Figure 2.47 shows fluid with density flowing through a two-dimensional conduit, whose width and length are b and h, respectively. At the entrance of the conduit, the velocity is u0 and is uniformly...

Figure 2.47 shows fluid with density flowing through a two-dimensional conduit, whose width and length are b and h, respectively. At the entrance of the conduit, the velocity is u0 and is uniformly distributed. The pressure at the entrance is pA. At the exit of the conduit, the velocity profile is a parabola, given by

where U is the maximum value of the velocity at the exit cross section and y = 0 represents the centerline. The pressure at the exit cross section is given by

(a) Determine the relationship between u₀
and U

(b) Determine the force applied per unit width of the conduit.