Problem 1: Two incompressible viscous fluids flow, one on top of the other, down an inclined plate at an angle (see Figure I). They both have the same density , but different viscosities 1 and 2. The lower fluid has depth h1 and the upper h2. Assuming that viscous forces from the surrounding air is negligible and that the pressure on the free surface is constant, calculate the viscosity profile in fluid 1