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Friction Loss Calculator

Calculate the friction loss in pipes for different materials using the Hazen-Williams equation.

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Friction head loss3.7866 m37.0672 kPa, 5.376 psi
Reynolds number199,242turbulent
Darcy friction factor0.018567from Colebrook–White, solved by iteration
Relative roughness ε/D0.00045
Head loss per metre0.037866 m/m3.7866 m per 100 m
Velocity head v²/2g0.20394 m
Equivalent length in diameters1,000 D
Fitting losses0.7138 mK = 3.5 × the velocity head
Total head loss4.5004 m44.0546 kPa
Fittings as a share of the loss15.86%on a short run, fittings often dominate the straight pipe entirely
Hydraulic power to overcome the loss692.0075 Wbefore pump and motor efficiency
At twice the velocity15.1465 mroughly four times the loss — it goes as the square of velocity, and the pumping POWER as the cube
In a pipe one size larger (125 mm)1.240798 ma 25% larger bore cuts the loss dramatically, because velocity falls with the square of diameter and loss with the square of velocity

The formula

h_f = f (L/D) (v² ÷ 2g), with f from Colebrook–White

Laminar friction ignores roughness

Head loss along a pipe is the friction factor times the length-to-diameter ratio times the velocity head. The friction factor is where the physics sits, and it behaves completely differently in the two regimes.

In laminar flow it is exactly 64/Re and roughness is irrelevant — the flow never interacts with the wall irregularities, because there is a smooth viscous layer over them. In turbulent flow roughness dominates, and the friction factor comes from the implicit Colebrook–White equation. This page solves that by iteration rather than using the Swamee–Jain approximation, since the iteration converges in a few steps and there is no reason to accept the approximation's error.

The exponents are what make pipe sizing worthwhile. Loss goes as the square of velocity, and pumping power as the cube. Since velocity falls with the square of diameter at fixed flow, going up one pipe size can cut the pumping energy by more than half — which usually repays the extra material cost many times over across a pump's life.

On short runs the fittings dominate. A few elbows and a valve can easily exceed the loss of the straight pipe, which is why the K-value sum is part of the calculation rather than a footnote.