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

fFriction factor (dimensionless)
fLLaminar flow friction factor (dimensionless)
ReReynolds number (dimensionless)
fTTurbulent flow friction factor (dimensionless)