Pumps Discharge Regulation

Overview

Engineering reference data for Pumps Discharge Regulation in fluid mechanics.

Key Formulas

Reynolds Number

$Re = \frac{\rho v D}{\mu}$

Ratio of inertial to viscous forces — determines flow regime.

Bernoulli's Equation

$P + \frac{1}{2}\rho v^2 + \rho g h = \text{const}$

Conservation of energy for steady, inviscid, incompressible flow.

Continuity Equation

$A_1 v_1 = A_2 v_2$

Conservation of mass for incompressible flow.

Darcy-Weisbach

$\Delta P = f \frac{L}{D} \frac{\rho v^2}{2}$

Pressure drop due to friction in a pipe.

Variables

Symbol	Description	Unit
$Re$	Reynolds number	—
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s
$D$	Characteristic dimension	m
$\mu$	Dynamic viscosity	Pa·s
$P$	Pressure	Pa
$f$	Darcy friction factor	—

Constant Speed Regulation Methods

Affinity Laws for Pump Regulation

The change in performance parameters (volume rate $Q$, head $H$, power $P$) with speed $n$ or impeller diameter $D$ can be estimated using the affinity laws.

For a change in speed (n): $\frac{Q_1}{Q_2} = \frac{n_1}{n_2}$ $\frac{H_1}{H_2} = \left( \frac{n_1}{n_2} \right)^2$ $\frac{P_1}{P_2} = \left( \frac{n_1}{n_2} \right)^3$

For a change in impeller diameter (D): $\frac{Q_1}{Q_2} = \frac{D_1}{D_2}$ $\frac{H_1}{H_2} = \left( \frac{D_1}{D_2} \right)^2$ $\frac{P_1}{P_2} = \left( \frac{D_1}{D_2} \right)^3$

References

• Original Source