$2\mathrm{.}20$ Consider steady flow through the duct with circular cross section illustrated below.

Use mass conservation to find $U_2$ in terms of $U_1$ assuming $\frac{D_2}{D_1}=2$ and:

a$.$ The flow is steady, incompressible, and uniform across the entrance and exit of the duct.

b$.$ The flow is steady, incompressible, with a parabolic distribution across the duct exit.

c$.$ The flow is steady, compressible, and uniform across the entrance and exit of the duct with $\frac{T_2}{T_1}=5$ and $\frac{P_2}{P_1}=2.$