Darcy–Weisbach equation

In fluid dynamics, the Darcy–Weisbach equation is an empirical 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. In fluid dynamics, the Darcy–Weisbach equation is an empirical 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: For laminar flow in a circular pipe of diameter D c {displaystyle D_{c}} , the friction factor is inversely proportional to the Reynolds number alone (fD = 64/Re) which itself can be expressed in terms of easily measured or published physical quantities (see section below). Making this substitution the Darcy-Weisbach equation is rewritten as