Example $4\mathrm{.}10$ Consider the hydropower plant shown in the figure. The water surface elevation

of the reservoir behind the dam is $135m$ whereas the tailwater elevation $($water surface in the

river downstream of the turbine$)$ is $45m.$ A turbine located at an elevation of $30m$ subtracts $60$

$m$ of head from the flowing water. Head losses along the pipes before and after the turbine

$($pipes $1$ and $2)$ are given as $\frac{3V_1^2}{2g}$ and $\frac{2V_2^2}{2g}$ respectively.

a$)$ Calculate the water discharge in the system

b$)$ Calculate the pressure just before and after the turbine $($at points $C$ and $D)$

c$)$ Draw EGL and HGL

d$)$ Compute the electric power produced if the turbine is operating at an efficiency of $80\%.$

$(z_A=135(m),z_B=45(m),z_C=z_D=30(m),D_1=0\mathrm{.}3(m),D_2=0\mathrm{.}6(m))$