Device that measures a pressure gradient along a fluid column
| (1) | G_p = \frac{dp}{dl} |
In case of stationary homogenous isothermal fluid flow the pressure gradient model can be correlated to fluid velocity as:
| (2) | G_p = G_{p0} + b \, q^n |
The constant term G_{p0} is related to pressure gradient in static fluid column:
| (3) | G_{p0} = \rho \, g \, \cos \theta |
where
\rho(T, p) | Fluid density at a given location with pressure p and temperature T |
g | standard gravity constant |
\theta | flow trajectory deviation |
This make
| (4) | G_p = a + b_l \, q^{n_l}+ b_t \, q^{n_t} |
In smaller range of flowrate variations this can be simplified to: