🚰 Pipe Flow

Written and maintained by the PhDino author · Last reviewed 21 September 2026 · Checked against 3 independent reference calculations · how PhDino checks its numbers

Related standards: ASHRAE

Velocity, Reynolds number, and friction pressure drop for flow through a pipe.

Fluid moving through a pipe experiences friction against the pipe wall, which shows up as a pressure drop along the length of the run. Whether that friction is dominated by smooth, orderly (laminar) flow or chaotic, mixing (turbulent) flow depends on the Reynolds number — a dimensionless ratio of inertial to viscous forces.

The Darcy–Weisbach equation relates that friction pressure drop to the flow velocity, pipe geometry, and a friction factor that itself depends on whether flow is laminar or turbulent (and, in turbulent flow, on pipe roughness).

Key formula

Re = vD/ν
Laminar (Re < 2300): f = 64/Re
Head loss: h_f = f(L/D)(v²/2g)

Variables

v

mean flow velocity

D

pipe inside diameter

ν

kinematic viscosity of the fluid

f

Darcy friction factor

L

pipe length

Notes & limitations

• For turbulent flow (Re ≥ 2300), the friction factor also depends on pipe roughness — this calculator uses the Swamee–Jain approximation to the implicit Colebrook equation rather than an iterative solve.
• This covers straight-pipe friction only; fittings, valves, and elbows add additional ("minor") losses not included here.