HYD-10

Darcy–Weisbach head loss

hf = f (L/D) V² / (2g). The pipe friction equation.

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Pipe flowDarcy–Weisbach

Governing equation

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

$V \in \left[0.2, 8\right]$

where

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

The figure, part by part

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①

Governing law — red

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

$V \in \left[0.2, 8\right]$

$V = 0.2$ $h_f = 0.014$

Along the curve

②

Domain of the variable — blue

V_{\min} = 0.2,\quad V_{\max} = 8

$V \in \left[0.2, 8\right]$

$V = 0.2$ $V = 0.2$

Along the curve

③

Response curve — green

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

$V \in \left[0.2, 8\right]$

$V = 0.2$ $h_f = 0.014$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}h_f}{\mathrm{d}V}

$V \in \left[0.2, 8\right]$

$V = 0.249$ $h_f^{\prime} = 0.169$

Along the curve

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-10 — Darcy–Weisbach head loss) is the form associated with Darcy–Weisbach. Working symbols: $f$ , $L$ , $D$ , $V$ $\rightarrow$ $h_f$ . f from Moody: laminar 64/Re, turbulent a function of Re and ε/D.

Purpose

Purpose: compute

h_f

from

f

L

D

V

in Hydraulics via

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

hf = f (L/D) V² / (2g). The pipe friction equation. 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 = 100.000\,\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 = 1.359\,\mathrm{m}

. A pipe, a velocity, a falling piezometric line. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Friction factor f0.02 —Length L100 mDiameter D0.3 mVelocity V2 m/s

Outputs

Head loss h_f1.359 m

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Narration of this film

A pipe, a velocity, a falling piezometric line.

f from Moody: laminar 64/Re, turbulent a function of Re and ε/D.

Reading speed

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