An external gear pump carries fluid in spaces between its gear teeth and housing. Two counter-rotating gears move those spaces around the outer sides of the chamber from inlet to outlet. Displacement and shaft speed set theoretical flow; leakage and operating conditions affect actual delivery. Use the calculator to estimate flow and fluid power for a chosen operating point.
Gear Pump Interactive Calculator
Estimate theoretical displacement flow, delivered flow using an entered volumetric efficiency, delivered hydraulic power and ideal displacement torque for a fixed-displacement pump.
Equation Used
- Fixed displacement per shaft revolution.
- Entered volumetric efficiency applies at the entered operating point.
- Pressure input is outlet-minus-inlet differential pressure.
- No mechanical efficiency, inlet/cavitation, viscosity, heat, load, strength, life or relief-valve model.
First-order operating-point arithmetic only. Pressure means differential pressure across the pump. Ideal torque excludes mechanical losses; input shaft power and torque will be higher. The calculator does not establish permissible speed, pressure, fluid, viscosity, inlet condition, cavitation margin, temperature or relief settings.
How an external gear pump carries fluid
Two external gears counter-rotate in a close housing. Their mesh separates inlet from outlet, while spaces between teeth and housing carry fluid around the two outer paths. The schematic shows this split peripheral transport path; tooth profiles, clearances, side plates and trapped-volume relief features are not designed by the drawing.
Operating-point estimate
The relations are useful for checking unit conversions and a hypothetical operating point when displacement, speed, differential pressure and an applicable volumetric efficiency are already known. A real pump must be selected from manufacturer data for the fluid, viscosity, temperature, inlet condition, speed, pressure, duty and life requirements.
Flow, fluid power and ideal torque
Theoretical flow is displacement per revolution multiplied by revolutions per minute. Estimated delivered flow is theoretical flow multiplied by the entered volumetric efficiency. Delivered hydraulic power is differential pressure multiplied by estimated flow. Ideal displacement torque is differential pressure multiplied by displacement per revolution divided by 2 pi.
Manufacturer literature distinguishes volumetric, mechanical and total efficiency. Because mechanical efficiency is not entered here, calculated torque is ideal fluid torque rather than required input-shaft torque.
Example: 10 cc/rev at 1800 rpm
Theoretical flow is 10 × 1800 = 18,000 cc/min, or 4.76 US gpm. At an entered volumetric efficiency of 90%, estimated delivery is 4.28 US gpm. At 3000 psi differential pressure, delivered fluid power is 7.49 hp and ideal displacement torque is 291.4 lb-in.
Halving speed halves both flow estimates and delivered fluid power while leaving ideal displacement torque unchanged. Reducing volumetric efficiency changes estimated delivered flow and fluid power, but not the ideal torque expression. Shaft torque requires mechanical-loss information.
At zero differential pressure, the computed fluid power and ideal fluid torque are zero while displacement flow remains nonzero. A real pump still requires torque to overcome friction and move fluid through its passages.
Scope and limitations
Volumetric efficiency is not a universal constant; it varies with the exact pump, clearances, differential pressure, speed, fluid viscosity and temperature. Safe application also requires manufacturer inlet-pressure limits, cavitation checks, filtration, materials, drive loads, case/seal conditions and pressure relief. None are established here.
Frequently asked questions
Which pressure belongs in the calculator?
Use the difference between outlet and inlet pressure, not absolute outlet pressure.
Why does speed not change ideal torque?
Ideal displacement torque is differential pressure times displacement per revolution divided by 2Ï€. Speed changes the amount displaced per minute, and therefore flow and power.
Is Ideal Fluid Torque the required shaft torque?
No. Mechanical losses add to the torque required from the driver.
Does the entered efficiency cover all losses?
No. It is volumetric efficiency, used to estimate delivered flow. Mechanical efficiency and total input power are not calculated.
Can these controls establish allowable pressure or speed?
No. Permissible operating conditions come from the selected pump’s data and its application, not from the slider endpoints.
Manufacturer technical references
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