Pump Flow Calculator
Imperial (Inches, Gallons, GPM)
Metric (mm, Liters, LPM)
Simplex (1 Head)
Duplex (2 Heads)
Triplex (3 Heads)
Quadruplex (4 Heads)
Quintuplex (5 Heads)
Theoretical Flow Rate (100% Eff)
0.00
GPM
Actual Flow Rate (At 95% Eff)
0.00
GPM
Displacement Per Stroke
0.000
cubic inches
Diaphragm Pump Flow Rate Calculation
Correctly sizing a diaphragm pump is critical for industrial processes, whether used in chemical dosing, water treatment, or agricultural spraying. This calculator allows you to determine the estimated output of a reciprocating positive displacement pump based on its physical geometry and operating speed.
How the Calculation Works
A diaphragm pump creates flow by displacing a specific volume of fluid with every stroke. Unlike centrifugal pumps, which create pressure to move fluid, a diaphragm pump moves a fixed volume regardless of pressure (theoretically). The calculation involves three main steps:
- Geometry Calculation: Determining the volume of the cylinder or diaphragm chamber.
- Total Displacement: Multiplying the chamber volume by the number of heads (Simplex, Duplex, etc.) and the pump speed (SPM).
- Efficiency Adjustment: Accounting for "slip" or volumetric efficiency losses.
The Formula
The mathematical formula used depends on your unit system:
Imperial (US Gallons)
$$Flow (GPM) = \frac{A \times L \times N \times H \times \eta}{231}$$
- A = Area of plunger/diaphragm (square inches) = $\pi \times (Diameter/2)^2$
- L = Stroke length (inches)
- N = Speed (Strokes Per Minute)
- H = Number of heads (e.g., 1 for Simplex)
- $\eta$ = Volumetric Efficiency (decimal, e.g., 0.95)
- 231 = Conversion factor (cubic inches per gallon)
Metric (Liters)
$$Flow (LPM) = \frac{A \times L \times N \times H \times \eta}{1,000,000}$$
- A = Area (square mm)
- L = Stroke length (mm)
- 1,000,000 = Conversion factor (cubic mm per liter)
Understanding Volumetric Efficiency
No pump is 100% efficient. In diaphragm pumps, losses occur due to:
- Check Valve Slip: A small amount of fluid backflows as the ball valves seat.
- Fluid Compressibility: Minor compression at very high pressures.
- Diaphragm Deformation: Flexibility in the material reducing effective stroke.
Most industrial diaphragm pumps operate between 85% and 97% volumetric efficiency. For general sizing, 90-95% is a safe standard value.
Example Calculation
Consider a Simplex (1 Head) pump with the following specifications:
- Diameter: 3 inches
- Stroke Length: 2 inches
- Speed: 100 SPM
- Efficiency: 90%
First, calculate the Area: $\pi \times (1.5)^2 \approx 7.068$ sq in.
Displacement per stroke: $7.068 \times 2 = 14.137$ cubic inches.
Total Volume per minute: $14.137 \times 100 = 1413.7$ cubic inches.
Convert to Gallons: $1413.7 / 231 \approx 6.12$ GPM (Theoretical).
Apply 90% Efficiency: $6.12 \times 0.90 = \mathbf{5.51 \text{ GPM}}$ (Actual).