IES
Mechanical Engineering2D

Pump Flow Calculator

Calculate pump flow rate from power, head, and efficiency using the hydraulic power formula.

Inputs
Enter your values below

0.75 = 75%

Result
Flow Rate
—
Enter values and click Calculate
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Formula
power_input × efficiency ÷ (density × 9.81 × head) × 3600
Result unit: m³/h

Q = P_shaft × η / (ρgH). P_shaft in W (engine converts kW→W); ×3600 converts m³/s to m³/h.

Introduction

Calculate the flow rate a pump will deliver given its shaft power, efficiency, and the system head. This inverts the standard hydraulic power equation to solve for Q.

How This Calculator Works

Q = P_shaft × η / (ρgH). P_shaft in W (engine converts kW→W); ×3600 converts m³/s to m³/h.

Step-by-step process:

  1. Enter your input values in the calculator above
  2. The engine converts all inputs to SI base units (meters, kg, Pa)
  3. The formula is evaluated: power_input * efficiency / (density * 9.81 * head) * 3600
  4. Result is formatted with the appropriate unit and precision

Calculation Example

15 kW pump at 75% efficiency pumping water to 40m head delivers ~103 m³/h.

Inputs: power_input=15, efficiency=0.75, head=40, density=1000
Result: 103.2 m³/h

Unit Conversion for Pump Flow

**Flow rate units**

- 1 m³/h = 0.2778 L/s = 4.403 US gpm

- 1 US gpm = 0.2271 m³/h = 3.785 L/min

- 1 L/s = 3.6 m³/h

**Volume units**

- 1 m³ = 1000 L = 264.17 US gal

Pump flow is the volumetric rate at the pump suction conditions. Convert all flow inputs to one consistent unit before applying the pump curve or affinity laws.

Engineering Applications

  • •Pump performance estimation
  • •System curve analysis
  • •Flow verification
  • •Retrofit planning

Frequently Asked Questions

How accurate is this calculation?

It gives rated flow at a specific operating point. Actual flow depends on where the pump curve intersects the system curve.

Why does flow decrease as head increases?

Centrifugal pumps have a falling head-flow curve. At higher system resistance (more head), less flow can be produced for the same power.

How do I convert flow between m³/h and gpm?

1 m³/h = 4.403 US gpm. For example, 50 m³/h = 220 gpm. Conversely, divide gpm by 4.403 to get m³/h. 1 m³/h also equals 0.2778 L/s.

Related Calculators

Pump Power CalculatorPump Head CalculatorPump Efficiency CalculatorPump Energy Cost CalculatorPump Affinity Law CalculatorPump Sizing CalculatorPump Selection CalculatorPipe Flow CalculatorFlow Rate CalculatorPressure Drop Calculator (Darcy-Weisbach)Reynolds Number Calculator

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Engineering Disclaimer: Calculations are for reference and educational purposes only. Always verify results independently for engineering design. See full disclaimer.
Reviewed by: Industrial Engineering Team
References: ASME B31.3, ASTM A36, Perry's Chemical Engineers' Handbook