A steady jet of air of constant density issues from a two-dimensional duct of width D

A steady jet of air of constant density ρ issues from a two-dimensional duct of width D and depth a (into the page), as shown in the figure, with velocity distribution that is parabolic. The jet supports a plate of width L, depth a (into the page) and weight W (not given in the problem), and the air is deflected horizontally. The side of the plate facing the jet experiences an average pressure p, and the pressure is atmospheric, p , everywhere else. Ignore the weight of the fluid. 

 

a) Find the average pressure p in terms of L, D, ρ,and U _m

 

b) Find the weight of the plate W in terms of L, D, ρ, and U _m