4. Flow between plates with a uniform cross flow. Reconsider the moving-plate driven flow (Couette) problem explored in class where the top plate is fixed and the bottom plate is moving with a velocity u. Now assume that the plates are porous and allowing a uniform cross-flow of fluid in the y-direction with a fixed velocity y at low flowrate (i.e. vy is not a function of x or z ). Hint: This means there is now one "entrance/exit" term in the balance that must be kept. a. Derive an expression for vx as a function of position y. b. Plot vx as a function of position y and compare this profile to the velocity profile without the crossflow. Assume that =9104kg/ms,=1gm/cm3,d=0.02m,vy=0.0002m/s2 and u= 0.1m/s