Physics calculator

Darcy–Weisbach Calculator

Q: Does this solve Colebrook for f?

No. f is an input. Use /calc/physics/colebrook for turbulent-pipe f from Re and ε/D.

Q: Is this Q = A·v?

No. Volumetric flow is /calc/physics/flow-rate. This page is head loss and pressure drop.

Q: Can I change g?

Yes on REST and MCP with g or g_m_s2. The web form uses gn = 9.80665 m/s².

Q: Where does this run?

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

Compute pipe head loss hf = f L v²/(2 g D) and Δp = ρ g hf from a given Darcy friction factor. Runs locally. Does not solve Colebrook for f.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Darcy–Weisbach hf = f L v²/(2 g D) and Δp = ρ g hf from a given f, + O3 mpmath tabulated hf/Δp.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: Darcy–Weisbach hf = f L v²/(2 g D) and Δp = ρ g hf from a given f, + O3 mpmath tabulated hf/Δp.
Assurance: Engineering
Declared partition coverage: PASS · 5/5 declared partitions (head_loss, zero_f, alias, awkward, invalid-domain) · Matrix
Deferred: Not Colebrook f from Re/ε/D, not Manning, not Hazen–Williams, and not Q=Av.
Numerical scope: O2: Darcy–Weisbach vs a separate-module identity (≤2 ULP). Not Colebrook f, not Manning, not Hazen–Williams, and not Q=Av. ≤2 ULP vs O3 applies only to the published tabulated Darcy–Weisbach vectors. Not Colebrook f, not Manning, not Hazen–Williams, and not Q=Av.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
Model: Darcy–Weisbach head loss and pressure drop from a given friction factor.
Scope: Incompressible
Verification: Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Darcy–Weisbach hf = f L v²/(2 g D) and Δp = ρ g hf from a given f, + O3 mpmath tabulated hf/Δp.· 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 7ea3fe04b44a
Legacy regression: 11/11 tests · Production surface contract 6/6
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 · 6/6 CVP boundary · 6/6 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources: ISO 80000-4 — Mechanics — Pressure and hydraulic head
White, F.M. Fluid Mechanics — pipe flow — Darcy–Weisbach equation
Sources
Evidence: 1 legacy golden · 5 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 6/6 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 losshf = f L v² / (2 g D)

Pressure dropΔp = ρ g hf

if is given. This page does not solve Colebrook–White. g defaults to 9.80665 m/s².

How to use

Enter friction factor f

f ≥ 0. Get f from Colebrook or another correlation; this page does not solve for f.

Enter L, v, D, and ρ

Length, mean velocity, inner diameter, and density. All lengths and speed must be greater than zero.

Read hf and Δp

hf = f L v²/(2 g D). Δp = ρ g hf.

Example calculations

Common configurations with formula and result.

Water in a 10 m pipe

f=0.02, L=10 m, v=2 m/s, D=0.1 m, ρ=1000 kg/m³

Δp = ρ f L v² / (2 D)

Δp=4000 Pa · hf≈0.40789 m

Zero friction

f=0, same L, v, D, ρ

hf = 0

hf=0 · Δp=0

Darcy–Weisbach calculator specification

Version 1.0.0 · Engine tested

Calculation status

Engine tested 11/11 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.0

Review policy · Evidence

Definition: Darcy–Weisbach: hf = f L v² / (2 g D). Pressure drop Δp = ρ g hf. Circular incompressible pipe. f is an input.
What it calculates: Darcy–Weisbach head loss and pressure drop from a given friction factor.
Inputs: f
L
v
D
rho
g?
Outputs: hf_m
dP_Pa
f
L
v
D
rho
g
Formula: hf = f L v²/(2 g D); Δp = ρ g hf
Assumptions: Incompressible
Constant Darcy friction factor
Circular full-flow pipe
g = 9.80665 m/s² unless given
Does not solve Colebrook for f
Not Hazen–Williams or minor-loss K
Units: SI; L and D in m; v in m/s; ρ in kg/m³; hf in m; Δp in Pa
Boundary conditions: missing f, L, v, D, or rho → MISSING_REQUIRED_INPUT
L, v, D, or rho ≤ 0 → VALUE_MUST_BE_POSITIVE
f < 0 → VALUE_OUT_OF_RANGE
g given and g ≤ 0 → VALUE_MUST_BE_POSITIVE
Example: f=0.02 L=10 v=2 D=0.1 rho=1000 → Δp=4000 Pa
Validation cases: 3 published on this page · 11/11 tests · Production surface contract 6/6 · View evidence
f=0.02 L=10 v=2 D=0.1 rho=1000 → Δp=4000 Pa; hf=4000/(ρ g)
f=0 L=10 v=2 D=0.1 rho=1000 → Δp=0
D=0 → VALUE_MUST_BE_POSITIVE
Sources: ISO 80000-4 — Mechanics — Pressure and hydraulic head
Supports: Δp = ρ g hf for a hydrostatic/hydraulic head
White, F.M. Fluid Mechanics — pipe flow — Darcy–Weisbach equation
Supports: hf = f L v² / (2 g D) for circular pipes
Calculation version: 1.0.0

Background

Interpretation and common distinctions.

Compute pipe head loss from Darcy–Weisbach.

Supported and not supported

Supported — hf and Δp from a given f · API physics.fluid.darcy_weisbach

Not supported — Colebrook solve for f, laminar 64/Re, Hazen–Williams, minor-loss K, compressible flow, Q=Av

Agent / API notes

Capability id: physics.fluid.darcy_weisbach · tool id: darcy-weisbach · pin 1.0.0.

{ "f": 0.02, "L": 10, "v": 2, "D": 0.1, "rho": 1000 }

Optional g (default 9.80665). Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE, VALUE_OUT_OF_RANGE.

Calculator URL stays /calc/physics/darcy-weisbach. 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.

Does this solve Colebrook for f?