What is the Darcy-Weisbach equation?

h_f = f · (L/D) · V²/(2g), where h_f is friction head loss (m), f is the Darcy friction factor (dimensionless), L is pipe length (m), D is inner diameter (m), V is mean velocity (m/s), and g is gravitational acceleration (9.81 m/s²). Pressure drop ΔP = ρ · g · h_f.

How is the friction factor calculated?

For laminar flow (Re < 2300), f = 64/Re exactly. For turbulent flow, this calculator uses the Colebrook-White implicit equation — 1/√f = −2 log₁₀(ε/(3.7D) + 2.51/(Re√f)) — solved iteratively with Newton-Raphson convergence to six significant figures.

What pipe roughness value should I use?

Typical absolute roughness (ε): drawn copper/brass tubing ≈ 0.0015 mm, commercial steel ≈ 0.046 mm, galvanized steel ≈ 0.15 mm, cast iron ≈ 0.26 mm, concrete ≈ 0.3–3 mm. PVC and smooth plastic pipes are often treated as hydraulically smooth (ε ≈ 0.0015 mm).

Does this include minor losses (fittings, bends, valves)?

No. This calculator covers major (straight-pipe friction) losses only. Minor losses from fittings, valves, and bends must be added separately using K-factor or equivalent-length methods.

What is the difference between head loss and pressure drop?

Head loss (m) is the energy loss expressed as an equivalent height of fluid column — it is fluid-independent in that sense. Pressure drop (Pa or psi) converts head loss back to pressure using ΔP = ρ · g · h_f, so it depends on fluid density.

Pipe Friction Loss Calculator

Enter pipe geometry, flow rate, and fluid properties to calculate friction head loss and pressure drop using the Darcy-Weisbach equation.

Pipe & Flow Parameters

Unit System

Pipe Inner Diameter (mm)

Pipe Length (m)

Wall Roughness ε (mm)

Volumetric Flow Rate (L/s)

Fluid

Results

Enter parameters and click Calculate.

Summary

The Darcy-Weisbach equation (h_f = f · L/D · V²/2g) is the standard method for calculating friction head loss in full pipes. This calculator solves for the Darcy friction factor using the Colebrook-White equation (iterated via Newton-Raphson), then returns head loss in meters and pressure drop in Pascals or psi. Both SI and imperial unit systems are supported.

How it works

Enter the pipe inner diameter, length, and wall roughness.
Enter the volumetric flow rate and select a fluid (or enter density and viscosity manually).
The calculator computes mean velocity from Q = V · A.
Reynolds number Re = ρVD/μ is computed to classify flow as laminar or turbulent.
For laminar flow (Re < 2300) the friction factor is f = 64/Re. For turbulent flow the Colebrook-White equation is solved iteratively.
Friction head loss h_f = f · (L/D) · V²/(2g) and pressure drop ΔP = ρ · g · h_f are displayed.

Use cases

Size pump head requirements for water supply and HVAC systems.
Check pressure drop along process plant piping runs.
Verify hydraulic grades in gravity-fed distribution networks.
Estimate energy losses in irrigation and agricultural piping.
Validate CFD boundary conditions for pipe flow simulations.
Solve fluid mechanics coursework and exam problems.

Frequently Asked Questions

Last updated: 2026-06-15 · Reviewed by Nham Vu