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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

where

*Q*_{1} = upstream volumetric flow, m³/s

*m*_{f} = mass flow rate at any point, kg/s

*C* = orifice flow coefficient

*Y* = expansion factor

*A* = cross-sectional area of orifice, m²

*P*_{1} = upstream pressure, Pa kg/(m ·s)

*P*_{2} = downstream pressure, Pa kg/(m ·s)

ρ_{1} = upstream fluid density, kg/m³

In practice , become a lumped constant along with any unit scaling- Let's call this constant , then

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

often one can figure out ,
and ρ_{1} by looking at two known flow rates.

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