This question refers to the problem of a falling film down an inclined plane (refer to Chapter II of the textbook). This type of flow is often encountered in thin-film coating processes and in many situations the fluid is actually non-Newtonian. It is possible to show using the Cauchy momentum equation that the velocity profile for a shear-thinning polymer described by the power-law equation (=kn), is given by: vz=(kgcos())1n+1n[1(x)(nn+1)] The symbols and notations are the ones used in the textbook. (a) Check that this expression reduces to that reported in the textbook when the fluid is Newtonian. (b) Determine the expression of the flow rate down the plane for a power-law fluid (Qn) (c) Plot the ratio Qn/Q1 vs the power law index n of a shear-thinning polymer, where Q1 is the flow rate of a Newtonian fluid. You may use =103kg/m3,=1mm and k= =1 Pa.s. Show plots for different values of the plane inclination . (d) Determine the expression of the drag force on the plane in the case of the power-law fluid. How does it compare with that of a Newtonian fluid