Darcy-Weisbach Equation

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Darcy-Weisbach equation, abbreviated as DW, a dimensionless number, is the most common way of expressing the pressure drop of a piped fluid.  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.

It is important to note that when using this equation, the Darcy friction factor, abbreviated as \(f_d\), must be used.  It can be estimated using several different methods.

 

Darcy-Weisbach equation formula

\(\large{ h_l = \frac { f_d \; l \; v^2 } { 2 \; d_p \; g } }\) 

Where:

 Units English Metric
\(\large{ h_l }\) = head loss \(\large{ ft }\) \(\large{ m }\)
\(\large{ f_d }\) = Darcy friction factor \(\large{ dimensionless }\)
\(\large{ g }\) = gravitational acceleration \(\large{ \frac{ft}{sec^2} }\) \(\large{ \frac{m}{s^2} }\)
\(\large{ l_p }\) = lenght of pipe \(\large{ ft }\) \(\large{ m }\)
\(\large{ v }\) = mean flow velocity \(\large{ \frac{ft}{sec} }\)  \(\large{ \frac{m}{s} }\) 
\(\large{ d_p }\) = pipe inside diameter \(\large{ in }\) \(\large{ mm }\)

Solve for:

\(\large{ d_p = \frac { f_d \; l \; v^2 } { 2 \; h_l \; g } }\)  
\(\large{ g = \frac { f_d \; l_p \; v^2 } { 2 \; h_l \; d_p } }\)  

 

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Tags: Pipe Sizing Equations Head Equations Hazen-Williams Equations