Pump Fan Power

Overview

Engineering reference data for Pump Fan Power 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	—

Example: Inline Pump Power Calculation

An inline water pump operates with the following parameters:

• Inlet pressure: $p_1 = 1 \, \text{bar} = 1 \times 10^5 \, \text{N/m}^2$
• Outlet pressure: $p_2 = 10 \, \text{bar} = 10 \times 10^5 \, \text{N/m}^2$
• Density of water: $\rho = 1000 \, \text{kg/m}^3$
• Volume flow rate: $Q = 1 \times 10^{-3} \, \text{m}^3/\text{s}$

Step 1: Determine the head Using the formula for head from pressure difference:

$$h = \frac{p_2 - p_1}{\gamma} = \frac{p_2 - p_1}{\rho g}$$

where $g = 9.81 \, \text{m/s}^2$. Substituting values:

$$h = \frac{(10 \times 10^5) - (1 \times 10^5)}{1000 \times 9.81} = \frac{9 \times 10^5}{9810} \approx 91.7 \, \text{m}$$

Step 2: Calculate the power gained by the fluid Applying the power equation:

$$P = \rho Q g h$$

Substitute the known values:

$$P = 1000 \times 0.001 \times 9.81 \times 91.7 = 899.6 \, \text{W} \approx 0.9 \, \text{kW}$$

This example demonstrates the practical use of pump power equations to relate pressure rise, flow rate, and fluid properties.

References

• Original Source