This note reviews my findings on orifice restriction of gas flow.
Theory: the downstream speed of a gas through an opening
is governed by Bernouillis theorem under the conditions of
adiabatic flow. The discharge rate reaches a maximum
however, when the pressure ration p2/p1 reaches a value rc
such that on substitution in the velocity formula yields the
velocity of sound. In c.g.s units the maximum flow is
where w is grams/sec, S2 is the aperture area, C is approx. 0.6,
a discharge coefficient, p1 the upstream pressure in dynes/cm²
[gamma] is Cp/C[gamma] = 1/4 for air, M is the molecular weight of air (29),
R is the gas contant per mole, 8.3 x 107 erg-deg-1.
Substitution of the above numbers yields
For example, if w1 is to be 100 cm³/min = 1.67 cm³/sec, then
the aperture area should be
the diameter is
Practice: The material on orifices in Chem. Eng. Handbook includes
comments about the importance of shape of orifices in determining
the flow. It would appear that the orifices should be constructed
with diameters of the opening of the order of those calculated
and tested under pressure conditions comparable to those expected,
ie atmospheric on one side, low pressure on the other.