Whenever a fluid flows through a conduit pressure loss occurs. Many methods are available to calculate frictional pressure losses. They range from simple empirical equations to rigorous mechanistic multiphase flow models.
Darcy-Weisbach flow equation:
The Darcy-Weisbach flow equation is theoretically sound equation derived from the Conservation of Mass and Conservation of Momentum laws. Named after Henry Darcy and Julius Weisbach, it relates the pressure loss due to friction along a given length of pipe to the average velocity of the fluid flow for an incompressible fluid.
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, flow coefficient, or Moody friction factor.
In a cylindrical pipe of uniform hydraulic diameter d, flowing full, the pressure loss due to density and viscous effects dp/dL is proportional to length L and can be characterized by the Darcy–Weisbach equation:
- dP/dL = Pressure Gradient (psi/ft)
- f = friction factor
- ρ = Fluid density (lb/ft3)
- v = Fluid velocity (ft/s))
- d = Hydraulic diameter (ft))
The equation can be written as shown below in both typical US oilfield units and SI units: