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Full text of "The Flow Of Gases In Furnaces"

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