The Flow Of Gases In Furnaces

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.
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