Pump Shaft Power Calculator Formula

Shaft Power Formula:

\[ P_s = \frac{Q \times \rho \times g \times h}{\eta} \]

Flow Rate (Q):

m³/s

Fluid Density (ρ):

kg/m³

Head (h):

Efficiency (η):

(0-1)

Shaft Power (P_s):

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1. What is Pump Shaft Power?

Definition: Shaft power is the mechanical power required at the pump shaft to deliver a specific hydraulic power to the fluid.

Purpose: This calculation helps engineers select appropriate pumps and motors for fluid systems.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ P_s = \frac{Q \times \rho \times g \times h}{\eta} \]

Where:

\( P_s \) — Shaft power (Watts)
\( Q \) — Flow rate (m³/s)
\( \rho \) — Fluid density (kg/m³)
\( g \) — Gravitational acceleration (9.81 m/s²)
\( h \) — Head (m)
\( \eta \) — Pump efficiency (0-1)

Explanation: The formula calculates the power needed to move fluid against gravity and system resistance, accounting for pump efficiency.

3. Importance of Shaft Power Calculation

Details: Proper shaft power estimation ensures correct pump selection, energy efficiency, and prevents motor overload.

4. Using the Calculator

Tips: Enter flow rate in m³/s, fluid density (default 1000 kg/m³ for water), head in meters, and pump efficiency (default 0.8). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is typical pump efficiency?
A: Centrifugal pumps typically range from 0.5-0.9, with 0.7-0.8 being common for most applications.

Q2: How do I convert the result to horsepower?
A: Divide Watts by 746 to get horsepower (hp).

Q3: What if my flow rate is in L/s?
A: Convert to m³/s by dividing by 1000 (1 L/s = 0.001 m³/s).

Q4: Why is density important?
A: More dense fluids require more power to pump. Water is 1000 kg/m³, oils are typically 800-900 kg/m³.

Q5: What does "head" mean in pumping?
A: Head represents the height the pump must lift the fluid, plus friction losses in the system.