Darcy–Weisbach Head Loss

h_{f} = f \frac{L}{D} \frac{V ^{2}}{2 g}

Major friction loss in a circular pipe. Friction factor f comes from the Moody chart (or Colebrook) using Re and relative roughness ε/D. Minor losses use h_m = K V²/2g.

$f$: Darcy friction factor
$L$ (m): Pipe length
$ε$ (mm): Absolute roughness

Step-by-step solved example

200 m of 250 mm pipe, V = 2.0 m/s, f = 0.018. Head loss?

Head loss hf = f (L/D) V²/2g in a circular pipe.

1. Apply Darcy
h_f = 0.018 × (200/0.25) × (4 / 19.62) = 0.018×800×0.204 = 2.93 m.
$h_{f} = 2.93 m$

Answer: 2.93 m

10 practice questions

0/10 correct

1.Minor loss for a sudden expansion uses K based on

2.Fully rough turbulent f depends mainly on

3.Hazen–Williams is an empirical alternative used for

4.If L doubles, h_f

5.Equivalent sand roughness ε of commercial steel is about

6.Laminar pipe flow: f =

7.Pump power P =

8.A globe valve typically has K

9.Parallel pipes share the same

10.V = 3 m/s, D = 0.2 m, L = 100 m, f = 0.02. h_f =