Problem $5$

The elevations of the Energy Grade Line $($EGL$)$ and Hydraulic Grade Line $($HGL$)$ at point G are $44\mathrm{.}0$

and $42\mathrm{.}0ft,$ respectively. The turbine between $G$ and $H$ is $90\%$ efficient and the EGL is lowered to $4\mathrm{.}00$

$ft$ exiting the turbine $($Point $H).$ Friction factor for the $12"$ pipe is $0\mathrm{.}0300,$ while friction factor for the $6"$

pipe is $0\mathrm{.}0100.$ Assume $K$ for valve $CD$ is $0\mathrm{.}400.$ Assume the pipe entrance is square.

For the system shown above, determine:

$($a$)$ the pressure heads at $E$ and $F,$ which are at elevation $20\mathrm{.}0ft.$

$($b$)$ the EGL, HGL$,$ flow, and velocity at Points A through $H$

$($c$)$ the horsepower extracted by the turbine at $GH.$

Hint: Horsepower from a turbine can be calculated using the same formula as for a pump, except

efficiency is reversed, i$.$e$.$

Horsepower from turbine $=\frac{Q{h}_t}{550}$

where ht is the energy extracted by the turbine.