Friction Factor

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Friction factor, abbreviated as f, also called Moody friction factor or Darcy-Weibach friction factor, a dimensionless number, is used in fluid dynamics to quantify the frictional losses or resistance to flow in pipes or conduits.  The friction factor is primarily used in the Darcy-Weisbach equation, which relates the pressure drop or head loss in a pipe to the flow rate, pipe diameter, and other parameters.

Friction Factor Index

The friction factor depends on various factors, including the nature of the fluid, the roughness of the pipe wall, and the Reynolds Number.  The Reynolds number is a dimensionless parameter that characterizes the flow regime, and it is defined as the ratio of inertial forces to viscous forces in the fluid.

The friction factor can be determined experimentally for different flow conditions or pipe geometries, but it is often estimated using empirical correlations or obtained from published charts and tables.  For laminar flow, the friction factor is calculated using the Hagen-Poiseuille equation, while for turbulent flow, several empirical equations, such as the Colebrook-White equation or the Swamee-Jain equation, are commonly used to estimate the friction factor.  Accurate determination of the friction factor is essential for assessing pressure losses, determining pipe sizing, and designing efficient piping systems.  It is also used in various engineering applications, including hydraulic calculations, fluid distribution systems, and HVAC systems.

laminar flow

In laminar flow, the friction factor is independent of the surface roughness, \(\epsilon\).  This is because the fluid flow profile contains a boundary layer where the flow at the surface through the height of the roughness is zero.

For \(Re<2100\), the friction factor may be calculated by:

 

laminar flow Formula

\( f \;=\;  64 \;/\; Re \)     (Friction Factor)

\( f \;=\; 64 \;/\; f \)

Symbol English Metric
\( f \) = friction factor
\( dimensionless \)
\( Re \) = Reynolds number \( dimensionless \)

 

transitional flow

For \(2100<Re<3x10^3\) (transitional flow regime), the friction factor may be estimated from the Moody Diagram.

turbulent flow

Methods for finding the friction factor f are to use a diagram, such as the Moody Diagram, the Colebrook-White Equation, or the Swamee-Jain Equation.

Using the diagram or Colebrook-White equation requires iteration. Where the Swamee-Jain equation allows f to be found directly for full flo                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    w in a circular pipe.

colebrook-white equation

The '''Colebrook-White equation''' is used to iteratively solve for the Darcy Weisbach Friction Factor ''f''.

 

Free Surface Flow Formula

\( 1 \;/\; \sqrt{f} \;=\; -2\; \log \; [ \; ( \epsilon \;/\; 12\;r_h ) + ( 2.51 \;/\; Re\sqrt{f} ) \; ]  \) 
Symbol English Metric
\( \epsilon \)  (Greek symbol epsilon) = absolute roughness \( in \) \( mm \)
\( f \) = friction factor \( dimensionless \)
\( r_h \) = hydraulic radius \( in \) \( mm \)
\( Re \) = Reynolds number \( dimensionless \)

 

Full Flow (Closed Conduit) Formula

\( 1 \;/\;  \sqrt{f} \;=\; -2\; \log \;[ \; ( \epsilon \;/\; 14.8\;r_h ) + ( 2.51 \;/\; Re\sqrt{f} ) \; ]  \)
Symbol English Metric
\( \epsilon \)  (Greek symbol epsilon) = absolute roughness \( in \) \( mm \)
\( f \) = friction factor \( dimensionless \)
\( r_h \) = hydraulic radius \( in \) \( mm \)
\( Re \) = Reynolds number \( dimensionless \)

Because the iterative search for the correct  \(f\)  value can be quite time-consuming, the Swamee-Jain equation can be used to solve directly for  \(f\).

swamee-jain equation

The Swamee-Jain Equation is accurate to 1.0% of the Colebrook-White Equation for  \( 10^{-6} < \epsilon \;/\; d < 10^{-2} \)  and  \( 5,000 < Re < 10^8  \).

 

swamee-jain equation Formula

\(  f \;=\; 0.25 \;/\; [ \;  log \; ( \; (\epsilon \;/\; 3.7\;d ) + ( 5.74 \;/\; Re^{0.9} ) \; ) \; ]^2  \) 
Symbol English Metric
\( f \) = friction factor \( dimensionless \)
\( \epsilon \)  (Greek symbol epsilon) = absolute roughness \( in \) \( mm \)
\( d \) = inside diameter of pipe \( in \) \( mm \)
\( Re \) = Reynolds number \( dimensionless \)

 

Friction Factor calculator

 

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Tags: Pipe Sizing Flow Laminar Flow Friction Loss Darcy