Danish-Kumar Solution (for Buckingham-Reiner equation)
A Bingham plastic is a viscoplastic material that behaves as a rigid body at low stresses but flows as a viscous fluid at high stress. It is named after Eugene C. Bingham who proposed its mathematical form.
It is used as a common mathematical model of mud flow in drilling engineering, and in the handling of slurries. A common example is toothpaste, which will not be extruded until a certain pressure is applied to the tube. It then is pushed out as a solid plug.
An exact description of friction loss for Bingham plastics in fully developed laminar pipe flow was first published by Buckingham. His expression, the Buckingham-Reiner equation, can be written in a dimensionless form in a number of versions.
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.
Danish et al. have provided an explicit procedure to calculate the friction factor f by using the Adomian decomposition method, as shown here.Related formulas
|fL||friction factor (dimensionless)|
|K1||K1 (see "K1 for Danish-Kumar Solution") (dimensionless)|
|K2||K2 (see "K2 for Danish-Kumar Solution") (dimensionless)|