
Vols.
(11) 	
60
80
100
120
140
180
260
340
420
500 	98.51
131.40
164.25
197.10
229.95
295.65
427.05
558.45
689.85
821.25 	-65.70
-32.85
0.0
+32.85
65.70
131.40
262.80
394.20
525.60
657.00 	-13.14
- 6.57
0.0
+ 6.57
13.14
26.28
52.56
78.84
105.12
131.40 	20.76
10.38 	5.52
2.76 	15.74
26.12
36.50
36.50
36.50
36.50
36.50
36.50
36.50
36.50 	22.68
25.34
28.20
28.20
28.20
28.20
28.20
28.20
28.20
28.20 		125.14
151.42
177.70
203.98
230.26
282.82
387.94
493.06
598.18
703.30 	189.84
216.02
242.40
275.25
308.10
373.80
505.20
636.60
768.00
899.40 	

	

	

		

	

	

	
	0.0
26.28
52.56
105.12
210.24
315.36
420.48
525.60 	

	

			

	

	

			

	

	

			

	

	

			

	

	

			

	

	

			

	

	

			

	

	

			

	

HEAT CAPACITY AND  CALORIFIC INTENSITY CURVES    361
TABLE 3
points for heat   capacity   curves   of   pkoducts   of   combustion
computations made on basis of 100 volumes of gas burned
Values of Heat Capacity per gram molecule from Les Sources de L'Energie
Calorifique by Damour, Carnot and Rengade, based on the work of Mallard
and Le Chatelier. Refer to Table 7.
heat capacity of products of combustion.   (Note Below)

(1)
Tempera-
tures 	(2) 	(3)
400° 	(4)
800° 	(5)
1200° 	(6)
1600° 	(7)
2000° 	(8)
2400° 	(9)
2800° 		
N2+
C02
H20 	51.42
15.74
22.68 	427
63
84 	881
143
187 	1370
245
315 	1,887
364
462 	2,431
501
630 	3,005
657
819 	3,607
832
1,035 	60% air 	
S~ 		574 	1211 	1930 	2,713 	3,562 	4,481 	5474 	Curve points 	
										
N2 +
C02
H2O 	164.56
26.12
25.34 	464
104
94 	958
237
209 	1489
406
351 	2,050
603
516 	2,641
832
703 	3,265
1,091
915 	3,920
1,380
1,156 	80% air 	
s — 		662 	1404 	2246 	3 169 	4 176 	5 271 	6 456 	Curve points 	
										
N2
CO2
H20 	177.70
36.50
28.20 	501
140
104 	1034
331
232 	1608
568
391 	2,213
843
574 	2,852
1,162
783 	3,526
1,524
1,048 	4,232
1,929
1,287 	100% air 	
S A — 		751 	1597 	2567 	3 730 	4 797 	6 098 	7448 	Curve points 	
										
33=20% 	32.85 	93 	192 	29S 	410 	526 	652 	783 	120% a:r 	
£/!+# = 		844 	1789 	2865 	4,140 	5,323 	6,750 	8,231 	Curve points 	
C=40% 	65.70 	185 	383 	595 	819 	1,055 	1,304 	1,565 	140% air 	
SA-j-C = 		936 	2172 	3460 	4,549 	5,852 	7,402 	9,013 	Curve points 	
£> = 80% 	131.40 	371 	765 	1189 	1,637 	2,109 	2,607 	3,130 	180% air 	
2A+I> = 		 	1122 	2362 	3756 	5,367 	6,906 	8,705 	10,578 	Curve points 	
$ = 160% 	262.8C 	742 	1530 	2378 	3,274 	4,218 	5,214 	6,160 	260% air 	
SA-j-# = 		1493 	3127 	4945 	7,004 	9,015 	11,212 	13,608 	Curve points 	
-P = 240% 	394.20 	1113 	2295 	3567 	4,911 	6,327 	7,821 		340% air 	
SA-fF = 		1864 	3892 	6134 	8,641 	11,124 	13,919 		Curve points 	
0 = 320% 	525.60 	1484 	3060 	4756 	6,548 	8,436 		 		420% air 	
SA+£ = 		2235 	4657 	7223 	10,278 	13,233 			Curve points 	
// = 400% 	657 00 	1853 	3824 	5946 	8 187 				500% air 	
										
2A + H-~ 		2609 	5421 	8513 	11 917 				Curve points 	
										
This computation has been carried out further than necessary in order to approximate
the limits in regard to combustion conditions, both with excess and deficient air supply.

362

APPENDIX X

TABLE 4
heat capacity of air supplies and gas. points for curves and to
be used in spotting the intersections jndicating the effects
of preheat
This particular producer gas is rather high in CH4 which will have a
tendency to dissociate at high temperatures. This has not been considered
in order to find the limiting combustion conditions due to air supply.
heat capacity of air supply

Temper-
tares,
Per
Cent. 	Vol. 	200° 	400° 	600° 	800° 	1000° 	1200° 	Reference
Letters
Table 5 	
Air    60
~80 	98.55 	137 	278 	425 	573 	732 	893 	D
II
K
L
M
N
P
0
R
S 	

	131.40 	183 	371 	566 	765 	976 	1189 	
	
100 	164.25 	228 	463 	708 	956 	1220 	1486 	
	
120 	197.10 	274 	556 	850 	1147 	1464 	1784 	
	
140 	229.95 	320 	648 	991 	1338 	1708 	2081 	
	
180
260 	295.65 	411
594 	834
1204 	1274 	1721 	2197 	2676 	

	427.05 	
	
	1840 	2485 	3173 	3865 	
	
340 	558.45 	776 	1575 	2407 	3251 	4149 		
	
420
500~ 	689.85 	959 	1945 	2973 	4015 	5126 		

	821 . 25 	1140 	2S21 	3535 	4774 	6094 		
	
heat capacity of gas 	

N2 + 	90.00 	125 	263 	368 	525 	669 	814 		
C02 	3.90 	7 	16 	25 	35 	48 	61 		
H2O 	0.60 	1 	2 	4 	5 	7 	8 		
CH4 	5.50 	12 	27 	44 	63 	87 	.112 		
S 		145 	308 	441 	623 	811 	995 	B 	

HEAT CAPACITY AND CALORIFIC INTENSITY CURVES   363
TABLE 5
computation for points on heat capacity curves showing the effects
of preheating gas, air supply and both the gas and the air
supply
The numerical values used are obtained from Tables 3 and 4, and are
combined as indicated.

Temperature
of Preheat 	0° 	200° 	400° 	600° 	800° 	1000° 	1200° 		
Calories Re-
leased Gas (A)
(B) 	2254 	145 	308 	441 	623 	811 	995 	60% air 	
A+B      2(C) 		2399 	2562 	2695 	2877 	3065 	3249 	points 	
(Z» 		137 	278 	425 	57 S 	732 	893 		
A+D*=E   S 		2391 	2532 	2679 	2827 	2986 	3147 	points 	
c+d       s 		253(3 	2840 	3120 	3450 	3797 	4140 	points 	
F
B + F**G    S 	•3124 	3179 	3432 	3565 	3747 	3935 	4109 	80% air
points 	
. H 		183 	371 	566 	765 	976 	1189 		
F~\-n       s 		3307 	3495 	3690 	3889 	4100 	4213 	points 	
G-{-H          S 		3362 	3803 	4131 	4612 	4911 	5298 	points 	
I
J           S 	3888 	4033 	4196 	4329 	4511 	4699 	4883 	100% air
points 	
K 		228 	463 	708 	956 	1220 	I486 		
li-K          2 		4116 	4351 	4596 	4844 	5108 	5374 	points 	
/-f/C          S 		4261 	4659 	5037 	5467 	5919 	6363 	points 	
L
J=L            S
J-f-L           £ 		274
4162
4307 	556
4442
4752 	850
4738
5179 	1147
5035
5658 	1404
5352
6163 	1784
5672
6667 	120% air
points
points 	
M
tf+I          2
J-f M         £ 		320
4208
4353 	648
4536
4844 	991
4879
5320 	1888
5226
5849 	1708
5596
6407 	2081
5969
6952 	140*2 air
points
points 	
JV
tf+J          S
N+J         V 		411
4299
4444 	834
4722
5030 	1274
5162
5603 	1721
5609
6232 	2107
6085
6896 	2676
6564
7559 	180% air
points
points 	
P
P+I          2
P+J          2 		594
4482
4627 	1204
5092
5400 	1840
5728
6169 	%485
6373
6996 	3178
7061
7872 	3865
7753
8748 	260% air
points
points 	
0
0-fJ            S
0-f/            2! 		776
4064
4809 	1575
5463
5771 	2407
6295
6736 	3251
7139
7762 	4149
8037
.9032 		$40% air
points
points 	
ft
72+1           S
R+J          2 		959
4847
4992 	1946
5833
C141 	&97S
6861
7302 	4015
7904
8526 	5126
8914
9825 		420% air
points
Opoints 	
,S
fl-fl            S
S+J           S 		1140
.5028
5173 	2S%1
6209
6517 	SfjSf)
7423
8046 	4774
8662
9285 	6094
10082
10793 		500% air
points
points 	
									
Those computations have been carried out to obtain limiting values on the curves.

364

APPENDIX X

TABLE 6
heat released by the combustion of the principal combustibles at
constant pressure.    water assumed to remain as vapor

I;;

					B.t.u. 			
Substance 	Molec- 						Calories 	
Burned, 	ular 	Molec- 	Reaction of Combustion 			Per 	per 	
Unit Weight
or Volume 	For-
mula 	Weight 	Formula 	Per
Pound 	Per
Cu.Ft 	Ounce
Mole- 	Gram
Molecule 	
						cule 		
Hydrogen. . . 	H2 	2 	H2 -f 0 . 5O2 = H2O 	52,384 	293.2 	6,548 	58.2 	
Carbon to CO 	C 	12 	C+0.502 = CO 	4,411 	148.1 	3,308 	29.4 	
Carbon . 	C 	12 	Q_i_Oo = CO 	14,640 	491.7 	10980 	97.6 	
Carbon mon- 								
oxide 	 	CO 	28 	CO + 0.5O2 = CO2 	4,366 	343.6 	7,673 	68.2 	
Methane .... 	CH4 	16 	CH4+202==CO+2H20 	21,961 	983.4 	21,961 	195.2 	
Acetylene. . . . 	C2H2 	26 	C2H2 + 2 . 5O2 = 2CO2 + H2O 	21,108 	1536.0 	34,300 	304.9 	
Ethylene .... 	C2H4 	28 	C2H4+3O2==2CO2+2H2O 	20,545 	1610.0 	35,955 	319.6 	
Ethane 	 	C2H6 	30 	C2H6 + 3 . 502 = 2CO2 + 3H2O 	20,392 	1812.5 	38,241 	339.9 	
Benzene (gas) 	C6H6 	78 	C6H6 + 7 . 5O2 = 6CO2 -f 3H2O 	17,308 	3779 . 2 	84,380 	750.2 	
Sulphur 	S 	32 	S 4- O2 = SO? 	3,893 	348.6 	7,785 	69.2 	
Sulphur 	 	S 	32 	S-f-1.5O2 = SO3 	5,164 	462.5 	10,328 	91.8 	
Evaporation 								
of water . . . 	H2O 	18 		1,073 	54 . 06 	1,207 	10.73 	

Low values are given for B.t.u. and calories released by different substances. Various
authorities differ on these values. The values given are from Les Sources de L'ttneryie
Calorifique, by Damour, Carnot and Rengade.

HEAT CAPACITY AND  CALORIFIC INTENSITY CURVES   365
TABLE 7
air supply, oxygen required and products of combustion of the
usual combustibles
This table is based upon the assumption that air = l volume of oxygen, 02-f-4 volumes
of nitrogen, N2. This assumption is sufficiently accurate for most purposes and greatly
simplifies the work of computation. If greater accuracy is desired, use 3.8 volumes for N2
and 4.8 volumes for air.
The volumes may be considered as cubic feet, cubic meters, ounce molecules or gram
molecules as desired for the purpose in hand.

Substance
Burned,
1 Volume 	Molecular 	Oxygen Required, 	d 	Required 	Products of Complete Com-
bustion with Air. 	

	| 	bfl 	o w
«?; 	Jo 	3 	
	
	|8 	.20
QO 	O
w
S 	I
o 	""3
o 	

	& 	£ 	°" 	p* 		£ 	^ 	3 	0 	£ 	2 	
	
Hydrogen. . . .
Carbon* to CO
Carbon* 	 	H2
C
CO
CH4
C2EU
c2!6
S
s 	2
12
12
28
16
26
28
30
78
32
32 	0.5 		0.5 	2 0 	2.5 			1.0 	2.0
2.0
4.0
2.0
8.0
10.0
12.0
14.0
30.0
4.0
0.0 	3.0
3.0
5.0
3.0
11.0
13.0
10. 0
19.0
39.0
5.0
7.0 	

	
	
	0.5
1.0 	0.5
1.0 	2.0
4 0 	2.5
5.0 	1.0 	i 6 	

	
Carbon   mon-
oxide 	 	
	
	'i.'o'
0.5
1.0
1.5
1.5 	0.5
1.0
2.0
2.0
2.0
6.0 	0.5
2.0
2.5
3.0
3.5
7.5
1 0 	2.0
8.0
10.0
12.0
14.0
30.0
4 0 	2.5
10.0
12.5
15.0
17.5
37.5
5 0 	"s62"
1 0 	1.0
1.0
2.0
2.0
2.0
6.0 	'2.'6'
1.0
2.0
3.0
3.0 	

[Methane 	

	

	

	

	
Acetylene. . . .
Ethylenc 	
Ethane. . 	

	

	

	

	
Benzene 	

	

	

	

	
Sulphur 	

	

	

	

	
Sulphur 	 	
	
			1.5 	6.0 	7.5 	1.0 			

	

	

			

* Carbon may be considered as a gas or as a solid.
TABLE 8
heat capacity in b.t.u. op gases measured from 32° to t = T—491
pee cubic foot of gas

Temperature,
Degrees F. 	N2 = 28, O2 = 32,
H2 = 2, CO = 28 	H2O=18 	C02 = 44 	CH4 = 16 	
32 	0.00 	0.00 	0.00 	0.00 	
392 	7.00 	8.71 	9.32 	11.03 	
752 	14.21 	18.59 	20.1 	24.43 	
1112 	21.71 	29.57 	32.44 	40.4 	
1472 	29.32 	41.46 	45.7 	57.7 	
1832 	37.43 	55.31 	62.57 	79.44 	
2192 	45.59 	69.87 	78.33 	102.6 	
2552 	54.05 	85.64 	96.5 	128.2 	
2912 	62.77 	102.5 	116.4 	156.1 	
3272 	71.58 	120.2 	137.1 	180.6 	
3632 	80.85 	139.8 	160.4 	219.4 	
3992 	90.22 	160.3 	184.6 	254.6 	
4352 	99.94 	181.9 	210.4 	292.3 	
4712 	109 . 87 	204.6 	237.6 	3-32.7 	
5072 	120 	229.9 	266.2 	374.9 	
5432 	130.4 	255.1 	296 . 5 	419.8 	
Adapted from Les Sources de L'Energie Calorifique, by Damour, Carnot and Rengade.
note.—as CBU and other hydrocarbons (CnKxn) break up at low temperatures around
1450° F., their heat capacity is valueless and such gases cannot be preheated successfully.
Some data as to the dissociation of CH4 and C«HW were given on page 1014 of The Iron Age,
April 24, 1913.

366

APPENDIX X

TABLE 9
Heat capacity in calories of gases above 0° per gram molecule (or for
22.32 liters ==0.78822 cubic foot of gas).

Tempera- 	N2 = 2S, 					
ture C.
*=r-273 	O2 = 32,
H2= 2, 	H20 = 18 	CO2-44 	CH4 = 16 	Molecular weights given 	
Degrees 	CO = 28 				in grams 	
0
200
400 	0.00
1.39
2.82 	0.00
1.73
3.69 	0.00
1.85
3.99 	0.00
2.19
4.85 	B.t.u. per cubic foot =
5.03794X calories per
gram molecule 	
600
800
1000 	4.31
5.82
7.43 	5.87
8.23
10.98 	6.44
9.07
12.42 	8.02
11.46
15.77 	Ounce molecule = 22.32
cubic feet 	
1200
1400
1600
1800 	9.05
10.73
12.46
14.21 	13.87
17.00
20.35
23.86 	15.55
19.18
23.10
27.21 	20.37
22.44
30.99
35.86 	B.t.u. per ounce molecule
= 112.472077X calories
per gram molecule 	
2000
2200
2400
2600 	16.05
17.01
19.84
21.81 	27.76
31.82
36.10
40.62 	31.84
36.65
41.76
47.16 	43.55
50.54
58.02
66.04 	Calories per cubic meter
=44.80287 X calorics
per gram molecule 	
Heat capacity values are based on the formulas developed by Mallard
and Le Chatelier.
As hydrocarbon gases dissociate when exposed to high temperatures the
heat capacity values for CH4 have a theoretical value above 800°.
Simmersbach in Journal of Chemical Industry, Feb. 28, 1913, page 186,
and in Journal fur Gasbeleuchtung, Dec. 13, 1913, page 1242, gives data
covering his experiments in regard to the decrease in heating value of gases
containing hydrocarbons.

HEAT  CAPACITY AND  CALORIFIC INTENSITY  CURVES   367
TABLE 10
P. 25, Les Sources de VEnergie Calorifique,
The formulas for the law for the heat capacity of gases at constant pressure
have been given by Mallard and Le Chatelier in terms of the absolute tem-
perature, and the total heat capacity from 0 absolute (—273°) to a tem-
perature T = 273+t can be expressed by a parabolic formula of two terms:
,
lOO(T   10002'
in which a is a constant common to all gases, equal to 6.5 and b is a constant
variable with the different gases, the value of which is
For nitrogen, hydrogen, oxygen and carbon monoxide = 0.6;
For water vapor = 2. 9;
For carbon dioxide = 3. 7;
For methane = 6.0.
From this, the molecular heat capacity for a gram molecule or 22.32 liters
of a gas between two temperatures to = TQ— 273 and t = T — 273 may be
expressed by the formula:
n=  t~tq   J*-TQ*
^ a 1000 +   iooo2 •
By taking the values derived from this formula the specific heat for a
particular temperature may be obtained by the formula:
^LfV=   a    I    26  T
dT	1000 "'"lOOO2

368

APPENDIX X

TABLE 11
graphical comparison of fuels
High
96
Calories per m3        =834        852
Weight kg. per m3 1.295 Ib. per cu. ft. 0.0809.
Low
Blast-furnace gas, No. 1.    B.t.u. per cubic foot= 94

Composition
Volumetric 	Products of Combustion per
100 Volumes of Gas 	Percentage Basis (Wet) 	

	Air Supply in Percentage of the Theoretical Requirements 	

	100% 	120% 	140% 	180% 	100% 	120% 	140% 	180% 	
H2          3.92
CO       23.95
02           0.39
C02      12.96
H20        1.65
N2        57.13
Total 100.00
Air vols 									

	0.00
36.91
5.57
111.33
153.81
67.75
1.413
0 0882 	2.71
36.91
5.57
122.17
167.36
81.30 	5.42
36.91
5.57
133.01
180.91
94.85 	10.84
36.91
5.57
154.69
208.01
121.95
1.381
0.0862 	0.00
23.99
3.62
72.39 	1.62
22.05
3.33
73.00 	2.99
20.40
3.08
73.53 	5.21
17.74
2.68
74.37 	
Weight, kg per m3
Ib per cu ft 	

	

	

	

	

	

	

	
		Percentage Basis (Dry) 	

	02
C02
N2 	0.00
24.90
75.10 	1.67
22.81
75.52 	3.09
21.05
75.86 	5.36
18.23
76.41 	

HEAT  CAPACITY AND  CALORIFIC INTENSITY CURVES     369

370

APPENDIX X
TABLE 12

graphical comparison op fuels
Low	High
Blast-furnace gas, No. 2.    B.t.u. per cubic foot = 105	107
Calories per m3        =940	955
Weight, kg per m3 = 1.295 = 0.0809 Ib per cubic foot

Composition
Volumetric 	Products of Combustion per
100 Volumes of Gas 	Percentage Basis (Wet) 	

	Air Supply in Percentage of Theoretical Requirements 	

	100% 	120% 	140% 	180% 	100% 	120% 	140% 	180% 	
H,          2.70
CH4       0.30
CO       27.50
O2          0.50
CO;         10.00
BUG 									

									

	0.00
37.80
3.30
119.80
160.90
76.00
1.408
0 0879 	3.04
37.80
3.30
131.96
176.10
91.20 	6.08
37.80
3.30
144.12
191.30
106.40 	12.16
37.80
3.30
168.44
221,70
136.80
1 . 3765
0.0860 	0.00
23.49
2.05
74.46 	1.73
21.46
1.87
74.94 	3.18
19.75
1.72
75.34 	5.48
17.05
1.49
75.98 	
N2        59.00
Total 100.00
Air vols 	 	

	

	

Weight, kg per m3
Ib per cubic foot 	

	

	

	

	

	

	

	
	
		Percentage Basis (Dry) 	

	02
CO2
No 	0.00
23.98
76.02 	1.76
21.87
76.37 	3.23
20.12
76.62 	5.57
17.30
77.13 	

HEAT  CAPACITY  AND  CALORIFIC  INTENSITY  CURVES     371

372

APPENDIX X

TABLE 13
graphical comparison of fuels
Low       High
Producer gas (mixed) HAW No. 5.    B.t.u. per cubic foot = 167        176
Calories per m3         = 1482       1570
Weight, kg per m3 = 1.098=0.06862 Ib per cubic foot

Composition
Volumetric 	Products of Combustion per 100 Volumes of Gas 	

	Air Supply in Percentage of Theoretical Requirements 	

	100% 	120% 	140% 	180% 	260% 	
H2        11.26
CH4       3.24
CO       29.65
02          0.19
C02        1.25
H20       3.72
N2        50.69
Total 100.00
Air vols 						

						

	0.00
34.14
21.47
157.70
213.31
133.75
1.321
0.0825
0.00
16.00
10.07
73.93
0.00
17.79
82.21 	5.35
34.14
21.47
179.11
240.07
160.51 	10.70
34.14
21.47
200.52
266.83
187.27 	21.41
34.14
21.47
243.33
320.03
240.79 	42.82
34.14
21.47
328.96
427.39
347.83
1.308
0.0817
10.02
7.99
5.02
76.97
10.55
8.41
81.04 	
Weight kg per m3
Ib per cubic foot
02 	

	

	

	
	Percei
2.23
14.20
8.93
74.54
Percei
2.45
15.61
81.94 	itage Basis
4.01
12.79
8.05
75.15
itage Basis
4.36
13.91
81.73 	(Wet)
6.68
10.66
6.70
75.96
:Dry)
7.16
11.42
81.42 	
	
COo  	 	

	

H2O 	 	

	

N2 	 	

	

02..  .. 	

	

C02 	 	

	

N2 	 	

	

	

	

HEAT CAPACITY AND  CALORIFIC INTENSITY  CURVES      373

3000	4000	6000	COCO
Calories Pet 100 Mol. Vol.(2.232 cu.m.)of Gaa Burnt
fig. 183.—Heat Capacity and Calorific Intensity Curve of Mixed Producer
Gas HAW No. 5. For composition, volume of products of combustion
refer to Table No. 13.

374

APPENDIX X

TABLE 14
graphical comparison of fuels
Low         High
Producer gas (mixed) SC-DSW.    B.t.u. per cubic foot=   142         152
Calories per m3         = 1265       1352
Weight = 1 kg 126 per m3 = 0.0703 Ib per cubic foot.

	Products of Combustion pei
100 Volumes of Gas 	Percentage Basis (Wet) 	
Composition 		
Volumetric 	Air Supply in Percentage of Theoretical Requirements 	
	100% 	120% 	140% 	180% 	100% 	120% 	140% 	180% 	
H->         12 10 									
CHi       2 60 									
CvHt      0 40 									
CO       21 78 									
0>          0.02 	0.00 	4.54 	9.09 	18.18 	0.00 	2.06 	3.75 	6.31 	
C02        5.68 	30.86 	30.86 	30.86 	30.86 	15.64 	14.03 	12.72 	10.71 	
H.O       3.82 	21.92 	21.92 	21.92 	21.92 	11.11 	9.97 	9.03 	7.61 	
N2        53.60 	144.48 	162.66 	180.83 	217.18 	73.25 	73.94 	74.50 	75.37 	
Total 100.00 	197.26 	219.98 	242.70 	288.14 					
Air supply . . 	113 60 	136 32 	159 04 	204 48 					
Weight kg per rn3 	1.3168 			1.283 					
Ib per cubic foot 	0 0822 			0 0801 					
									
		Percentage Basis (Dry) 	
	O2 	0.00 	2.29 	4.12 	6.83 	
	CO2 	17.60 	15.58 	13.97 	11.59 	
	N2 	82.40 	82.13 	81.91 	81.58 	

HEAT CAPACITY AND  CALORIFIC  INTENSITY CURVES     375

376

APPENDIX X

TABLE 15
graphical comparison of fuels

Clean cold producer gas No. 3.
Tar returned to producer
Weight = 1.057 kg per :

B.t.u. per cubic foot =
Calories per m3        =
= 0.066 Ib per cubic foot

Low
'     195
= 1742

High
211
1875

Composi-
tion,
Volumetric 	Products of Combustion per 100 Volumes of Gas. 	

	Air Supply in Percentage of Theoretical Requirements 	

	60% 	80% 	100% 	120% 	140% 	180% 	260% 	340% 	420% 	
Ha     16.60
CH4    5.50
CO   27.10
C02    3.90
O2       0.00
H20    0.60
N2    46.30
Tot. 100. 00
Air vol ....
Weight:
kg per m3
Ib per cu ft
H2
CO
02
C02
B20
N2
H2
CO
02
CO2
N2 	5.52 	2.76 								

	

	20.76
15.74
0.00
22.68
125.14
189.84
98.55
1.231
0.0769
2.91
10.94 	10.38
26.12
0.00
25.44
151.42
216.12
131.40 								

	
	36.50
0.00
28.20
177.70
242.40
164/25 	36.50
6.57
28.20
203.98
275.25
197.10 	36.50
13.14
28.20
230.26
308.10
229.95 	36.50
26.28
28.20
282.82
373.80
295.65 	36.50
52.56
28.20
387.94
505.20
428.07 	36.50
78.84
28.20
493.06
636.60
559.45 	36.50
105.12
28.20
598.18
768.00
690.85
1.298
0.0811 	

								

	
	1.28
4.80 	Percentage Basis (Wet) 	

	

	
	
	0.00
15.06
11.63
73.31
I 	2.39
13.26
10.24
74.11
>ercenti 	4.27
11.85
9.15
74.73
ige Bas 	7.03
9.77
7.54
75.66
is (Dry 	10.40
7.23
5.58
75.79
) 	12.39
5.73
4.43
77.45 	13.69
4.75
3.67
77.89 	

	8.29
11.94
65.92
3.30
12.42 	12.09
11.77
70.06
1.45
5.44 	

	

	

	

	
	
	0.00
17.04
82.96 	2.66
14.77
82.57 	4.70
13.04
82.26 	7.61
10.56
81.83 	11.02
7.65
81.33 	12.96
6.00
81.04 	14.21
4.93
80.86 	

	9.42
74.86 	13.70
79.41 	

	

	

HEAT   CAPACITY AND  CALORIFIC  INTENSITY  CURVES     377

378

APPENDIX X

TABLE 16
graphical comparison of fuels
Low	High
Coke oven rich gas, No. 11.    B.t.u. per cubic foot = 467	527
Calories per m3        =4160	4691
Weight=0 kg 492 per m3= 0.03072 Ib per cubic foot.

Composition
Volumetric 	Products of Combustion pe
100 Volumes of Gas 	Pe~centage Basis (Wet) 	

	Air Supply in Percentage of Theoretical Requirements. 	

	100% 	120% 	140% 	180% 	100% 	120% 	140% 	180% 	
Ho        55.00
CH4     25.40
C,H4      2.30
CO         5.70
O2           0.20
C02       2.10
H>O    	 									

									

	00.0
37.80
110.40
360.70
508.90
439.25
1.215 	17.57
37.80
110.40
430.98
596.75
527.10 	35.14
37.80
110.40
501.26
684.60
614.95 	70.28
37.80
110.40
641.82
860.30
790.65
1.246
0.0778 	0.00
7.42
21.69
70.88
Perc
0.00
9.49
90.51 	2.94
6.34
18.40
72.22
entage
3.61
7.77
88.62 	5.13
5.52
16.13
83.22
Basis (I
6.12
6.58
87.30 	8.17
4.39
12.83
74.61
Dry)
9.37
5.04
85.59 	
N2          9.30
Total 100.00
Air vol 	

	

	

Weight:
kg per m3 	 	

	

	

Ib per cubic foot 	0.0759 			

	

	

	

	
	O
CO
N 	

	

HEAT  CAPACITY AND CALORIFIC INTENSITY CURVES     379

\
pq »

\

\

o +,
j2 o
gffi

I
TJ      C3
s ^
w
3   -d
S  S
8 I
<51
«
eu
a
1*"*
.a    o   P
s J s 8
O    0*0
3       [§ 1
ol
"o
I
o

o
fi

380
APPENDIX X
TABLE 17
graphical comparison or fuels
Low	High
Blue water gas, No. 9.    B.t.u. per cubic foot= 290	318
Calories per m3        =2585	2831
Weight = 0 kg 695 per m3 =0.0434 Ib per cubic foot.

Composition
Volumetric 	Products of Combustion per 100 Volumes of Gas 	

	Air Supply in Percentage of Theoretical Requirements 	

	30% 	100% 	120% 	140% 	180% 	260% 	
H2        50.80
CH4       0.20
CO       40.90
O2          0,90
CO;        3.40
H20       0.80
N2          3.80
Total 100.00
Air supply. . 	5.00 						

						

	13.10
0.00
31.40
47.00
149.00
245.50
181.60
1 245 						

	0.00
44.50
52.00
185.40
281.90
227.00 	9.10
44.50
52.00
221.70
327.30
272.40 	18.20
44.50
52.00
258.00
372.70
317.80 	36.40
44.50
52.00
330.60
463.50
408.60 	72.80
44.50
52.00
476.00
645 . 30
590.20
1.291
0.0806 	
Weight:
kg; per m3   .... 	

	

	
Ib per cubic foot
Ho 	 	0.0777
2.04
5 34 					

	
	Percentage 	Basis (Wet) 	
	
CO 	 	
						
o. 	 	0.00
12.79
19.14
61.09
2.52 	0.00
15.78
18.45
65.77
P 	2.78
13.59
15.89
67.74
ercentage 	4.88
11.94
13.95
69.23
Basis (Di 	7.85
9.60
11.52
71.33
T) 	11.28
6.90
8.06
73.76 	
CO- 	 	

	

	
HO 	

	

	
No 	 	

	

	
H2 	 	

	

	
CO 	 	6.60 						
Oo 	 	
	0.00
19.35
80.65 	3.31
16.16
80.53 	5.68
13.87
80.45 	8.85
10.81
80.34 	12.27
7.50
80.23 	
COo 	 	15.82
75.07 	

	

No 	 	

	

	

	

	

3000
2700
2.400
 
Capacity
of Combustion
Heat-Capacity-
B.t.u. per cu. ft. of Gas Burnt
50.379      100.738       151.1         201.5        £51.9        302.3	352.7        403.1	453.4        503.79        554.2       604.6
20	30	4u	.50	60	70	80	90	100	110	150        F
Calories per Gramme- Moleeule of Gas Burned
187.—Heat Capacity and Calorific Intensity Curve of Blue Water Gas No. 9.    For composition, volume of products of com-
bustion and their composition refer to Table 17.

O
d
o
>
b
a
2
o
o

00
00

382

APPENDIX X

TABLE 18
graphical comparison op fuels
Low	High
Natural gas "C," No. 6.    B.t.u. per cubic foot =  924	1025
Calories per m3        = 8226	9126
Weight = 0 kg 743 per m3=0.0465 Ib per cubic foot.

	Products of Combustion per
100 Volumes of Gas 	Percentage Busis (Wet) 	
Composition 		
Volumetric 	Air Supply in Percentage of Theoretical Reruircmcnts 	
	100% 	120% 	140% 	180% 	100% 	120% 	140% 	180% 	
Ho           2 10 									
CH4      92 10 									
CoH4       0 50 									
CO         0 40 									
O2           0.20 	0.00 	37.35 	74.70 	149.40 	0.00 	3.08 	5.31 	8.40 	
H,O     	 	187.30 	187.30 	187.30 	187.30 	18.14 	15.36 	13.32 	10.52 	
C02         0.50 	94.00 	94.00 	94.00 	94.00 	9.10 	7.71 	6.69 	5.28 	
N2           4.20 	751.20 	900.60 	1050.00 	1348.80 	72.76 	73.87 	74.68 	75.80 	
Total 100.00 	1032.50 	1219.25 	1406.00 	1779.50 					
Air supply . . . 	933.75 	1120.50 	1307.25 	1680.75 					
Weight: 									
kg per m3 	1.242 			1 268 					
Ib per cu ft 	0.0775 			0.0792 					
					Perc 	entage 	Basis (] 	3ry) 	

	

	0, 	0.00 	3.62 	6.13 	9.39 	
	C02 	11.11 	9.10 	7.72 	5.90 	
	Ns 	88:89 	87.28 	87.15 	84.71 	

HEAT  CAPACITY AND CALORIFIC  INTENSITY  CURVES     383

384

APPENDIX X

TABLE 19
graphical comparison of fuels
Low	High
Fuel oil (No. 17).    B.t.u. per pound = 18,840	20,080
Calories per kg  =10,467	11,154
Specific Gravity 0.90 =7.5 Ib per gallon.
Products of Combustion, Cu M per Kg

Composition 	Air or Mechanical -Atomizing 	Atomizing Steam = 0.30 Weight of Oil. 	
by
Weight 			

	Air Supply in Percentage of Theoretical Requirements. 	
	100% 	120% 	140% 	180% 	100% 	120% 	140% 	180% 	
H2       12 . 80 									
C         83 . 00 									
02          1 '. 40 	0.00 	0.45 	0.90 	1.80 	0.00 	0.45 	0.90 	1.80 	
CO2 	1.54 	1.54 	1.54 	1.54 	1.54 	1.54 	1.54 	1.54 	
H2O      1 . 50 	1.45 	1.45 	1.45 	1.45 	1.82 	1.82 	1.82 	1.82 	
N2         1 - 30 	9.00 	10.80 	12.60 	16.20 	9.00 	10.80 	12.60 	16.20 	
Total 100. 00 	11.99 	14.24 	16.49 	20.99 	12.36 	14.61 	16.86 	21 . 36 	
Air supply. . 	11.24 	13.49 	15.74 	20.23 	11.24 	13.49 	15.74 	20.23 	
	1 .293 			1   9Q1 	1   9.7K 			1.274 	
kg p6r m*> 		Products of Combustion, Cu Ft per Pound 		
O2 	0.00 	7.21 	14.41 	28.82 	0.00 	7.21 	14.41 	28.82 	
COo 	24.73 	24.73 	24.73 	24.73 	24.73 	24.73 	24.73 	24.73 	
H20 	23.18 	23.18 	23.18 	23 . 18 	29.14 	29.14 	29.14 	29.14 	
N2 	144.21 	173.17 	201.82 	259 . 50 	144 . 21 	173.17 	201.82 	259 . 50 	
Total. . . . 	192.12 	218.29 	264.14 	336.23 	198.08 	234.25 	270.10 	342 . 19 	
Ib per cu ft 	0 . OS07 			ft nsnfi 	0 0798 			0 . 0795 	
	Percentage Basis (Wet) 	Percentage Basis (Wet) 	
O2 	0.00 	3.16 	5.45 	8.57 	0.00 	3.08 	5.33 	8.42 	
COo 	12.87 	10.84 	9.36 	7.35 	12.49 	10 . 56 	9.15 	7.23 	
H9(5 	12.06 	10.16 	8.77 	6.89 	14.71 	12.45 	10.79 	8.51 	
Nj 	75.07 	75.84 	76.42 	77.19 	72.80 	73.91 	74 . 73 	75.84 	
O2 	Pe
0.00 	jrcentage
3.51 	Basis (Dr
5.98 	y)
9.21 		
C02 	14.64 	12.07 	10.26 	7.90 		
N2 	85.36 	S4.42 	83.76 	82.89 		

HEAT  CAPACITY  AND CALORIFIC INTENSITY CURVES     385

2800
Complete Instantaneous
Combustion
Athermal Chamber
753    44)0
o         c fs
32        o^	1	1	1	
p      C °     „	2000	4000 Calories 6000	8000     kg.    10000
Heat      3600 Released 7900  B.t.u,  10800    pe*    14400     Ib       18000
18000
16000
12000        .      14000
Of	Oil
	      3600   v	"^ 7900  B.t.u,  10800    r        14400     Ib.      18000	21i
fig. 190.—Heat Capacity and Calorific Intensity Curve of Fuel Oil No. 17, Mechanical Atomizing.    For composition, volume of
products of combustion and their composition refer to Table 19.

co
00
I
*
U
H
M

HEAT  CAPACITY AND  CALORIFIC INTENSITY  CURVES      387

388

APPENDIX X

TABLE 20
graphical comparison of fuels
Low
Coal tar, by-product oven.    B.t.u. per pound = 16,042
Calories per kg = 8,913
Specific gravity = 1.165 = 9.7 Ib per gallon.
mechanical atomizing

High
16,076
8,931

Composition
by
Weight 	Products of Combustion 	

	Cubic Meters per Kg 	Cubic Feet per Pound 	

	Air Supply in Percentage of Theoretical Requirements 	

	100% 	120% 	140% 	180% 	100% 	120% 	140% 	180% 	
H2          6.00
C         86 . 82
S            0.75
O2          3.11
CO2 									

									

	0.00
3.26
1.42
15.66 	0.78
3.26
1.42
18.79 	1.57
3.26
1.42
21.92 	3.13
3.26
1.42
28.18 	0.00
52.14
22.76
250.78 	12.54
52.14
22.76
300 . 95 	25.07
52.14
22.76
351.10 	50.14
52.14
22.76
431.30 	
H2O       3.10
N2         0.12
Ash       0.10
Total 100. 00
Air supply . .
Weight:
kg per m3
Ib per cu ft
02
CO*
H20
N2 	

	

	

	20.34
19.57
1.337 	24.25
23.48 	28.17
27.39 	35.99
35.22
1 317 	325.68
313.43 	388 . 39
376 . 30 	451.07
438 . 80 	556 . 34
564.08 	

				0 0834 			0.0822
ti
9.06
9.41 	

	pc
0.00
15.98
6.99
77.03 	vreentage
3.23
13.42
5.86
77.49 	Basis (We
5.56
11.55
5.05
77.84 	t)
8.70
9.04
3.95
78.31 	pc
0.00
17.20 	rcentage
3.43
14 . 25 	Basis (Dr
5.86
12.76 	

	

	
	82.80 	82.32 	81.38 	81.53 	

HEAT CAPACITY AND CALORIFIC INTENSITY CURYES   389

390

APPENDIX X

TABLE 20—(continued)
With steam atomizing, the weight of steam being 0.30 the weight of the tar, the following
changes in the waste gases will be produced:

	Cubic Meters per Kiligram 	Cubic Feet per Pound 	

	Air Supply in Percentage of Theoretical Requirements. 	

	100% 	120% 	140% 	180% 	100% 	120% 	140% 	180% 	
H20
Total ....
02
C02
H20
N2 	2.17
21.09
pc
0.00
15.43
10.29
74.28 	2.17
25.00
ircentage
3.13
13.00
8.68
75.19 	2.17
28.92
Basis (We
5.42
11.25
7.50
75.83 	2.17
36.74
t)
8.52
8.85
5.90
76.73 	34.73
337.65 	34.73
400 . 36 	34 . 73
463 . 04 	34.73
508.31 	

	

		
When the weight of the atomizing steam is 0.60 time the weight of the tar, the waste
gases change as follows: 	
	Cubic Meters per Kilogram 	Cubic Feet per Pound 	

	Air Supply in Percentage of Theoretical Requirements 	

	100% 	120% 	140% 	180% 	100% 	120% 	140% 	180% 	
H2O
Total. . . .
Oo
C02
H2O
N2 	2.91
21.83
P<
0.00
14.90
13 . 35
71.75 	2.91
25.74
jrc'entage
3.04
12 . 04
11.32
73 . 00 	2.91
29.66
Basis (We
5.28
11.00
9.83
73 . 89 	2.91
37.49
t)
8 . 35
8 . OR
7.78
75.19 	46.68
349.60 	46.68
412.31 	46.68
474 . 99 	46.08
580.20 	

	

		

HEAT CAPACITY AND CALORIFIC INTENSITY CURVES   391

392

APPENDIX X

TABLE 21
graphical comparison op fuels

Pittsburgh coal, pulverized, No. 21.

Low	High
B.t.u. per pound = 13,336       13,806
Calorics per kg  = 7,409         7,671

Products of Combustion

Composition
by
Weight
as Fired 	Cubic Meters per Kilogram 	

	Air Supply in Percentage of 1 heoretical Requirements 	

	100% 	120% 	140% 	180% 	260% 	
•H,           4.87
C          73.28
S             1.77
O2           5.63
CO2       .... 						

						

	0.00
1.38
0.57
6.31 	0.31
1.38
0.57
7.56 	0.63
1.38
0.57
8.82 	1.26
1.38
0.57
11.33 	2.51
1.38
0.57
16.35 	
H2O        2.28
N2           1.35
Ash       10.82
Total    100 . 00
Air supply 	

	

	8.26
7.84
1.341
0.00
22.03
9.08
101.05
132.16
125.66
0.00
16.66
6.93
76.41
0.00
17.91
82.09 	9.82
9.41 	11.40
10.98 	14.54
14.12 	20.81
20.39
1.341
40.22
22.03
9.08
261.90
333.23
326.80
12.07
6.61
2.75
78.57
12.41
•     6.80
80.79 	
Weight:
kg per cu m . . .
Oo..     	  	 	

	

	
	Cubic
5.03
22.03
9.08
121.12
157.26
150.80
Percei
3.19
14.03
5.82
76.96
Perce]
3.39
14.87
81.74 	Feet per P<
10.06
22.03
9.08^
141.25
182.42
175.90
itage Basis
5.51
12.07
5.02
77.40
itage Basis
5.80
12.71
81.49 	)und
20.11
22.03
9.08
181.45
232.67
226.20
(Wet)
8.66
9.47
3.93
77.94
(Dry)
8.99
9.86
81.15 	
	
CO, 	
H2O 	 	

	

No 	 	

	

Total 	 	

	

Air sudd!v  .... 	

	

Oo. 	

	

COo 	 	

	

H2O 	

	

No 	 	

	

02 	 	

	

COo 	

	

No 	 	

	

	

	

2600
9600
2400'
2500
2000
1800'
1600
1400
1200
 
14400  16200  18000  19800
3600
5400
1800
B.t.u. perlb, of Coal Burnt
7200   9000   10800  12600
9000       10000      11000
1000
!?000
3000        4000         5000       6000        7000         8000
Caloiyies per Kilogramme of Coal Burnt

fig. 194.—Heat Capacity and Calorific Intensity Curve of Pittsburgh Coal No. 21, Pulverized.    For composition,
volume of products of combustion and their composition refer to Table 21.

F

w
o
o
Q
O
S3
l
CO
CD
CO

394

APPENDIX X

TABLE 22
heat capacity and calorific intensity curves
Comparison of five gases arranged in the order of their calorific intensity
giving their thermal value, thermal value of combustible mixture, the heat
contained in their products of combustion, the volume of the air supply, the
combustible mixture and the products of complete combustion.

	Blue
Water
Gas,
No. 9 	Coke
Oven
Rich
Gas,
No. 11 	Natural
Gas
"C,"
No. 6 	Pro-
ducer
Gas
"HAW/
No. 5 	Blast
Furnace
Gas,
No. 1 	
Calorific intensity:
100% air supply C      	 	1920° 	I8600 	1840° 	1650° 	1310° 	
F 	3488° 	3380° 	3344° 	3002° 	2390° 	
180% air supply C 	1340° 	1295° 	1230° 	1225° 	1050° 	
F      	 	2444° 	2363° 	2246° 	2237° 	1922° 	
Calories per in3 of °-as 	2585 	4180 	8260 	1482 	835 	
B.t.u. per cubic foot of gas 	
Combustible  mixture,   100%   ait
supply: Calories per m3 	
B.t.u. per cubic foot. . . .
Products of combustion, 100% aii
supply: Calories per in3 	 	291
917
103
1050 	468
776
87
823 	925
800
90
800 	167
636
72
693 	93
497
55
546 	
B.t.u. per cubic foot . .
Combustible  mixture,   ISO %  nil
supply: Calories per m3. 	119
618 	92
469 	90
464 	78
331 	61
376 	
B.t.u. per cubic foot . . .
Products of combustion, 180% air
supply: Calories per m3 	 	70
680 	53
486 	52
464 	37
346 	42
401 	
B.t.u. per cubic foot. . .
Volumes per 100 volumes of gas
burned completely of:
Air supply, theoretical 100%. . .
Combustible mixture, theoreti-
cal 	77
182
282 	55
439
539 	52
933
1033 	39
133
233 	45
68
168 	
Products of combustion, theoretical
Air supply, 180% 	 	245
318 	508
791 	1032
1681 	214
348 	153
122 	
Combustible  mixture,   180%  air
supply. . 	418 	891 	1781 	448 	222 	
Products of combustion, 180% air
supply 	 	380 	860 	1780 	429 	208 	
						
8G<£>

ALPHABETICAL INDEX

Air heaters, iron tube, 108
Air supply required for combustion,
365
Analogy between  the flow of gases
and the flow of liquids, 3
Annealing furnaces, drop of temper-
ature in, 77
for malleable iron, 116
for plates, 128
for sheets, defective, 52
temperature of waste gases, 79
vertical, 123
Apparatus, experimental, 3
Arch brickwork, formulas and tables
for, 176
Balloon, hydrostatic; pressure in, 14
Becker hot-blast stove, 100
Bessemer converters, 183
Blast-furnace gas, combustion of, 316
instantaneous   calorific   intensity,
319
heat-capacity curve of, 368, 309
mains, hydrostatic pressure in, 24
Boilers, breeching, flow of gases in, 10
settings, 320
steam, 109
suggestions for baffling, 336
waste   heat   available   for,   from
open-hearth furnace, 295
waste heat on open-hearth furnace,
233
••   waste heat setting for, 236
water circulation in, 331
Brick arches, formulas and tables for,
176.	7
flues, friction of gases in, 168

Brick kilns, II?
downdraft, 7
model of, 3
poor design of, 60
regenerative fired, 58
ring or multiple chamber, 116
temperature drop in, 77
temperatures required, 185
up draft, 4
Brick temperature on  center lines,
222
Cementation furnaces, 115
Chamber furnaces, 57, 112
Chamber volume of furnaces, 183
Change of area of gas passages, effect
of, 35
direction of flow, effect of, 35
Chimneys, draft formulas, 184
hydrostatic pressure in, 25
open-hearth practice, 247
required for open-hearth furnaces,
287
Classification of industrial heating, vii
Coal, pulverized, heat-capacity curve
for, 393
Coal tar, heat-capacity curve for, 389
391
Coke-oven gas, heat-capacity curve
for, 379
Combustibles, heat released per unit
of, 364
Combustion, air supply required for,
365
Combustion and boiler settings, 320
chamber for hot-blast stove, 102
Jf blast-furnace gas, 316

396

ALPHABETICAL INDEX

Comparison of five gases, 394
Computation for heat capacity and
calorific intensity curves, 358
Computation, methods  of,  for fur-
naces, 72
Computations for Continuous Fur-
naces, 43
for design of open-hearth furnace,
253
Computations for regenerators, 228,
260
for reverberatory furnace, 80
Conclusion, 149
Continuous heating furnace, 43, 138
length of, 56
temperature drop in, 77
Convection, according to Langmuir,
269
currents, velocity of, 187, 188
Converters, Bessemer, 183
Cowper hot-blast stove, 98
Currents of hot gases, subdivision of,
88
Damour, classification of industrial
heating by, vii
Darling,  heat losses  from  furnace,
walls, 270
Dedication, iv
Defective designs of furnaces, 92
Design assumptions, gas composition,
74
computations for furnaces, 72
computation for open-hearth fur-
nace, 80
computation for reverberatory fur-
nace, 80
of continuous heating furnaces, 43
of open-hearth furnaces, 194
Downdraft brick kiln, 7
Draft conditions in hot-blast stoves,
303
fallacy of metallurgical furnaces,
15
formulas for chimneys, 184
Drop of flame in open-hearth fur-
naces, 67

Effect of ascending, horizontal and
descending roofs, 51
Experimental apparatus, 3
Experiments, first, 4
second, 7
Experiments to show the analogy
between the flow of hot gases
and the flow of water, 3
Firebox, function of, 19
First experiment, 4
Flame, character of, 74
drop of, in open-hearth furnaces, 67
Flow of gases in boiler flue, 10
in open-hearth furnace, 37
through an orifice, 27
under thick-crested weirs, 40
Foreword, by Groume-Grjimailo, xv
Friction of gases in brick flues, 168
Frictional resistance in hot-blast
stoves, 307
Fuel bed, resistance of, 82
consumption of various furnaces,
186
gases, comparison of, 394
Fundamental viewpoint, 1
Furnaces,    considered   as   inverted
weirs, 56
hydrostatic pressure in, 13
methods of computation for, 72
rational construction of, 87
Gas factors, 160, 162
Gas flues, hydrostatic pressure in, 21
Gas mains, hydrostatic pressure in,
24
Gas pipes, hydrostatic pressure in, 15
Gas producer, connection to furnace,
24
with sleeping grate, 22
Gas siphon, Siemens, 22
Gases, flow of, through an orifice, 27
Gases leaving heating chamber, tem-
perature of, 79
Grates, slooping, 22
Groume-Grjimailo, foreword by, xv
Groume-Grjimailo, preface to English
Edition by, ix

ALPHABETICAL INDEX

397

Hartmann hot-blast stove, 102
Harvey hot-blast stove, 102
Heads, relation between pressure and
velocity, 32
table of velocity, 163
velocity required, 31
Heat capacity and calorific intensity,
348
and calorific intensity curves, 36S-
393
of various gases, 365
Heat loss from exterior walls, 270
transfer in checkerwork, 2o8
Heat treating furnaces, temperature
of waste gases in, 79
vertical, 123
Hoffman furnaces, 116
Horizontal tempering furnaces, 126
Hot-blast heaters, iron tube, 108
Hot-blast stoves, 97, 300
brick and pass volume, 308
combustion chamber for, 102
combustion of blast-furnace gas in,
316
design of, 300
draft conditions in, 303
empirical data for, 185
frictional resistance in, 307
heating time, 311
model of, 99
test of, 313
Hot-blast temperature equalizers, 107
Hot gases, application of the laws of
hydrostatics to, 11
subdivision of current of. 88
Hydrostatic pressure in a balloon, 14
in furnaces, 13
in gas mains, 24
in gas pipes, 15
in metallurgical furnaces, 21
in open-top chambers,  chimneys,
25
Hydrostatics, application of the law
of, to hot gases, 11
Industrial heating, classification of,
by Damour, vii
Inverted stream, comparison to, 8

Inverted weir, formula for, 41, 152
gas velocity under, 52
Iron tube air or hot-blast heaters, 108
Jet theory, application, of, to hot
gases, 63
Kennedy hot-blast stove, 102
Krupp armor-plate furnace, 134
Lange, chimney-draft formulas, 184
Langmuir, convection according to,
269
Le Chatelier, Preface to the French
Edition, xi
Length of continuous heating fur-
naces, 56
Location of waste-gas ports, 30
Macco hot-blast stove, 102
Malleable iron, annealing furnace for,
116
Massick and Crook hot-blast stove,
100
Melting furnace for scrap, 60
Metallurgical furnaces, draft fallacy
of, 16
hydrostatic pressure in, 21
Metric conversion table, 189
Metric formulas, conversion of, 192
Model of brick kiln, 3
continuous furnace, 47
Hot-blast stove, 99
open-hearth furnace, 37
Mojarow, friction of gases in brick
flues, 168
Morgan continuous furnace, 49
Muffle furnace, 121
Petrogard Arsenal, 122, 171
vertical, 126
Multiple-chamber kilns, 116
Natural gas, heat-capacity curve for,
383
Oil, fuel, heat capacity and calorific
intensity curve, 385-387

398

ALPHABETICAL INDEX

Open-hearth furnaces, chamber com-
putation, 265
chamber variations, 208
checker temperature rise, 222
chimney, 243, 251, 287
deposit in checkerwork, 225
depth of bath, 195
design of, 194
design of 100-ton furnace, 253
draft conditions, 241
draft required, 287
drop of flame in, 67
frictional resistance in, 272
gas explosions in, 234
hearth area, 197, 201
hearth data from practice, 198,
199
hearth profile*. 202
heat available for making steam,
296
heat insulation, 294
heat transfer in checkers, 268
heating chamber, Groume-Grji-
mailo, 200
jet theory of ga.se? applied to, 63
length of heart!'.., X95
model of, 37
port angle of, 68, 259
port area determination, 284
port areas of, 203
port arrangements, 206
port velocity, how impressed, 33
regenerator computation, 228, 260
regenerator temperature change,
224
regenerators, 36, 210
reversal period, 219
skewback construction, 210
temperature drop in, 77
temperature, pressure, velocity and
time data, 226
valve areas, 244
valve leakage, 247
valve practice, 235
valve resistance, 249
valve strangulation, 39
velocity and friction, 281
velocity head required, 272

Open-hearth furnaces, volume of
checker brick, 213
waste gas temperatures, 79
waste gas velocity, 292
waste heat, 233, 296
waste-heat boilers, 233
water-cooling, 293
width of hearth, 196
wind, effect crt operation, 290
Open-top chambers, hydrostatic pres-
sure in, 25
Orifice, flow of gases through, 27
Petrograd Arsenal, muffle furnace at,
121, 171
Pit furnaces, 135
Plate-heating furnaces, 61, 128
Port, gas velocity in open-hearth fur-
naces, 33
Ports, waste gas, location of, 30
Pottery kilns, 112
Pouring gases, 9
Preface    to    English    Edition,    by
Groume-Grjimailo, ix
to   French   Edition,    by   Henry
Le Chatelier. xi
by translator, v
Pressure, head and velocity, relation
between, 32
Producer gas, heat capacity and cal-
orific intensity curve, 373, 375,
377
Puddling furnace, temperature of
waste gases, 79
Rational construction of furnaces, 87
Regenerative brick kiln, 58
heating furnaces, 131
Regenerators, computations for, 228,
260
heat transfer in, 268
horizontal, 95
open-hearth furnaces, 36, 210
temperature changes in, 224
vertical, 93
Relation between head, pressure, and
velocity, 32