This calculator determines the theoretical displacement of a single-acting plunger power pump. Enter any four of displacement flow, number of plungers, plunger diameter, rotating speed, and stroke length to calculate the fifth.
The formula
Qdisp = M · (πD²/4) · SL · N. The circular plunger area πD²/4 multiplied by stroke length gives the swept volume of one plunger per pumping stroke. A single-acting plunger completes one displacement stroke per crankshaft revolution, so multiplying by plunger count and revolutions per unit time gives theoretical flow.
Solve in any direction
- Displacement flow (Qdisp) — theoretical flow from known pump geometry and speed.
- Number of plungers (M) — the mathematical plunger count required for a target displacement.
- Plunger diameter (D) — the bore required for a known count, stroke, speed, and flow.
- Rotating speed (N) — crankshaft rpm required for the target flow.
- Stroke length (SL) — plunger travel required for the target displacement.
Volumetric efficiency
The calculated Qdisp assumes 100% volumetric efficiency. Actual delivered flow is lower because of leakage, liquid compressibility, incomplete filling, and valve timing. Calculate actual flow from Qactual = Qdisp · ηv, with volumetric efficiency entered as a decimal. For example, a theoretical 36.72 gpm pump at 90% volumetric efficiency delivers approximately 33.05 gpm.
Plunger count must be practical
When solving for M, the algebra can return a fractional value. That is a mathematical requirement, not a buildable pump arrangement. Select a practical whole-number count and recalculate diameter, stroke, speed, or flow as appropriate.
Single-acting assumption
The formula assumes every plunger displaces fluid on one stroke per crankshaft revolution. It does not apply the two-sided displacement used for double-acting cylinders. It also assumes all plungers have the same diameter and stroke and are driven at the entered crankshaft speed.
Worked example
A triplex pump with three 2 in plungers, a 3 in stroke, and a speed of 300 rpm displaces 28.274 in³ per revolution. Its theoretical flow is 36.720 gpm (8.340 m³/h) at 100% volumetric efficiency.