$2$A$.$ Using the power law $=k(d\frac{}{d}t{)}^n$ derive the relationship for apparent viscosity and discuss how the differences between Newtonian and NonNewtonian behavior could be detected as a function of shear rate.

B$.$ Write the expression that relates shear stress $$ to shear rate, $d\frac{}{d}t$ for a Bingham Newtonian fluid. Discuss the peculiarity of a Bingham fluid.

C$.$ Obtain an expression for shear rate tensor $(d\frac{}{d}t{)}_{ji}$ for a fluid flowing through an inverted capillary tube.

D$.$ Show that the rate of deformation tensor for a fluid flowing through an inverted capillary tube has a finite third invariant $I_3.$ Derive the expression for $I_3$ in terms of strain rate $(\frac{d}{\frac{?}{?}}dt{)}_{ii-}.$