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Physics calculator

Minor Loss Calculator

Compute fitting minor loss h_m = K v²/(2g). Optional Δp = ρ g h_m. Runs locally. Not Darcy–Weisbach, not Hazen–Williams, and not an orifice.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 17/17 tests · Production surface contract 3/3 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Fitting minor loss from K and mean velocity. Invert for K or v. Optional Δp from ρ.
Scope
h_m = K v² / (2g); g = 9.80665 m/s² unless given
Verification
Engine tested · 17/17 tests · Production surface contract 3/3 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
Sources
Evidence
2 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) @ 2026-09-17T06:27:56.932Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

Head lossh_m = K v² / (2g)
Pressure dropΔp = ρ g h_m = ρ K v² / 2
iSI. g defaults to 9.80665 m/s². Sum fitting K values yourself. This page is not Darcy–Weisbach, not Hazen–Williams, and not an orifice.

How to use

1

Enter K

K is the dimensionless minor-loss coefficient. It may be zero. Typical elbows are about 0.3–0.9; a sharp entrance is 0.5.

2

Enter mean velocity v

v must be greater than zero. This is not Q=Av: send v, not Q.

3

Read h_m

h_m is metres of head. Optional ρ reports Δp. Invert for K or v on the other tabs.

Example calculations

Common configurations with formula and result.

ϟ

Sharp entrance

K=0.5, v=2 m/s

h_m = 0.5 · 2² / (2 g)
h_m≈0.10197 m
ϟ

With density

Same K and v, ρ=1000 kg/m³

Δp = ρ K v² / 2
Δp=1000 Pa

Minor Loss calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
Minor loss: h_m = K v² / (2g). Optional Δp = ρ g h_m. K is an empirical fitting coefficient. Not equivalent length L_eq = K D / f.
What it calculates
Fitting minor loss from K and mean velocity. Invert for K or v. Optional Δp from ρ.
Inputs
  • mode?
  • K
  • v
  • hm?
  • rho?
  • g?
Outputs
  • hm
  • K
  • v
  • g
  • dP_Pa?
Formula
h_m = K v² / (2g)
Assumptions
  • h_m = K v² / (2g); g = 9.80665 m/s² unless given
  • K is an empirical fitting coefficient; not Darcy f
  • Not equivalent length L_eq = K D / f
  • Not Hazen–Williams, not orifice, not Q=Av
Units
  • SI; v in m/s; hm in m; K dimensionless; ρ in kg/m³; Δp in Pa
Boundary conditions
  • missing K or v when required → MISSING_REQUIRED_INPUT
  • v ≤ 0, or K < 0, or hm < 0 → VALUE_MUST_BE_POSITIVE or VALUE_OUT_OF_RANGE
  • f, L, D, L_eq, C, n, C_d, Q, A, or Re → MIXED_INPUT_ENCODING
  • darcy, hazen, orifice, or manning as mode → INVALID_MODE
Example
K=0.5 v=2 → h_m=K v²/(2g)
Validation cases

3 published on this page · 17/17 tests · Production surface contract 3/3 · View evidence

  • K=0.5 v=2 → hm=0.5*4/(2*9.80665)
  • K=0.5 v=2 rho=1000 → dP=1000 Pa
  • K=0.5 v=2 f=0.02 → MIXED_INPUT_ENCODING
Sources
  • ISO 80000-4 — Mechanics — Hydraulic head and kinetic energy
    Supports: Head has dimension of length; dynamic head v²/(2g)
  • White, F.M. Fluid Mechanics — Minor losses in pipe systems
    Supports: h_m = K v²/(2g) for valves, bends, and fittings; K is empirical
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute fitting minor loss h_m = K v²/(2g).

Supported and not supported

Supported — h_m, K, or v from the minor-loss formula · optional Δp from ρ · API physics.fluid.minor_loss

Not supported — Darcy–Weisbach fL/D, equivalent length, Hazen–Williams, orifice, Q=Av, fitting catalogs

Agent / API notes

Capability id: physics.fluid.minor_loss · tool id: minor-loss · pin 1.0.0.

{ "K": 0.5, "v": 2 }

Optional density: { "K": 0.5, "v": 2, "rho": 1000 }. Invert K: { "mode": "K", "v": 2, "hm": 0.102 }. Modes: head_loss (default), K, velocity. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE, MIXED_INPUT_ENCODING, INVALID_MODE.

Calculator URL stays /calc/physics/minor-loss. There is no /calc/fluid.

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

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

Key distinctions behind the calculation.

Is this Darcy–Weisbach?

No. Pipe friction from a given f is /calc/physics/darcy-weisbach. Sending f, L, D, or equivalent length is MIXED_INPUT_ENCODING.

Is this Hazen–Williams?

No. Empirical water-pipe hf from C is /calc/physics/hazen-williams. Sending C is MIXED_INPUT_ENCODING.

Is this an orifice?

No. Tank or meter Q=C_d… is /calc/physics/orifice-discharge. Sending C_d is MIXED_INPUT_ENCODING.

Is this Q = A·v?

No. Volumetric flow from area and velocity is /calc/physics/flow-rate. Sending Q or A is MIXED_INPUT_ENCODING. Give v.

Do you convert K to equivalent length?

No. L_eq = K D / f composes Darcy. This page stops at h_m = K v²/(2g).

Where does this run?

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