Darcy-Weisbach Formula for Pressure and Head Loss

The Darcy-Weisbach formula is used to calculate pressure or head loss due to friction - major loss - in ducts, pipes and tubes

The Darcy-Weisbach formula and Pressure Loss

The Darcy-Weisbach equation for pressure loss can be expressed as:

p_loss = λ (l / d_h) (ρ v² / 2) (1)

where

p_loss = pressure loss (Pa, N/m²)

λ = friction factor or coefficient

l = length of duct or pipe (m)

d_h = hydraulic diameter (m)

The Darcy-Weisbach equation is valid for fully developed, steady, incompressible flow.

The friction factor or coefficient - λ -depends on the flow - if it is laminar, transient or turbulent (the Reynolds Number) - and the roughness of the tube or duct. The friction coefficient can be calculated by the Colebrooke Equation or by using the Moody Diagram.

The Darcy-Weisbach equation and Head Loss

Alternatively the Darcy-Weisbach equation can be expressed as head loss:

h_loss = λ (l / d_h) (v² / g 2) (1)

where

h_loss = head loss (m, ft)

λ = friction coefficient

g = acceleration of gravity (32.2 ft/s², 9.81 m/s²)

The Darcy-Weisbach equation with the Moody diagram are considered to be the most accurate model for estimating frictional head loss in steady pipe flow. Since the approach requires a trial and error iteration process, an alternative less accurate empirical head loss calculation that do not require the trial and error solutions as the Hazen-Williams equation, may be preferred.

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