Relation between pressure drop and mass flow rate

For incompressible fluid, the mass flow rate is

.

(5)

where A is the minimum cross section area of the flow passage  in case of orifice meter and . in case of venturi.

For flow of gases one has to take into account the compressibility factor or expansion factor  so that

(6)

where

(7)

Orifice plates are simplest and cheapest types of flow meters but they cause permanent pressure drop in the systems. The permanent pressure drop can be calculated from

 

In the venturi the flow passage is designed so that the friction is minimum. Permanent pressure drop can be taken to be equal to 10% of the measured pressure differential.

References:
D. R. Poirier and G.H.Geiger: Transport: Transport Phenomena is materials processing 1994.
R. Schuhmann: metallurgical Engineering, vol .1 Engineering principles