Problem $4(10$ points$)$ Consider steady flow of water over a bent circular tube with a

radius $R=0\mathrm{.}1m$ as shown in the figure. At the entrance $"1",$ the pressure is uniform

$P_1=301$kPa and the velocity is uniform with a magnitude $|v_1|=8\frac{m}{s}.$ At the exit $"2",$

the pressure is uniform and atmospheric, $P_2=101$kPa, and the velocity is parabolic

and satisfies the no$-$slip condition on the tube wall as shown. Neglect the weight of the

water inside the bend and the weight of the pipe. Use control volume analysis $($you must

draw and show your control volume, as well as your coordinate system$)$ to:

$($a$)$ Find the maximum velocity at Section $"2"$;

$($b$)$ Find the anchoring force required to hold the bend stationary. Use arrows to

indicate the directions of the two force components.