Physics calculator

Minor Loss Calculator

Q: 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.

Q: Is this Hazen–Williams?

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

Q: Is this an orifice?

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

Q: 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.

Q: Do you convert K to equivalent length?

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

Q: Where does this run?

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

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 CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · h_m = K v^2/(2g), optional Δp = ρ g h_m, plus K and v solves, + O3 mpmath tabulated head loss.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: h_m = K v^2/(2g), optional Δp = ρ g h_m, plus K and v solves, + O3 mpmath tabulated head loss.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (head, solve, pressure, awkward, invalid-domain) · Matrix
Deferred: Not Darcy, not Hazen–Williams, and not Q=Av.
Numerical scope: O2: minor loss vs a separate-module identity (≤2 ULP). Not Darcy, not Hazen–Williams, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated minor-loss vectors. Not Q=Av, not Manning, and not Darcy.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
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 · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · h_m = K v^2/(2g), optional Δp = ρ g h_m, plus K and v solves, + O3 mpmath tabulated head loss.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-25.o2-o3.1
Verification revision: 2026-09-25.o2-o3.1 · 1/1 property · digest e4e386b82e55
Legacy regression: 17/17 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 · 9/9 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 5/5 CVP contract · Manifest
Sources: ISO 80000-4 — Mechanics — Hydraulic head and kinetic energy
White, F.M. Fluid Mechanics — Minor losses in pipe systems
Sources
Evidence: 2 legacy golden · 10 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 9/9 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.

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

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.

Enter mean velocity v

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

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.

Sharp entrance

K=0.5, v=2 m/s

h_m = 0.5 · 2² / (2 g)

h_m≈0.10197 m

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

Engine tested 17/17 tests · Production surface contract 5/5
Named expert review Not performed
Calculation version 1.0.0

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 5/5 · 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: 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 Darcy–Weisbach?