Darcy-Weisbach Equation

Written by Jerry Ratzlaff. 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:

\( h_l\) = head loss due to friction

\(f\) = friction factor

\(l\) = length

\(v\) = fluid velocity

\(D\) = inside diameter

\(g \) = gravitational acceleration

Solve for:

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

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

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

\(v =   \sqrt {  \frac  { 2  {h_l}   D    g   }   { fl   }        }  \)

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