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Full text of "Economics in engineering / by Stuart Troy Haywood"






Stuert Troy Haywood 








The application of economics in engine er- 
inr is so irxpottant thst too much emphrsis cpnnot 
be pieced upon it, T^---o examples pre given. One 
treats v.^th transmission of electrical pov^er; the 
other treats ''rith the econorny of e rectifying' col- 
umn. The examplea^re of the most elementsry char- 
acter, but nevertheless they serve to indicate how 
economics rffecte engineering. Although only tvo 
fields, i,e, electricel and chemical, pre touched 
because of the necessery brevity of the thesis, it 
is not to be assumed thst otl^er types of engineering 
87'e devoid of ppplicetions of econoFiics. 



An understanding of the fundamental principles of 
economics and a knowledge of practical economics con- 
stitute an extremely important division of an engineer's 
information. <iuite frequently the undergraduate 
engineer is confronted with the necessity of making 
allowances in his problems for economic factors. The 
same la even more true for engineers who are actively 
engaged in the field. From an engineei^s viewpoint the 
most efficient method is likewise the most economic 
method, and that Is why he must be able to employ eco- 
nomics in the solution of his problems. Two examples 
in the fields of electrical and chemical engineering 
will serve to indicate the importance of economics in 

The transmission and distribution of electric 
power Is one of the most complicated problems with 
which an electrical engineer must cope. He finds it 

necessary to balance various Items such as initial 

cost, maintenance, and depreciation against the 

power loss in the transmission line in such a manner 
as to arrive at a minimum total cost. IJie size of 
wire which satisfies this condition is the correct 
size to use. A simple example will be presented for 


purposes of Illustration, 

The cost of a conductor of a given material 
and of fixed length is proportional to its size, '■'•'he 
annual outlay chargeable to conductors for taxes, In- 
terest, and depreciation is therefore directly pro- 
portional to the area of the conductor. Mathematically 
this may be expressed as C,;^icA wherein C, represents 
the cost, k, is a constant, and ^ represents the area 
of the conductor. The constant k, contains all the 
economic factors. When a given amount of power Is 
transmitted over a given distance, however, the amount 
of heat energy lost in the conductors during any oper- 
ating period Is Inversely proportional to the con- 
ductor area. The money value of this lost energy may 
be represented by G^^x* Wherein k^ is another constant. 
The total cost is therefore C=G,+G^»l^+^ . Application 
of the calculus easily shows that G is a mlnlmtun when 
G*C^ or when ^tia-jj*-. The area of the conductor is, 


therefore, •"■'"Jic • "^^ evaluation of the constant k^is 
relatively simple matter based upon known physical 
laws. The evaluation of the constant k^ , on the other 
hand. Is difficult because it involves the afareraen- 
tioned economic factors, which are not sub.lect to 
rigid physical laws. A graphical analysis of the 
problem would appear as follows. 



The relation .^ust derived is Important 
enough to be known as Kelvin's law, Which may be 
stated as follows: The most economical area of con- 
ductor is that for which the annual cost of energy 
wasted is equal to the interest on that portion of 
the capital outlay which can be considered propor- 
tional to the welf^ht of conductor used. It is quite 
evident, therefore, that economics has an Important 
role In electrical engineering. 

1. Loew, Direct and Alternating Gurrentg , p. 289 


A very similar example can be cited in the 
field of chemical engineering for the case of a rec- 
tifying or fractionating colximn. With a reflux just 
greater than the minimum, the diameter of the column 
is small "but the number of plates is very lar^e. As 
the reflux ratio is increased slowly, the diameter of 
the column Increases slowly but the number of plates 
decreases rapidly, thereby decreasing the cost of the 
column. As the reflixx ratio continues to increase, the 
diameter of the column increases proportionally, but 
the number of plates is not greatly decreased, and 
hence the cost of the column increases again. The 
cost of heat for the still increases in proportion to 
the reflux ratio. The sum of column and heat costs is 

a minimum for most economical operation. The graphical 


picture is as follows. 




2. Badger and McCabe, Elements of Chemical Engineering 
p. 365 


Here again, since the column costs Include 
such items as maintenance and depreciation, it is 
evident that economics plays an important part. 

These examples are hut two from a myriad of 
such instances in which economics is involved. The two 
which were chosen are relatively ; simple; other prohlems 
are quite complex. 

Application of economics is so necessary 
throughout all engineering that too much emphasis 
cannot he placed upon it. Although trained In the 
exact sciences, the average engineering graduate 
plunges into the world of industry to find that eco- 
nomic factors combined with technical factors determine 
proceedure and success In carrying out any plan. En- 
gineers, in contributing so liberally to the material 
advance of civilization through invention and mechan- 
ization, are faced with meeting those problems of an 


economic nature which this advance has brought about. 

3, Lester, Applied Economics for Engineers , p, 3 



1, Loew, ill. A., Direct and Alternating Currents 
( 2nd ed., 4th impression. New York: McGraw- 
Hill Book Company, Inc., 1958 }, p. 289 

2, Badger, Walter 1,, and McCabe, Warren L,, 
Elements of Chemical En,'^lneering ( 2nd ed., 
6th impression. New York; Mc3raw-Hlll Book 
Company, Inc., 1936 ), p, 365 

3, Lester, Bernard, Ap plied Economics for 
Engineers , New York, J, Wiley & Sons, Inc., 
London, Chapman & Hall, Limited, 1959, Gh, 1 

4, Pish, John Charles Lounsbury, Engineering 
Eeonomlcs ( 2nd ed., 1st impression, New York: 
McGraw-Hill Book Company, Inc., 1923 ), p. 5 

5, Kimball, Dexter Simpson, Industrial Economics 

( 1st ed.. New York: McGraw-Hill Book Company, 
Inc., 1929 ) p, 280