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Darcy–Weisbach equation

Friction between the fluid and the pipe wall causes a pressure loss along the pipe, which depends on the length, diameter, speed and a friction factor. The friction factor has a simple formula for laminar flow, while for turbulent flow it must be found from tables or charts.

h_f = f\dfrac{L}{D}\dfrac{v^2}{2g}

friction loss, Darcy–Weisbach

f = \dfrac{64}{Re}

friction factor, laminar flow

Symbols

$h_f$	friction loss	m
$f$	friction factor
$L$	pipe length	m

Example

Water flows at $v = 1.5$ m/s in a pipe with $D = 30$ mm and $L = 20$ m, with $f = 0.027$ . $h_f = 0.027\cdot\dfrac{20}{0.03}\cdot\dfrac{1.5^2}{2\cdot 9.81} \approx 2.06$ m.

f = 64/Re

only applies to laminar flow – for turbulent flow

f

must come from the Moody chart or a given value.

Practise pipe flow and dimensionless numbers for free →

← Reynolds number · Minor losses →

Part of Fluid Mechanics: Pipe flow and dimensionless numbers.