Pipe Friction Loss Calculator

Friction loss is the pressure drop caused by fluid flowing through a pipe. It depends on the pipe diameter, length, internal roughness, flow velocity, and the fluid's density and viscosity. Accurately calculating friction loss is essential for sizing pumps, selecting pipe diameters, and ensuring adequate pressure at downstream equipment.

Darcy-Weisbach Method

The Darcy-Weisbach equation is the most general and theoretically rigorous approach to calculating friction losses. It works for any Newtonian fluid (water, oil, gas, refrigerants), any flow regime (laminar, transitional, turbulent), and any pipe size.

• $h_f$ — head loss due to friction (m)
• $f$ — Darcy friction factor (from Colebrook-White equation)
• $L$ — pipe length
• $D$ — internal diameter
• $V$ — flow velocity
• $g$ — gravitational acceleration

The friction factor f is determined iteratively using the Colebrook-White equation, which relates f to the Reynolds number and the pipe's relative roughness (ε/D). This calculator solves it automatically.

Hazen-Williams Method

The Hazen-Williams formula is an empirical equation widely used in water distribution system design. It replaces viscosity and roughness with a single C-factor (roughness coefficient), making it simpler but less general.

• $h_f$ — head loss due to friction (m)
• $C$ — Hazen-Williams coefficient (typically 100-150)
• $Q$ — volumetric flow rate
• $D$ — internal diameter
• $L$ — pipe length

Hazen-Williams is only reliable for water near room temperature (5-25 °C) in turbulent flow through pipes larger than about 50 mm. It cannot be used for gases, oils, or refrigerants.

Which Method Should You Use?

Darcy-Weisbach is recommended as the default for general-purpose engineering calculations. It is more accurate and applicable to all fluids and flow conditions.

Hazen-Williams is appropriate when designing municipal water distribution networks, importing EPANET models, or when project specifications reference C-factors directly.

For a deeper comparison, see our blog post: Darcy-Weisbach vs Hazen-Williams.

Fittings and Equivalent Length

Pipe fittings (elbows, tees, valves, reducers) create additional pressure losses beyond straight-pipe friction. This calculator uses the equivalent length method (Crane TP-410 L/D ratios) to express each fitting as an equivalent length of straight pipe, which is then added to the total pipe length for the friction calculation.

For how to apply these losses correctly — K-factor versus equivalent length, and where each method breaks down — see: Minor losses in pipes.

Water at 20 °C (ρ = 998.2 kg/m³, μ = 1.002 mPa·s) flowing at 20 L/s through 50 m of DN 100 Schedule 40 commercial steel pipe (internal diameter 102.26 mm, roughness 0.045 mm), no fittings. The numbers below are evaluated by the same functions the calculator above runs, so entering these inputs reproduces them exactly.

1. Flow area A = π·D²/4 = 0.008213 m², so the mean velocity V = Q/A = 2.435 m/s.
2. Reynolds number Re = ρ·V·D/μ = 248,076 — fully turbulent.
3. Relative roughness ε/D = 4.40e-4; solving the implicit Colebrook-White equation gives the Darcy friction factor f = 0.01814.
4. Head loss h_f = f·(L/D)·V²/(2g) = 0.01814 × (50/0.10226) × V²/(2 × 9.80665) = 2.68 m.
5. Pressure drop ΔP = ρ·g·h_f = 26.2 kPa.

Adding two standard 90° elbows (Crane L/D = 30 each) contributes an equivalent length of 6.14 m, raising the loss to 3.01 m (29.5 kPa) — the same fold-in the fittings picker above performs.

Because f comes from the implicit Colebrook-White equation rather than an explicit approximation (Churchill, Swamee-Jain, Haaland), a textbook or a Moody-chart reading worked on Colebrook-White matches to the last digit; explicit correlations typically read 0.5–2% higher.