This Demonstration plots the velocity profile for the vertical laminar flow of a Bingham fluid (blue curve) and a Newtonian fluid (red curve) down a wall ([1] and [2]).

The calculations assume that the viscosity of the Newtonian fluid is equal to the zero-shear viscosity of the Bingham fluid.

You can set the values of the zero-shear viscosity, , and the yield stress, . It can be seen in the snapshots that both profiles are identical when the yield stress is equal to zero.

For increasing values of the yield stress, one gets a larger region where the velocity profile is flat (i.e. velocity gradient is zero) corresponding to , where is the shear stress.

[1] H. Binous,"Introducing Non-Newtonian Fluid Mechanics Computations with Mathematica in the Undergraduate Curriculum," Chemical Engineering Education, 41(1), 2007 pp. 59–64.

[2] J. O. Wilkes, Fluid Mechanics for Chemical Engineers, Upper Saddle River, NJ: Prentice Hall, 1999.