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Also known as the Moody Friction Factor or Darcy Weibach friction factor it is 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.

f =  \frac{0.25}{[log (\frac{\epsilon}{3.7D} + \frac{5.74}{Re^{0.9}})]^2}
  • roughness height, Œµ ( ft)
  • pipe diameter, D ( ft)
  • Reynolds Number, Re (unitless).