Physics GRE Discussion Forums

A power-law fluid, or the Ostwald–de Waele relationship, is a type of generalized Newtonian fluid (time independent Non-Newtonian fluid) for which the shear stress, τ, is given by

τ = A(du/dy)^n +B

Where A, B and n are constants that depend upon the type of fluid and conditions imposed
on the flow. Comment on the value of these constants so that the fluid may behave as:

I) an ideal fluid
II) a Newtonian fluid
III)a non-Newtonian fluid

The corresponding term in the Navier-Stokes equations is div τ. So assuming A and B are constants:

i) If A = 0, then τ = B and div τ = 0. Alternatively if n = 0, then τ = A + B and div τ = 0. Thus in both of these cases viscous drag force would be zero.
ii) For any value of A and B, and for n = 1, the fluid would behave in a Newtonian fashion because div τ scales as (d^2 u/dy^2)
iii) In all other cases, the fluid would be non-Newtonian.

Hope this helped!