Q9/ Tank draining with a power-law fluid. A very viscous non-Newtonian liquid in simple shear obeys the relation: T = C√s, where is the shear stress, s is the strain rate (of a typical form Ovx/dy), and c is a constant. A uniform thin film of the liquid, of thickness h, flows steadily under gravity down a vertical plate. Show that the mass flow rate m per unit plate width is: p³gh m= 4c2 For a vertical plate from which the liquid is now draining, h will be a function of time and of the vertically downward distance x. Prove, by means of a suitable transient mass balance on a differential element, and using the above equation for m, that: ah p²g²h³ Əh at 2 მე 1/3 A tank with vertical sides is initially full, and at t = 0 is rapidly drained of the liquid. If x is measured from the top of the tank, verify that the film thickness on the sides is given by h =