# Friction Factor

Related

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 (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.

$\frac{1}{\sqrt{f}} = -2 \log (\frac{e}{12R} + \frac{2.51}{Re\sqrt{f}})$
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 $10^{-6} < \frac{\epsilon}{D} < 10^{-2}$ 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).