# Darby-Melson equation (for Buckingham-Reiner equation)

## Description

Although an exact analytical solution of the Buckingham-Reiner equation can be obtained because it is a fourth order polynomial equation in f, due to complexity of the solution it is rarely employed. Therefore, researchers have tried to develop explicit approximations for the Buckingham-Reiner equation.

n 1981, Darby and Melson, using the approach of Churchill and of Churchill and Usagi, developed an expression to get a single friction factor equation valid for all flow regimesm, which is a combined equation for friction factor for all flow regimes.

Both Swamee-Aggarwal equation and the Darby-Melson equation can be combined to give an explicit equation for determining the friction factor of Bingham plastic fluids in any regime. Relative roughness is not a parameter in any of the equations because the friction factor of Bingham plastic fluids is not sensitive to pipe roughness.

Related formulas## Variables

f | Friction factor (dimensionless) |

f_{L} | Laminar flow friction factor (dimensionless) |

Re | Reynolds number (dimensionless) |

f_{T} | Turbulent flow friction factor (dimensionless) |