Question 2 The 2D Navier-Stokes equation in Cartesian coordinates are (au P +u+v -- + at au) + x2 ay av av P +u at + v =- + (a v a v\ + - pg ax2 ay) Consider the flow between two very long parallel plates, as shown in Figure Q2. There is a pressure gradient in the x direction, which fluctuates sinusoidally with time. dp/dx u(y,t) h Figure Q2: Flow between two parallel plates. a) Simplify the Navier-Stokes equations, explaining any justifications you make b) If the velocity profile in the channel is u(y,t) = Umax y(h - y) sin wt Where y = 0 corresponds to the bottom surface. Find an expression for the pressure gradient, dP/dx. c) If the max pressure gradient at the wall is A, find an expression for Umax