Friction Factor and Darcy-Weisbach Equation

In fluid dynamics, the pipe flow equation most commonly used is the Darcy-Weisbach equation that prescribes the head loss hf to be:

head loss

Where ‘L’ is the pipe length,
‘D’ is the internal pipe diameter,
‘V’ is the average fluid velocity, and
‘f’ is the Moody friction factor (Darcy-Weisbach friction factor) is a non-dimensional factor which is a function of several non-dimensional quantities:

moody function

where (ρV D/μ) is the Reynolds number Re, and
‘ε’ is the specific surface roughness of the pipe material.

The Moody friction chart (friction factor vs Reynolds number) is the most convenient method of getting the value of moody friction factor ‘f’. For laminar pipe flows (Reynolds number R less than 2000), f = 64/R; because R head loss in laminar flows is independent of wall roughness.

If the duct or pipe is not of circular cross-section area, an equivalent hydraulic diameter Deq as defined earlier is used for calculating head loss or friction factor.

The Swamee-Jain empirical equation may be used to calculate a pipe design diameter directly. The relationship is:
Swamee-Jain empirical equation

where hydraulic diameter ‘D’ is a function of:
Roughness height ‘ε’  (m, ft),
Volume flow rate ‘Q’ (m3/s, ft3/s),
Length ‘L’ (m, ft),
Velocity ‘v’ (m/s, ft/s),
Gravitational constant ‘g’ is in (m/s2, ft/s2), and
Head loss ‘hf‘, (m, ft).

Moody friction factor chart

Moody friction factor chart: Friction factor vs Reynolds number. Image source: pipeflow.com

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