A polymeric liquid is coated onto a surface by flowing the liquid down an inclined plate making an angle a with the vertical. Assume that the polymeric liquid behaves as a (non- Newtonian) power-law fluid with an apparent viscosity for a unidirectional flow is given by: n-1 -dur n=--m dy where the shear stress is: n Tyr = n dv. dy -m -du dy Here m and n are constants. Because you are not dealing with a Newtonian fluid, you cannot use the Navier-Stokes equation to solve this problem. Instead you should use the Cauchy Momentum equation in Cartesian coordinates (Table 6.1 in Deen) for the momentum conservation equation. Using the coordinate system indicated in the sketch below: (a) Obtain an expression for shear stress (Tyr) as a function of y. (b) Obtain an expression for the velocity distribution in the film as a function of y. (c) You measure a flow rate per unit width of q by collecting the polymeric liquid coming off the surface. Obtain an expression relating q with the film thickness d. (d) Using your result in (b-c) show what your velocity profile (i.e. Uz(y)) and film thickness expressions reduce to in the limit that the fluid is Newtonian. Do not re-solve the entire problem for a Newtonian fluid. air 8 polymeric liquid X y gravity