Pumps Temperature Increase

Overview

Engineering reference data for Pumps Temperature Increase 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

Calculation Examples

The temperature rise ($\Delta T$) in a pump can be calculated using the following formula:

$\Delta T = \frac{P_s (1 - \mu)}{c_p \cdot q \cdot \rho}$

Where $\Delta T$ is the temperature rise ($^\circ\text{C}$), $P_s$ is the brake power (kW), $\mu$ is the pump efficiency (dimensionless), $c_p$ is the specific heat capacity of the fluid ($\text{kJ/kg}^\circ\text{C}$), $q$ is the volume flow rate ($\text{m}^3/\text{s}$), and $\rho$ is the fluid density ($\text{kg/m}^3$).

Example 1: Normal Operating Conditions

For a water pump with a flow rate of 6 m³/h (0.0017 m³/s), brake power of 0.11 kW, and an efficiency of 28% (0.28), the temperature rise is:

$\Delta T = \frac{(0.11\ \text{kW})(1 - 0.28)}{(4.2\ \text{kJ/kg}^\circ\text{C})(0.0017\ \text{m}^3/\text{s})(1000\ \text{kg/m}^3)} = 0.011^\circ\text{C}$

The specific heat of water ($c_p$) is taken as 4.2 kJ/kg°C.

Example 2: Throttled Flow Condition

If the flow is reduced to 2 m³/h (0.00056 m³/s) by throttling the discharge valve, with a corresponding brake power of 0.095 kW and a reduced efficiency of 15% (0.15), the temperature rise increases significantly:

$\Delta T = \frac{(0.095\ \text{kW})(1 - 0.15)}{(4.2\ \text{kJ/kg}^\circ\text{C})(0.00056\ \text{m}^3/\text{s})(1000\ \text{kg/m}^3)} = 0.035^\circ\text{C}$

Key Insight: Reducing pump flow via throttling decreases pump efficiency and dramatically increases the fluid's temperature rise. This relationship, linking temperature rise to flow rate, is typically characterized by specific pump curves provided in manufacturer documentation.

References

• Original Source