# Friction Factor

Friction factor, abbreviated as f, also called Moody friction factor or Darcy-Weibach friction factor, a dimensionless number, is 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.

## laminar flow

In laminar flow, the friction factor is independent of the surface roughness, \(\epsilon\). This is because the fluid flow profile contains a bou ndary 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:

\(\large{ f = \frac{64}{Re} }\) |

### Where:

Units |
English |
Metric |

\(\large{ f }\) = friction factor |
\(\large{ dimensionless }\) | |

\(\large{ Re }\) = Reynolds number | \(\large{ dimensionless }\) |

## 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

\(\large{ \frac{1}{\sqrt{f}} = -2\; \log \;(\frac{\epsilon}{12\;r_h} + \frac{2.51}{Re\sqrt{f}}) }\) |

### Where:

Units |
English |
Metric |

\(\large{ \epsilon }\) (Greek symbol epsilon) = absolute roughness | \(\large{ in }\) | \(\large{ mm }\) |

\(\large{ f }\) = friction factor | \(\large{ dimensionless }\) | |

\(\large{ r_h }\) = hydraulic radius | \(\large{ in }\) | \(\large{ mm }\) |

\(\large{ Re }\) = Reynolds number | \(\large{ dimensionless }\) |

### Full Flow (Closed Conduit) Formula

\(\large{ \frac{1}{\sqrt{f}} = -2\; \log \;(\frac{\epsilon}{14.8\;r_h} + \frac{2.51}{Re\sqrt{f}}) }\) |

### Where:

Units |
English |
Metric |

\(\large{ \epsilon }\) (Greek symbol epsilon) = absolute roughness | \(\large{ in }\) | \(\large{ mm }\) |

\(\large{ f }\) = friction factor | \(\large{ dimensionless }\) | |

\(\large{ r_h }\) = hydraulic radius | \(\large{ in }\) | \(\large{ mm }\) |

\(\large{ Re }\) = Reynolds number | \(\large{ dimensionless }\) |

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 \(\large{ 10^{-6} < \frac{\epsilon}{d} < 10^{-2} }\) and \(\large{ 5,000 < Re < 10^8 }\).

\(\large{ f = \frac{0.25}{[log \; (\frac{\epsilon}{3.7\;d} + \frac{5.74}{Re^{0.9}})]^2} }\) |

### Where:

Units |
English |
Metric |

\(\large{ f }\) = friction factor | \(\large{ dimensionless }\) | |

\(\large{ \epsilon }\) (Greek symbol epsilon) = absolute roughness | \(\large{ in }\) | \(\large{ mm }\) |

\(\large{ d }\) = inside diameter of pipe | \(\large{ in }\) | \(\large{ mm }\) |

\(\large{ Re }\) = Reynolds number | \(\large{ dimensionless }\) |

## Friction Factor calculator