# Darcy friction factor - Serghides's solution

## Description

In fluid dynamics, the Darcy friction factor formulae are equations that allow the calculation of the Darcy friction factor, a dimensionless quantity used in the Darcy–Weisbach equation, for the description of friction losses in pipe flow as well as open-channel flow.

The Darcy friction factor is also known as the Darcy–Weisbach friction factor, resistance coefficient or simply friction factor; by definition it is four times larger than the Fanning friction factor.

Serghides’s solution is used to solve directly for the Darcy–Weisbach friction factor f for a full-flowing circular pipe. It is an approximation of the implicit Colebrook–White equation. It was derived using Steffensen’s method.

The equation was found to match the Colebrook–White equation within 0.0023% for a test set with a 70-point matrix consisting of ten relative roughness values (in the range 0.00004 to 0.05) by seven Reynolds numbers (2500 to 108).

The variables A, B and C in the shown formula can be calculated using the following formulas:

**See also**

Variable ( A ) formula

Variable ( B ) formula

Variable ( C ) formula

## Variables

f | Darcy friction factor (dimensionless) |

A | Variable in Serghides's solution (dimensionless) |

B | Variable in Serghides's solution (dimensionless) |

C | Variable in Serghides's solution (dimensionless) |