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Physics calculator

Pump Power Calculator

Compute incompressible pump power P=ρgQH/η and affinity-law scaling Q∝ND, H∝N²D², P∝N³D³. Runs locally. Not an orifice, not a weir, not Q=Av, and not Darcy.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 16/16 tests · Production surface contract 3/3 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Incompressible pump hydraulic/shaft power and affinity-law scaling of a similar pump.
Scope
Incompressible pump; P_h = ρ g Q H; P = P_h/η; default ρ=1000 kg/m³; η in (0, 1]
Verification
Engine tested · 16/16 tests · Production surface contract 3/3 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
Sources
Evidence
1 golden · 10 boundary · 5 property · Production surface contract 3/3 · Artifact integrity PASS
Production
Embedded snapshot: STALE · Last attested schema matched 1.0.0 snapshot / local build · Semantic contract ✓ · Last attestation PASS · current evidence changed · re-attestation required · Public/cache ✓ · Origin ✓ · Live production status PASS (0 stale; 163 CURRENT) @ 2026-09-17T03:09:03.307Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

HydraulicP_h = ρ g Q H
ShaftP = P_h / η
AffinityQ ∝ N D · H ∝ N² D² · P ∝ N³ D³
iSI g = 9.80665 m/s² unless given. Default ρ = 1000 kg/m³. Default η = 1. η must be in (0, 1]. This page is not an orifice, not a weir, not Q=Av, not Darcy–Weisbach, and not NPSH.

How to use

1

Choose power or affinity

Power is P from Q and H (or invert). Affinity scales a known duty with speed and/or impeller diameter. This is not an orifice.

2

Enter the duty

Power needs Q and H (or Δp), optional η and ρ. Affinity needs Q1, H1, and N1/N2 and/or D1/D2. Optional P1 scales P2.

3

Read P or the scaled point

Shaft P is in W. P_h = ρ g Q H. Affinity returns Q2, H2, and P2 when P1 is given.

Example calculations

Common configurations with formula and result.

ϟ

Water 0.05 m³/s at 20 m, η=0.75

Q=0.05 m³/s, H=20 m, η=0.75, default ρ=1000 kg/m³

P = ρ g Q H / η
P=13075.53 W · P_h=9806.65 W
ϟ

Speed 1450 → 1740 rpm

Same duty as P1, N2/N1=1.2

Q2=Q1·1.2 · H2=H1·1.44 · P2=P1·1.728
Q2=0.06 m³/s · H2=28.8 m · P2≈22594.52 W

Pump Power calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Power: P_h = ρ g Q H; P = P_h/η. Affinity: Q2/Q1 = (N2/N1)(D2/D1); H2/H1 = (N2/N1)²(D2/D1)²; P2/P1 = (N2/N1)³(D2/D1)³.
What it calculates
Incompressible pump hydraulic/shaft power and affinity-law scaling of a similar pump.
Inputs
  • mode?
  • Q
  • H|dP
  • P?
  • eta?
  • rho?
  • Q1,H1,N1/N2|D1/D2,P1?
Outputs
  • P
  • P_h
  • eta
  • Q
  • H
Formula
P = ρ g Q H / η | Q2/Q1 = (N2/N1)(D2/D1)
Assumptions
  • Incompressible pump; P_h = ρ g Q H; P = P_h/η; default ρ=1000 kg/m³; η in (0, 1]
  • Affinity: Q∝N D, H∝N² D², P∝N³ D³; geometrically similar; same fluid
  • Not orifice, not weir, not Q=Av, not Darcy, not NPSH, not a catalog curve
Units
  • SI; Q in m³/s; H in m; P in W; ρ in kg/m³
Boundary conditions
  • missing Q+H, Q+P, H+P, or affinity N/D pairs → MISSING_REQUIRED_INPUT
  • Q, H, P, η, ρ, N, or D ≤ 0 → VALUE_MUST_BE_POSITIVE
  • η > 1 or shaft P < P_h → VALUE_OUT_OF_RANGE
  • Q+H+P+η, H and Δp, C_d, crest L, area A, or power mixed with N2 → MIXED_INPUT_ENCODING
  • orifice, weir, Manning, Darcy, NPSH, or Q=Av as mode → INVALID_MODE
Example
Q=0.05 H=20 eta=0.75 → P=ρgQH/η
Validation cases

3 published on this page · 16/16 tests · Production surface contract 3/3 · View evidence

  • Q=0.05 H=20 eta=0.75 → P=13075.53 W
  • mode=affinity Q1=0.05 H1=20 N1=1450 N2=1740 → Q2=0.06
  • mode=orifice Q=0.05 H=20 → INVALID_MODE
Sources
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute incompressible pump power and affinity-law scaling.

Supported and not supported

Supported — hydraulic and shaft power · invert H or Q · η from Q, H, and P · speed/diameter affinity · API physics.fluid.pump

Not supported — orifice discharge, weir overflow, Q=Av identities, Darcy–Weisbach, NPSH, manufacturer curves, viscous corrections

Agent / API notes

Capability id: physics.fluid.pump · tool id: pump-power · pin 1.0.0.

{ "mode": "power", "Q": 0.05, "H": 20, "eta": 0.75 }

Affinity: { "mode": "affinity", "Q1": 0.05, "H1": 20, "P1": 13075.533333333334, "N1": 1450, "N2": 1740 }. Optional "rho" (default 1000). Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/pump-power. There is no /calc/fluid.

Other calculators in this family: Orifice discharge, Flow rate, Darcy–Weisbach .

Q Orifice discharge › Q Flow rate › hf Darcy–Weisbach ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this an orifice?

No. A hole under head or a pipe orifice plate is /calc/physics/orifice-discharge. A pump adds shaft work. Sending C_d is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from a given area and velocity is /calc/physics/flow-rate. This page uses Q as a pump duty, not as A·v.

Does this solve NPSH or a catalog curve?

No. NPSH, viscous corrections, and manufacturer curves are out of scope.

Where does this run?

Locally in the browser by default. REST and MCP call the same fluid-engine pumpPower wrapper.