For a selected positive-displacement pump displacement Vd, speed N and volumetric efficiency ηv, theoretical flow is Qth = VdN and selected delivered flow is Q = ηvQth. Hydraulic output is Ph = ΔpQ and ideal displacement torque is Tideal = ΔpVd/(2π).
Selected Positive-Displacement Pump Model
Calculate theoretical flow, selected delivered flow, hydraulic output and ideal displacement torque from selected pump inputs.
Equation Used
- Displacement per revolution is constant at the selected value.
- Volumetric efficiency is a valid user-supplied operating-point value.
- Delivered flow is incompressible volumetric flow at the stated operating point.
- Mechanical losses, fluid compression, inlet limitations, dynamics and ratings are excluded.
The external-gear animation is illustrative; the formulas apply to the selected positive-displacement abstraction, not to every rotary-pump architecture.
Selected positive-displacement model
Displacement per revolution and speed set ideal volumetric throughput. The selected volumetric-efficiency input applies a simple proportional reduction to that flow.
Pressure rise and delivered flow determine hydraulic output. Pressure rise and displacement determine ideal displacement torque. These identities do not calculate actual shaft input because mechanical and total efficiency are not supplied.
What the calculator determines
Select displacement, shaft speed, volumetric efficiency and pressure rise. The calculator returns theoretical flow, selected delivered flow, hydraulic output power and ideal torque.
The selected inputs are not equipment ratings; verify manufacturer pump curves, fluid properties, inlet conditions, NPSH or inlet-pressure requirements, speed range, pressure rating, relief protection, driver capacity and efficiency for the actual equipment.
Bounded pump identities
Qth = VdN. Q = ηvQth. Ph = ΔpQ. Tideal = ΔpVd/(2π). The calculator converts cubic centimetres to litres or cubic metres, rpm to per-minute flow and psi to pascals.
Actual input torque and power are higher than these ideal or hydraulic-output values when mechanical losses are present. Volumetric efficiency is an input, not a prediction from clearance, viscosity, pressure or speed.
Selected-input example
For 10 cc/rev, 1,800 rpm and 80% selected volumetric efficiency, theoretical flow is 18.0 L/min and selected delivered flow is 14.4 L/min. At a selected 3,000 psi pressure rise, hydraulic output is about 4.964 kW and ideal displacement torque is about 32.92 N·m.
This arithmetic does not establish that a particular pump, coupling or driver is rated for those inputs.
Scope and correction boundary
The calculator's dimensionally valid positive-displacement identities are retained. The former article added universal pressure, viscosity, clearance, material, relief, cavitation, maintenance, failure and product-selection claims that cannot be inferred from the four selected inputs.
Those claims, the fabricated greenhouse example and unrelated video are removed. Never treat the pressure slider as permission to operate a pump at that pressure or intentionally deadhead a system.
Questions
Does selected volumetric efficiency predict leakage?
No. It is a user-supplied aggregate value. Actual volumetric efficiency depends on the pump, fluid, temperature, pressure, speed, clearances, wear and inlet conditions.
Is hydraulic output the required motor power?
No. Required shaft input is higher because mechanical and other losses must be included.
Is ideal torque actual shaft torque?
No. It is the lossless displacement torque associated with selected pressure rise and displacement.
Does the calculator check cavitation or safe operation?
No. Consult the manufacturer pump curve and installation requirements, including inlet conditions and relief protection.
Technical references
- Hydraulic Institute — industry standards and pump-system guidance; use applicable manufacturer and HI methods for real selection.
- OpenStax College Physics, Flow Rate — volumetric-flow definitions and unit relationships.
- NIST Special Publication 811 — SI unit and conversion guidance.
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