Answer Happy

Problem 1 A Newtonian liquid (density p, viscosity n) flows through a wide and shallow rectangular vertical slit of thickness h. At the slit exit the liquid keeps flowing on the vertical wall. The pressure is atmospheric everywhere. Assuming laminar (to be verified), well-developed flow, and neglecting all effects related to the presence of the inlet and outlet slit section, answer the following questions assuming steady-state conditions: 1) write the mass and momentum balance equation for both the slit section and d the free surface section, keeping only the non-zero or non-negligible terms and including the appropriate boundary conditions. Justify all the assumptions and in particular verify the laminar flow assumption; 2) determine the expression of the velocity profiles in the two sections of the flow field; 3) calculate the maximum velocity in the slot; 4) calculate the thickness, d, of the liquid in the free-surface section. 5) Prove that the strict inequality d <h always holds. Data: p = 0.925- cm3 = 1.5 Pa; h = 1cm.