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Positive Displacement Pump Sizing Calculator

Reciprocating & rotary PD pumps — displacement flow, delivered flow, volumetric efficiency / slip, and brake horsepower (API 674/675/676)

🛢️ Positive Displacement Pump Sizing
Choose a pump mode, then enter geometry and operating conditions. The calculator returns displacement flow, delivered flow, volumetric efficiency (reciprocating) or slip (rotary), and the required brake horsepower. Relations are fundamental PD theory; API 674/675/676 are the governing equipment standards.

Pump Geometry

in
in
Simplex 1, duplex 2, triplex 3, quintuplex 5.
rpm

Operating Conditions

%
Delivered flow = displacement × η_v. Typical 90–97% (slip 3–10%).
psi
Discharge minus suction pressure.
%
Typical 85–92% for power-end + gear losses.

Pump Geometry

in³/rev
Theoretical swept volume of the rotor set per shaft turn.
rpm
gpm
Internal leakage at the rated ΔP; rises with pressure, falls with viscosity.

Operating Conditions

psi
Discharge minus suction pressure.
%
Typical 85–92% for bearing, timing-gear, and seal losses.

What This Calculates

Displacement Flow:
Reciprocating Q_disp = A·L·n·N/231; rotary Q_disp = D·N/231 — the theoretical swept volume per unit time, in gpm.
Delivered Flow:
Reciprocating Q = Q_disp·η_v; rotary Q = Q_disp − slip — the actual flow after leakage and compressibility losses.
Volumetric Efficiency / Slip:
η_v = 1 − slip. Reports volumetric efficiency for reciprocating pumps and slip flow for rotary pumps.
Required Brake Power:
BHP = Q·ΔP/(1714·η_mech) — the shaft power the driver must supply at the delivered flow and differential pressure.

📘 PD Displacement & Volumetric Efficiency

A positive-displacement pump moves a fixed volume per stroke or revolution, so flow is set by geometry and speed — almost independent of discharge pressure (a near-vertical pump curve).

Reciprocating: Q_disp = A·L·n·N / 231  (A = π/4·d²)
Rotary: Q_disp = D·N / 231
Delivered: Q = Q_disp·η_v  or  Q = Q_disp − slip
Power: BHP = Q·ΔP / (1714·η_mech)

Volumetric efficiency η_v = 1 − slip captures leakage past valves, packing, and rotor clearances plus fluid compressibility. Slip rises with ΔP and falls with viscosity.

Reciprocating vs Rotary (API 674/675/676)

Reciprocating (API 674 power, API 675 controlled-volume): plunger, piston, or diaphragm sweeps a bore — very high pressure at low flow, pulsating delivery, needs pulsation dampers. Best for high-pressure injection, glycol charge, and metering.

Rotary (API 676): gear, screw, lobe, vane, or progressive-cavity rotors mesh to carry a fixed volume per turn — smoother flow, excellent for viscous liquids such as lube/seal oil, heavy crude, asphalt, and polymers.

⚠️ Relief valve mandatory: a PD pump cannot deadhead. Provide a discharge relief (PSV) sized for full capacity and set below the lowest component rating.

Note: relations here are fundamental PD theory; the API 674/675/676 PDFs were not on hand, so no API-specific clause or coefficient was verified against the source.

Standards Reference

  • API 674: Positive Displacement Pumps — Reciprocating (power pumps)
  • API 675: Positive Displacement Pumps — Controlled-Volume (metering)
  • API 676: Positive Displacement Pumps — Rotary (gear / screw / lobe)
  • HI 6.1–6.5: Reciprocating & rotary pump test/application

The API 674/675/676 PDFs were not on hand for this build. The displacement, volumetric-efficiency, and brake-power relations are fundamental PD theory; no API-specific clause or coefficient was verified against the source.

Frequently Asked Questions

What is the difference between a reciprocating and a rotary positive-displacement pump?

A reciprocating pump (plunger, piston, or diaphragm — API 674/675) displaces a fixed volume each stroke as the plunger sweeps its bore, giving a pulsating flow ideal for very high pressure at low flow. A rotary pump (gear, screw, lobe, vane, or progressive-cavity — API 676) displaces a fixed volume per shaft revolution between meshing rotors, giving a smoother flow well suited to viscous liquids. Both deliver flow that is nearly independent of discharge pressure.

What are volumetric efficiency and slip in a positive-displacement pump?

Volumetric efficiency (η_v) is the delivered flow divided by the theoretical displacement. The shortfall is slip — leakage back past valves, packing, or rotor clearances plus losses from fluid compressibility. Slip rises with differential pressure and falls with viscosity, so volumetric efficiency drops as ΔP increases. Reciprocating power pumps typically run 90–97% volumetric efficiency; rotary pumps are usually expressed as a slip flow at the rated differential.

Why does a positive-displacement pump require a discharge relief valve?

A positive-displacement pump moves a fixed volume regardless of discharge resistance, so it cannot deadhead. If the discharge is blocked it keeps building pressure until the casing, piping, seal, or driver fails. A discharge relief (pressure-safety) valve set below the lowest component rating is mandatory for every PD pump, sized to pass the full pump capacity.