HYD-02

Darcy–Weisbach head loss

Frictional head hf = f (L/D) V² /(2g).

Reading speed

Pipe flowDarcy–WeisbachISO 5167

Governing equation

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

where

f: Friction factor (—)
L: Length (m)
D: Diameter (m)
V: Velocity (m/s)
h_f: Head loss (m)

Lecture brief

Historical brief

Open-channel and pipe flow were written by Chezy, Manning, Darcy and Weisbach in the nineteenth century, then Bakhmeteff and Bélanger on the hydraulic jump. The sheets compute conveyance, head loss and gradually varied profiles. This sheet (HYD-02 — Darcy–Weisbach head loss) is the form associated with Darcy–Weisbach · ISO 5167. Working symbols: $f$ , $L$ , $D$ , $V$ $\rightarrow$ $h_f$ . Dimensional analysis of wall shear in a circular pipe yields the Darcy–Weisbach equation; f is read from a Moody chart or Colebrook.

Purpose

Purpose: compute

h_f

from

f

L

D

V

in Hydraulics via

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

Frictional head hf = f (L/D) V² /(2g). Use it when a real hydraulics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

f = 0.020\,\mathrm{—}

L = 200.000\,\mathrm{m}

D = 0.300\,\mathrm{m}

V = 2.000\,\mathrm{m/s}

, the governing relation

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

yields

h_f = 2.718\,\mathrm{m}

. Enter f from Moody. Circular full pipe. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Friction factor f0.02 —Length L200 mDiameter D0.3 mVelocity V2 m/s

Outputs

Head loss h_f2.718 m

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

Enter f from Moody. Circular full pipe.

Dimensional analysis of wall shear in a circular pipe yields the Darcy–Weisbach equation; f is read from a Moody chart or Colebrook.

Reading speed

Watch on YouTube