# Friction Factor

Written by Jerry Ratzlaff on . Posted in Classical Mechanics

## Friction Factor

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, abbreviated as f, may be calculated one of several ways.

• Abbreviated as $$f$$

## 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''.

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

'''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:

$$e$$ = roughness height (m, ft)

$$R$$ = hydraulic radius (m, ft)

$$Re$$ = Reynolds Number (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 $$5,000 < Re < 10^8$$.

$$f = \frac{0.25}{[log (\frac{\epsilon}{3.7D} + \frac{5.74}{Re^{0.9}})]^2}$$

Where:

$$Œµ$$ = roughness height ( ft)

$$D$$ = pipe diameter ( ft)

$$Re$$ = Reynolds Number (unitless).