Pump Horsepower Head

Overview

Engineering reference data for Pump Horsepower Head 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	—

Key Pump Calculations and Definitions

The following terms are essential for understanding pump performance and hydraulic systems. Definitions and common formulas are provided for reference.

• Pressure Head: The equivalent height of fluid column corresponding to a given pressure. Formula: $H_p = \frac{P}{\rho g}$ where $P$ is pressure, $\rho$ is fluid density, and $g$ is gravitational acceleration.

• Total Dynamic Head (TDH): The total head a pump must overcome, including static head, friction head, and velocity head. Formula: $TDH = H_s + H_f + H_v$ with typical components defined by system design.

• Bowl Horsepower: The hydraulic power required at the pump impeller or bowl, often in horsepower. For water pumps: $BHP = \frac{\rho g Q H}{550}$ in U.S. units, where $Q$ is flow rate and $H$ is head.

• Total Thrust on Driver Thrust Bearing: The axial force on the thrust bearing due to hydraulic thrust and rotating weight. Estimation depends on pump geometry and operating conditions.

• Field Head: The head measured under actual field conditions, which may include additional losses not present in laboratory tests.

• Power Loss due to Shafting: Energy dissipated in the shaft from friction, bending, or misalignment, often estimated from shaft torque and speed.

• Power Loss in Thrust Bearings: Power consumed by thrust bearing friction, calculated from bearing load, speed, and lubrication properties.

• Motor Load: The percentage of rated motor power being utilized. Formula: $\text{Motor Load (\%)} = \frac{P_{\text{actual}}}{P_{\text{rated}}} \times 100$

• Field Efficiency: The pump system efficiency under operating conditions, accounting for all losses. Formula: $\eta_{\text{field}} = \frac{\text{Output Power}}{\text{Input Power}} \times 100\%$

• Input Horsepower: The mechanical power supplied to the pump driver (e.g., electric motor). Formula: $P_{\text{in}} = \frac{P_{\text{out}}}{\eta_{\text{driver}}}$ where $\eta_{\text{driver}}$ is driver efficiency.

• Shaft Elongation: The increase in shaft length due to axial forces, using Hooke's law: $\Delta L = \frac{F L}{A E}$ where $F$ is axial force, $L$ is shaft length, $A$ is cross-sectional area, and $E$ is Young's modulus.

Source: Adapted from engineeringtoolbox.com for pump horsepower and head calculations.

References

• Original Source