Calculate head loss due to friction in pipes using the Darcy-Weisbach equation with friction factor calculation.
The Darcy–Weisbach equation is the universal formula for friction-induced pressure loss in pipe flow, valid for any incompressible fluid at any Reynolds number. This calculator returns ΔP from pipe length, diameter, mean velocity, density, and the Darcy friction factor f, which it solves automatically from Reynolds number and pipe roughness using the explicit Swamee–Jain correlation for turbulent flow and 64/Re for laminar.
ΔP = f × (L/D) × (ρv²/2) where f is the dimensionless Darcy friction factor, L is pipe length (m), D is hydraulic diameter (m), ρ is fluid density (kg/m³), v is the mean velocity (m/s). The Fanning friction factor is f_D / 4 and should not be confused. For laminar flow f = 64 / Re. For turbulent flow the Colebrook implicit equation is the reference, but the Swamee–Jain explicit form is within 1% and far easier to compute: 1/√f = −2 × log₁₀(ε / 3.7D + 5.74 / Re^0.9). Roughness ε in millimeters: 0.0015 drawn steel, 0.046 commercial steel, 0.15 cast iron, 0.26 galvanized iron. The Moody chart is the graphical form of the same relationship.
A facilities engineer sizing a 200 m cooling-water main at 250 m³/h through DN150 commercial steel computes Re = 1.2 × 10⁶, f = 0.018, and ΔP = 1.6 bar, then selects a pump head budget accordingly.
A pneumatics designer pushing 5 m³/min air through a 50 m, 25 mm steel line computes the equivalent ΔP, confirms it stays below 0.5 bar so end-of-line pressure remains at the 6 bar tool requirement.
A piping engineer verifying a short distillation-feed pipeline at 80 °C with viscous oil applies the laminar form because Re computes to 1,800, confirming the actual ΔP matches the field gauge reading within 5%.
Fanning factor f_F = f_D / 4. Both are dimensionless. Pipe flow texts in the US sometimes use Fanning; SI-oriented texts use Darcy. Always check which the formula expects before plugging in.
Hagen–Poiseuille (a special case of Darcy–Weisbach for laminar flow) applies at Re < 2,300 and gives ΔP = (128 × μ × L × Q) / (π × D⁴), depending on viscosity rather than density.
In laminar flow the viscous sublayer fully covers the wall asperities, so roughness has no effect on friction factor. In turbulent flow eddies impinge on the asperities, and the friction factor depends on the relative roughness ε/D.