DarcyWeisbach Equation  Major Pressure and Head Loss due to Friction
The DarcyWeisbach equation can be used to calculate the major pressure and head loss due to friction in ducts, pipes or tubes.
Pressure Loss
The pressure loss (or major loss) in a pipe, tube or duct can be calculated with the DarcyWeisbach equation
Δp_{major_loss} = λ (l / d_{h}) (ρ_{f} v^{2} / 2) (1)
where
Δp_{major_loss} = major (friction) pressure loss in fluid flow (Pa (N/m^{2}), psf (lb/ft^{2}))
λ = DarcyWeisbach friction coefficient
l = length of duct or pipe (m, ft)
v = velocity of fluid (m/s, ft/s)
d_{h} = hydraulic diameter (m, ft)
ρ_{f} = density of fluid (kg/m^{3}, slugs/ft^{3})
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 DarcyWeisbach 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.
Example  Pressure Loss in Air Duct
Air flows with velocity 6 m/s in a duct with diameter 315 mm. The density of air is 1.2 kg/m^{3}. The friction coefficient is estimated to 0.019 and the length of the duct is 1 m. The friction loss can be calculated as
Δp_{major_loss} = 0.019 ((1 m) / (0.315 m)) ((1.2 kg/m^{3}) (6 m/s)^{2} / 2)
= 1.3 Pa
Note!  in addition to friction loss  there is almost always minor loss in a flow.
Online Pressure Loss Calculator
The calculator below, which is based on formula (1), can be used to calculate the pressure loss in a duct, pipe or tube if the velocity of the fluid is known. The default values are for air flow 20^{o}C, 1.2 kg/m^{3} and 6 m/s  the same as in the example above. The friction coefficient can be calculated with the Colebrook equation.
This calculator is generic and can be used with SI and Imperial units. Just substitute the values with the values for the actual application.
The calculator below can be used if the volume flow is known
Head Loss
Alternatively the DarcyWeisbach equation can express head loss as water column by dividing the pressure loss (1) with the specific weight of water
Δh_{major_loss,w} = λ (l / d_{h}) (ρ_{f} v^{2} / 2) / γ_{w}
= λ (l / d_{h}) (ρ_{f} v^{2} / 2) / ρ_{w} g
= λ (l / d_{h}) (ρ_{f} / ρ_{w}) (v^{2} / (2 g)) (2)
where
Δh_{major_loss,w} = major head loss (water column) in fluid flow (m H2O, ft H2O)
l = length of pipe or duct (m, ft)
d_{h} = hydraulic diameter (m, ft)
v = velocity of fluid (m/s, ft/s)
γ_{w} = ρ_{w} g = specific weight of water (9807 N/m^{3}, 62.4 lb_{f}/ft^{3})
ρ_{w} = density of water (1000 kg/m^{3}, 62.425 lb/ft^{3})
g = acceleration of gravity (9.81 m/s^{2}, 32.174 ft/s^{2})
Note!  in the equation above the head is related to water as the reference fluid. Another reference fluid can be used  like Mercury Hg  by replacing the density of water with the density of the reference fluid.
If the density in the fluid flow is the same as the density in the reference fluid  as typical with water flow  eq. (2) can be simplified to
Δh_{major_loss} = λ (l / d_{h}) (v^{2} / (2 g)) (2b)
where
Δh_{major_loss} = major head loss (column of flowing fluid) (m "fluid", ft "fluid")
For metric units the head loss can alternatively be modified to
Δh_{major_loss,w (mmH2O)} = λ (l / d_{h}) (ρ_{f} / ρ_{w}) (v^{2} / (2 g)) / 1000 (2c)
where
Δh_{major_loss,w (mmH2O)} = head loss (mm H2O)
For imperial units the head loss can alternatively be modified to
Δh_{major_loss,w (inH2O)} = 12 λ (l / d_{h}) (ρ_{f} / ρ_{w}) (v^{2} / (2 g)) (2d)
where
Δh_{major_loss,w (inH2O)} = head loss (inches H2O)
The DarcyWeisbach 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 HazenWilliams equation, may be preferred.
Online Head Loss Calculator
The calculator below, which is based on eq. (2), can be used to calculate the head loss in a duct, pipe or tube. The default values used in the calculator are for air flow 20^{o}C, 1.2 kg/m^{3} and 6 m/s. The default density of water commonly used as reference fluid is 1000 kg/m^{3}. The friction coefficient is calculated with the Colebrook 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.
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