Calculator Inputs
Formula Used
This calculator uses an engineering estimate for an external gear pump:
Vd = k × (π / 8) × (Do2 − Dr2) × b
- Vd = theoretical displacement per revolution
- k = geometry factor for tooth-space utilization
- Do = outer diameter
- Dr = root diameter
- b = face width
Then the calculator finds flow, hydraulic power, shaft power, and torque using standard fluid power relationships:
Qth = Vd × rpm
Qact = Qth × volumetric efficiency
Phyd = ΔP × Qact
Pshaft = Phyd / mechanical efficiency
T = Pshaft / ω
This is a practical estimate, not a manufacturer-certified displacement model. For final design, compare against supplier catalog values.
How to Use This Calculator
- Enter the outer diameter, root diameter, and face width.
- Select the length unit that matches your measurements.
- Input teeth count and operating speed in rpm.
- Enter the pressure rise across the pump.
- Provide volumetric and mechanical efficiencies.
- Adjust the geometry factor if you have calibration data.
- Click the calculation button.
- Review displacement, flow, power, torque, and the Plotly graph.
- Export the results with the CSV or PDF buttons.
Example Data Table
| Outer Diameter | Root Diameter | Face Width | Teeth | Speed | Pressure | Vol. Eff. | Mech. Eff. | Geometry Factor | Displacement | Actual Flow |
|---|---|---|---|---|---|---|---|---|---|---|
| 60 mm | 40 mm | 25 mm | 14 | 1450 rpm | 120 bar | 92% | 88% | 1.00 | 19.6350 cc/rev | 26.1931 L/min |
| 75 mm | 52 mm | 30 mm | 16 | 1750 rpm | 140 bar | 90% | 87% | 1.03 | 33.4760 cc/rev | 52.7250 L/min |
| 2.8 in | 1.9 in | 1.1 in | 12 | 1200 rpm | 1800 psi | 91% | 89% | 0.98 | 22.9480 cc/rev | 25.0580 L/min |
FAQs
1. What does gear pump displacement mean?
Gear pump displacement is the fluid volume moved in one shaft revolution. It is usually expressed in cc/rev or in³/rev and helps estimate flow rate.
2. Why are actual flow and theoretical flow different?
Theoretical flow assumes zero leakage. Actual flow is lower because internal leakage, compression, and clearances reduce delivered volume. Volumetric efficiency accounts for that difference.
3. What is the geometry factor used for?
The geometry factor tunes the displacement estimate to match tooth-space utilization and practical pump geometry. Use 1.00 first, then adjust from known catalog or test data.
4. Why is outer diameter larger than root diameter?
Outer diameter measures tooth tips, while root diameter measures the base between teeth. The difference defines tooth depth and contributes to trapped fluid volume.
5. How does pump speed affect flow?
Flow increases almost linearly with speed for a fixed displacement. When rpm doubles, theoretical flow roughly doubles, unless efficiency changes significantly at higher speeds.
6. How does pressure affect required torque?
Higher pressure increases hydraulic power demand. That increases shaft power and torque requirements, even if displacement and speed remain unchanged.
7. Can I use this for internal gear pumps?
This page is best for external gear pump estimates. Internal gear pumps have different geometry, so their displacement should be checked with manufacturer equations or catalog data.
8. Is this calculator suitable for final equipment sizing?
It is excellent for engineering estimates, comparisons, and early sizing. Final selection should still verify displacement, speed limits, efficiency, and pressure ratings from the pump supplier.