2. Testing the "thin separation" assumption. Reconsider the pressure-driven flow problem between two fixed plates problem that we explored in class. Now assume that the pressure varies in the y-direction due to the hydrostatic pressure of the fluid shown below. The pressure gradient with respect to the x-direction can be shown to varies (by solving the y-balance) as: Thus, you can substitute the red dashed expression for P/x in the x-balance. a. Solve for vx as a function of y. b. Plot vx with and without this additional pressure dependence given that =8.9104kg/ms,=1gm/cm3, y0=0.001m,L=1m,g=9.8m/s2 and (P0Pl)=20Pa. Simplify the equation when g=0 and show this is the same form when the hydrostatic pressure is not considered. c. Give the y position for the maximum velocity with the additional hydrostatic pressure dependence. d. Give the Re for the average velocity between the plates with the additional hydrostatic pressure dependence. Is the assumption of laminar flow valid