An incompressible fluid flows between two infinite stationary parallel plates. The velocity profile is given by u=umaxðAy2 + By+CÞ, where A, B, and C are constants and y is measured upward from the lower plate. The total gap width is h units. Use appropriate boundary conditions to express the magnitude and units of the constants in terms of h. Develop an expression for volume flow rate per unit depth and evaluate the ratio V=umax

At steady state, air at 200 kpa, 325 k, and mass flow rate of 0.5 kg/s enters an insulated duct having differing inlet and exit cross-sectional areas. the inlet cross-sectional area is 6 cm2. at the duct exit, the pressure of the air is 100 kpa and the velocity is 250 m/s. neglecting potential energy effects and modeling air as an 1.008 kj/kg k, determine ideal gas with constant cp = (a) the velocity of the air at the inlet, in m/s. (b) the temperature of the air at the exit, in k. (c) the exit cross-sectional area, in cm2