Problem $2$:

The jet pump in the figure below injects water at $U_1=40f\frac{t}{s}$ through a $3-$inch pipe and entrains a secondary flow of water $U_2=3f\frac{t}{s}$ in the annular region around the small pipe. The two flows become fully mixed downstream, where $U_3$ is approximately constant across the cross$-$section.

$($a$)[4$ points$]$ For steady incompressible flow, compute $U_3$ in $f\frac{t}{s}.$

$($b$)2$ points$]$ Assume that the injected fluid in the $3-$inch pipe carries a chemical with a concentration of $0\mathrm{.}5M$ and that the incoming flow in the annular region is initially free of the chemical. What is the concentration of the chemical once the fluids are fully mixed downstream?