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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.