Darcy friction factor
In fluid dynamics, the Darcy–Weisbach equation is a phenomenological equation, which relates the head loss, or pressure loss, due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid. The equation is named after Henry Darcy and Julius Weisbach.
The Darcy–Weisbach equation contains a dimensionless friction factor, known as the Darcy friction factor. This is also variously called the Darcy–Weisbach friction factor, friction factor, resistance coefficient, or flow coefficient.
In a cylindrical pipe of uniform diameter D, flowing full, the pressure loss due to viscous effects Δp is proportional to length L and can be characterized by the Darcy–Weisbach equation:
where the pressure loss per unit length Δp/L (SI units: Pa/m) is a function of:
The head loss Δh (or hf) expresses the pressure loss due to friction in terms of the equivalent height of a column of the working fluid, so the pressure loss is
where
It is useful to present head loss per length of pipe (dimensionless):
where L is the pipe length (m).
Therefore, the Darcy–Weisbach equation can also be written in terms of head loss, S:
The relationship between mean flow velocity ⟨v⟩ and volumetric flow rate Q is
...
Wikipedia