HYD-02

Darcy–Weisbach head loss

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

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Pipe flowDarcy–WeisbachISO 5167

Governing equation

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

$V \in \left[0.1, 8\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

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

$V \in \left[0.1, 8\right]$

$V = 0.1$ $h_f = 0.007$

Along the curve

②

Domain of the variable — blue

V_{\min} = 0.1,\quad V_{\max} = 8

$V \in \left[0.1, 8\right]$

$V = 0.1$ $V = 0.1$

Along the curve

③

Response curve — green

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

$V \in \left[0.1, 8\right]$

$V = 0.1$ $h_f = 0.007$

Along the curve

④

Rate of change — amber

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

$V \in \left[0.1, 8\right]$

$V = 0.15$ $h_f^{\prime} = 0.203$

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-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

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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