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Engineering ToolBox > DArcy-Weisbach Equation for Pressure and Head Loss
The pressure loss (or major loss) in a pipe, tube or duct can be expressed with the D'Arcy-Weisbach equation
Δp = λ (l / dh) (ρ v2 / 2) (1)
where
Δp = pressure loss (Pa, N/m2)
λ = D'Arcy-Weisbach friction coefficient
l = length of duct or pipe (m)
dh = hydraulic diameter (m)
ρ = density (kg/m3)
Note! Be aware that there are two alternative friction coefficients present in the literature. One is 1/4 of the other and (1) must be multiplied with four to achieve the correct result. This is important to verify when selecting friction coefficients from Moody diagrams. The Colebrook friction coefficient calculator corresponds to equation (1).
The D'Arcy-Weisbach equation is valid for fully developed, steady state and 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 calculator below, which is based on formula (1), can be used to calculate the pressure loss in a duct, pipe or tube if velocity is known. The default values are for air flow 20oC, 1.2 kg/m3 and 6 m/s. The friction coefficient can be calculated with the Colbrook equation.
The calculator is generic and can be used with SI and Imperial units. Just substitute the values with the values for the actual application.
This calculator can be used if the volume flow is known
Alternatively, the Darcy-Weisbach equation (1) can also express the head loss as
Δh = λ (l / dh) (v2 / g 2) (2)
where
Δh = head loss (m)
l = length of pipe or duct (m)
dh = hydraulic diameter (m)
v = velocity (m/s)
g = acceleration of gravity (9.81 m/s2)
The D'Arcy-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 like the Hazen-Williams equation, may be preferred.
The calculator below, which is based on formula (2), can be used to calculate the head loss in a duct, pipe or tube. The default values are for air flow 20oC, 1.2 kg/m3 and 6 m/s. The friction coefficient is calculated with the Colbrook equation.
The calculator is generic and can be used for both SI and Imperial units. Just substitute the values with the values for the actual application. Note! Hydraulic diameter in feet for Imperial units.