Centrifugal Pumps Maximum Shut Off Head

Overview

Engineering reference data for Centrifugal Pumps Maximum Shut Off Head in pumps.

Key Formulas

Pump Power

$P = \frac{Q \cdot H \cdot \rho \cdot g}{\eta}$

Hydraulic power / efficiency.

NPSH Available

$NPSH_a = \frac{P_s}{\rho g} + \frac{v_s^2}{2g} - \frac{P_v}{\rho g}$

Net Positive Suction Head available.

Affinity Laws

$Q \propto n, \quad H \propto n^2, \quad P \propto n^3$

Flow, head, power vs speed.

Variables

Symbol	Description	Unit
$P$	Power	W
$Q$	Flow rate	m³/s
$H$	Head	m
$\eta$	Efficiency	—
$n$	Rotational speed	RPM

Maximum Shut-Off Head Calculation

The maximum "shut-off" head for a centrifugal pump can be estimated using the following formula:

$h_s = \left( \frac{d \cdot n}{1840} \right)^2$

Variables:

• $h_s$ = Maximum shut-off head (feet)
• $d$ = Outside diameter of impeller (inches)
• $n$ = Rotational speed (rpm)

Note: This empirical formula provides a quick estimation where the constant 1840 incorporates unit conversion and typical pump characteristics. The shut-off head represents the maximum head a pump can achieve at zero flow rate.

Practical Considerations

The formula for maximum shut-off head estimates the theoretical head at zero flow (BEP shut-off condition). In practice:

• Impeller Diameter (d): Head increases with the square of the impeller diameter. Minor changes in diameter significantly affect shut-off head.
• Rotational Speed (n): Head also increases with the square of the speed. This relationship is fundamental to pump affinity laws.
• Constant 1840: This empirical constant (units: rpm·in) is derived from typical pump specific speed ranges and fluid properties (water at standard conditions). Its use provides a quick estimation for standard centrifugal pumps.

This estimation is useful for initial sizing and understanding pump capability limits, but actual shut-off head should be confirmed from the manufacturer's performance curve, which accounts for real hydraulic losses and design specifics.

Additional Formula Reference

Shut-Off Head Estimation (Imperial Units)

The maximum "shut-off" head for a centrifugal pump can be estimated using the following formula:

$$h_s = \left( \frac{d \cdot n}{1840} \right)^2$$

Where:

• $h_s$ = shut-off head (feet)
• $d$ = outside diameter of the impeller (inches)
• $n$ = rotational speed of the impeller (revolutions per minute - rpm)

Note: This formula provides a simplified estimate. Actual shut-off head depends on specific impeller design, pump casing geometry, and fluid properties.

References

• Original Source