Water flows through a $12in.$ pipe at a rate of $12\mathrm{.}5f\frac{t^3}{s}$ before entering a turbine$/$generator and discharging through a similar pipe $600ft$ below the reservoir.

Calculate:

i$)$ The efficiency of the turbine$/$generator combination.

ii$)$ The pressure $($psig$)$ at the inlet to the turbine.

iii$)$ The power $($kW$)$ dissipated by pipe friction.

Given that:

Commercial steel

the effective length of pipe is $1500ft.$

turbine$/$generator produces $425kW$ of useful electrical power.

Ans check: psig and $P=83\mathrm{.}3kW$

Hints:

Part A: Turbine efficiency $($Lec$\_11)=($power x $737)/($work x mass flow rate$)$

You need to find the mass flow rate.

The work can be found via energy balance $1$ to $3.$

The $F$ and $f_F$ equations are in $($Lec$\_10).$

Part B: energy balance from $2$ to $3$

Part c: Power dissipated by pipe $=m***F$ and you need to unfiy the units