When a differential pressure cell is used to transmit a flow measurement the output of the transmitter is not linear. Therefore, in many flow measurement installation a square root extractor is fitted to the output of a differential pressure transmitter.
Relationship between differential pressure and flow
DP flow can be derived from the bernoulli equation
By assuming density is constant, the continuaty equation can be writte A1V1 = A2V2
The equation can be abbreviated as follows:

Cancel the potential energy in bernoulli equation (assume the pipe is level )

Solve V1 and V2 using the continuity equation

Substitude V1 in term of V2
Then the velometric flow equation can be obtained by multiplying by the cross sectional area of the throat,
if the mass flow is required, multiply both sides by flowing density