Pumps Speed Torque

Overview

Engineering reference data for Pumps Speed Torque 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	—

Speed Torque Characteristics

The speed torque curve of a centrifugal pump is a parabola starting from the origin, meaning torque is proportional to the square of the speed.

The torque relationship is expressed as:

$T = k n^2$

where $T$ is torque, $k$ is a constant, and $n$ is the pump speed.

Discharge Valve Closed

When the discharge valve is closed, the torque at full speed ranges from 30% to 50% of the nominal torque.

Full Load Torque Formula

The full load torque can be calculated using:

$T = \frac{30 P}{\pi n}$

with $T$ in kN·m, $P$ in kW, and $n$ in rpm.

References

• Original Source