Physics calculator

Pump Power Calculator

Q: 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.

Q: 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.

Q: Does this solve NPSH or a catalog curve?

No. NPSH available is /calc/physics/npsh. Viscous corrections and manufacturer curves stay out of scope.

Q: Where does this run?

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

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 CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Pump hydraulic/shaft power P_h=ρgQH, P=P_h/η, plus affinity laws, + O3 mpmath tabulated P.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: Pump hydraulic/shaft power P_h=ρgQH, P=P_h/η, plus affinity laws, + O3 mpmath tabulated P.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (power, affinity, alias, awkward, invalid-domain) · Matrix
Deferred: Not orifice, not weir, not Manning, not Darcy, and not NPSH.
Numerical scope: O2: pump power/affinity vs a separate-module identity (≤2 ULP). Not orifice, not weir, not Manning, not Darcy, and not NPSH. ≤2 ULP vs O3 applies only to the published tabulated pump vectors. Not orifice, not weir, not Manning, not Darcy, and not NPSH.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
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 · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Pump hydraulic/shaft power P_h=ρgQH, P=P_h/η, plus affinity laws, + O3 mpmath tabulated P.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-26.o2-o3
Verification revision: 2026-09-26.o2-o3 · 1/1 property · digest ce18e1b48677
Legacy regression: 16/16 tests · Production surface contract 5/5
Trust layers: Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review: Not performed
Named expert review: Not performed
CVP suite: 4/4 golden · 9/9 CVP boundary · 10/10 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 CVP contract · Manifest
Sources: ISO 9906 — Rotodynamic pumps — Hydraulic performance acceptance tests — Pump power and efficiency definitions
Stepanoff, A.J. Centrifugal and Axial Flow Pumps — Affinity laws
Sources
Evidence: 1 legacy golden · 10 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 10/10 invalid · Artifact integrity PASS
Semantic contract: PASS

Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

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

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.

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.

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.

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

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

Engine tested 16/16 tests · Production surface contract 5/5
Named expert review Not performed
Calculation version 1.0.0

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 5/5 · 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: ISO 9906 — Rotodynamic pumps — Hydraulic performance acceptance tests — Pump power and efficiency definitions
Supports: P_h = ρ g Q H; η = P_h / P for the overall pump
Stepanoff, A.J. Centrifugal and Axial Flow Pumps — Affinity laws
Supports: Geometrically similar incompressible pumps: Q∝ND, H∝N²D², P∝N³D³
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: Alternate Depth Calculator, Bernoulli Equation Calculator, Broad-Crested Weir Calculator, Cavitation Number Calculator, Chezy Formula Calculator, Colebrook Friction Factor Calculator, Concentric Reducer Calculator, Critical Depth Calculator . Explore all Fluid Mechanics.

Frequently asked questions

Key distinctions behind the calculation.

Is this an orifice?