Problem $2(10$ points$)$: Learning Outcome #$3$

Water flows into the pipe at A with an average uniform velocity of $0\mathrm{.}2\frac{m}{s}$ and through pipe $B$ with an average uniform velocity of $0\mathrm{.}10\frac{m}{s}$ and through pipe $D$ with an average uniform velocity of $0\mathrm{.}15\frac{m}{s}.$ Find the maximum velocity of the water as it emerges from pipe C where the velocity distribution is parabolic:

$V=V_{\text{m}\text{a}\text{x}}**(1-80r^2)$

where $r$ is in meters and it is the radial distance from the centerline of the pipe. Draw your control volume including the velocity and surface normal vectors. Let the density of the oil be $900k\frac{g}{m^3}.($D in the figure is the diameter of the circular pipe$)$