80 E.W. Blake on the flow of Elastic Fluids through Orifices. 
orifice with a diminished density ; for otherwise the elastic force 
of the fluid in the orifice would be a perfect counterpoise to the 
iii etd there could be no flow 
at precedes it will be apparent that in the application 
of the coal expression, 
VDS x2 
to the case of elastic fluids, the 7 ape of the fluid in the orifice, 
represented by D, is an unknown quantity, having a value some- 
where intermediate between cypher and the density of the fluid 
in the discharging vessel; also that the efficient pressure which 
produces the discharge, represented by P, is an unknown quantity 
whose value is dependent on that of D. We will now proceed 
to elicit a general rule for the determination of the values of D 
— 
discharging vessel containing fluid whose 
density is A, and let d be the receiving 
vessel, which for the present we will con- 
4 d 
sider a vacuum. Let the smallest place 
in the passage leading from one to the 
other be the orifice, and let its area be S, Pf 
and let D represent the unknown density 
with which the fluid passes the orifice. Since the pressure is as 
the density, the density may be employed to express the pressure. 
Then it follows from the preceding observations that the efficient 
pressure which produces the discharge is A -~D. Since the 
velocity will be directly as the square root of the Rierg: and 
inversely as the square root of the density, we hav 
yn ee 
Multiplying this sgn by D and reducing, we have 
VD » Y( AD—D? 
Now if we conceive several sections to be made across the 
passage at different points on each side of the orifice, and it the 
areas of these sections are respectively S’, S”, &c. the velocities 
of the fluid in them V’, V’, &c. and the densities YY, D4. 
VDSS’, V’D’S”, &c. are the measures of the quantities of fluid 
that pass through these sections respectively in a given time. 
But when the current is established, the same quantity dome 
througheach in a given time. Therefore V'D’/S’= V”D/S” = 
Now VDS being a constant quantity, if each of the factors vary, 
VD will be amaximum when § isa minimum. But S$ is a min- 
imum at the orifice ; and therefore VD is a maximum oa the ori- 
Somes weer we mere before found VD = vi AD sioner | Y 
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