Pumps Power

Overview

Engineering reference data for Pumps 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

Shaft Power Calculation Details

The shaft power $P_s$ represents the actual mechanical power transmitted from the motor to the pump shaft. It is derived from the hydraulic power by accounting for the pump's internal efficiency $\eta$.

The relationship is defined as: $P_s(\text{kW}) = \frac{P_h(\text{kW})}{\eta}$ where $P_s(\text{kW})$ is the shaft power in kilowatts and $\eta$ is the pump efficiency (a value between 0 and 1).

Worked Examples

SI Units Example

Problem: 1 m³/h of water is pumped to a head of 10 m. Given: Flow rate $q = 1 \, \text{m}^3/\text{h}$, Head $h = 10 \, \text{m}$, Density of water $\rho = 1000 \, \text{kg/m}^3$, Gravity $g = 9.81 \, \text{m/s}^2$. Calculation: The theoretical hydraulic power is calculated as: $P_h(\text{kW}) = \frac{q \rho g h}{3.6 \times 10^6} = \frac{(1)(1000)(9.81)(10)}{3.6 \times 10^6} = 0.027 \, \text{kW}$

Imperial Units Example

Problem: 600 gpm of water is pumped to a head of 110 ft. The pump efficiency is 60% (0.6). Given: Flow rate $q = 600 \, \text{gpm}$, Head $h = 110 \, \text{ft}$, Specific Gravity $SG = 1$, Efficiency $\eta = 0.6$. Calculation: The hydraulic power in horsepower is calculated using the alternative formula: $P_h(\text{hp}) = \frac{q \cdot h \cdot SG}{3960 \cdot \eta} = \frac{(600)(110)(1)}{(3960)(0.6)} = 27.8 \, \text{hp}$

Additional Notes

• The specific weight of water, used in some Imperial unit calculations, is approximately $62.4 \, \text{lb/ft}^3$.
• Understanding the relationship between Density ($\rho$), Specific Weight ($\gamma$), and Specific Gravity ($SG$) is crucial for accurate unit conversions.

References

• Original Source