Gas Flow Factor "f_M" (Multi-Orifice)

When multiple orifices appear in series, or when a restrictor has several stages, there is a non-uniform distribution of the overall pressure drop through the restrictor. See Restrictors in Series or in Parallel for more information.

The effect of the above flow behavior is that the gas flow rate of a multi-orifice device is higher than would be expected from a single-orifice device of the same Lohm rate, and at the same pressure conditions. This characteristic is reflected in the flow factor, “f_M”, which reaches a maximum value of 1.3 at a pressure ratio of 3/1. See the graph below for values of f_M at any pressure ratio for multi-orifice flow restrictors.

Sonic condition:

EXAMPLE: 

What multi-orifice restriction will permit a flow of 0.5 std L/min. of hydrogen at 70℉, with supply pressure at 40 psig, discharging to atmosphere.

K = 1030 (see Volumetric Flow Units table)

T₁ = 70℉, f_T = 1.0 (see Temperature Correction Factor graph)

P₁ = 40.0 + 14.7 = 54.7 psia

P₂ = 14.7 psia

P₁ / P₂ = 54.7 / 14.7 = 3.72

f_M = 1.30 (see graph below)

Q  = 0.50 std L/min

flow factor “f_m” (Multi-Orifice)

Sonic flow:

for P1 / P2 > 3, use f_M = 1.3