Device that measures a pressure gradient along a fluid column:
(1) | G_p = \frac{\Delta p}{\Delta l} |
where
\Delta p = p_1 - p_2 | difference between pressure sensors readings |
\Delta l | distance between pressure sensors |
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: