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Mass Flow by square root extraction

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Measuring the flow of fluids with an orifice plate

Sometimes we want to measure the flow of a material that isn't happy going through an impeller (or we might want to avoid having to maintain the shaft seal). One way to accomplish this is with a differential pressure transducer that looks at the difference of pressure across an orifice plate.

We can get volume or mass flow using the following equation

m_f = \rho_1\;Q_1 = C\;Y\;A\;\sqrt{2\;\rho_1\;(P_1-P_2)}


where


Q1 = upstream volumetric flow, m³/s
mf = mass flow rate at any point, kg/s
C = orifice flow coefficient
Y = expansion factor
A = cross-sectional area of orifice, m²
P1 = upstream pressure, Pa   kg/(m ·s)
P2 = downstream pressure, Pa   kg/(m ·s)
ρ1 = upstream fluid density, kg/m³

In practice C\;Y\;A_2\; become a lumped constant along with any unit scaling- Let's call this constant k\; then

m_f = k\;\sqrt{2\;\rho_1\;(P_1-P_2)}

The flow is a constant times the square root of a constant times the pressure difference.

Panel meters often can figure out k\; and ρ1 by looking at two known flow rates.

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