Oil $(S=0\mathrm{.}87)$ is transported through the system as shown below. If the pressure head

difference between points B and $A$ is $\frac{P_B-P_A}{}g=62m,$ calculate the horsepower supplied

by the pump to the system. Pipe $1$ has a diameter of $8cm$ and length $59m,$ while pipe $2$ has a

diameter of $6cm$ and length $47m.$ Assume, $=1\mathrm{.}00$ at all locations, and Elev. $1=85m,$ Elev.

$2=142m,$ and Elev. $3=38m.$ Head losses in the pipes are given as $h_l=0\mathrm{.}022\frac{V^{2}L}{2gD}$ for pipe

$1,$ and $h_l=0\mathrm{.}032\frac{V^{2}L}{2gD}$ for pipe $2.$ Assume that the losses between A and B are negligible and

are at the same elevation. $[10]$

Hint: Apply energy equation at reservoir surface and exit point. Velocity in pipe $1$ can be

determined in terms of velocity in pipe $2$ using $Q_1=Q_2.$ Thus, pump head can be determined

in terms of the velocity. Now apply energy equation at A and B$,$ the elevations of A and B are

same, and the pressure head difference is known. Plugging in pump head value in terms of

velocity, the velocity in one of the pipes can be found.