Friction Factor

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Also known as the Moody Friction Factor or Darcy Weibach friction factor it isis a dimensionless number used in internal flow calculations with the Darcy-Weisbach equation. Depending on the Reynolds_Number, the friction factor may be calculated one of several ways.

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:

$f=64/Re$

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 flow in a circular pipe.

Colebrook-White Equation

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

For Free Surface Flow:

$\frac{1}{\sqrt{f}} = -2 \log (\frac{e}{12R} + \frac{2.51}{Re\sqrt{f}})$

For Full Flow (Closed Conduit):

$\frac{1}{\sqrt{f}} = -2 \log (\frac{e}{14.8R} + \frac{2.51}{Re\sqrt{f}})$

Where f is a function of:

roughness height, e (m, ft)
hydraulic radius, R (m, ft)
Reynolds Number Re (unitless)

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 $10^{-6} < \frac{\epsilon}{D} < <tex>10^{-2}$ and $5,000 < Re < 10^8$ .