# Darcy-Weisbach Equation

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

The most common way of expressing the pressure drop of a piped fluid is to use the Darcy-Weisbach equation.  The equation is valid for fully developed, steady state and incompressible flow. The Darcy-Weisbach equation with the Moody Diagram are considered to be the most accurate model for estimating frictional head loss in steady pipe flow.

Abbreviated as $$DW$$

## FORMULA

$$h_l = \frac { f l v^2 } { D g }$$

Where:

$$h_f$$ = head loss due to friction

$$f$$ = friction factor

$$l$$ = length

$$v$$ = fluid velocity

$$D$$ = inside diameter

$$g$$ = gravitational acceleration

Solve for:

$$f = \frac { 2 {h_f} D g } { l {v^2} }$$

$$l = \frac { 2 {h_f} D g } { f v^2 }$$

$$D = \frac { f l v^2 } { 2 {h_f} g }$$

$$v = \sqrt { \frac { 2 {h_f} D g } { fl } }$$

$$g = \frac { f l v^2 } { 2 {h_f} D }$$