The Wivenhoe Power Station, located near Brisbane, is situated between the Splityard Creek Dam

$($SCD$)$ and Lake Wivenhoe $($LW$).$ It generates hydroelectricity by extracting hydro power from the

SCD situated $100$ m above LW$.$ The power station has two turbines. Each turbine has a discharge rate

of $231$ m$3$

$/$s$.$ The friction head loss is $0\mathrm{.}05$ m per $1$ m of the pipe. The total length of the pipe

between SCD and LW is $200$ m$.$

You are assigned a task to evaluate a strategy to using ONE of the turbines to draw water from the

SCD in the peak time $(8$am $8$pm$)$ to produce electrical power for Brisbane and pump water from

LW during the off$-$peak time $(8$pm $-8$am$)$to restore the situation $($at $8$am each day, the water level at

SCD must be kept the same$).$ Other information includes:

i$)$ electricity generated and supplied to the grid at a selling price of $$0\mathrm{.}3$ per kWh during

peak time $(8$am $8$pm$).$ The turbine$$s efficiency is $76\%.$

ii$)$ cost of using electricity to pump water during off$-$peak time at $$0\mathrm{.}15$ per kWh during offpeak time $(8$pm $-8$am$).$ The pump$$s efficiency is $90\%.$

Answer the following questions:

a$)$ How much electrical power is generated through one turbine during the $12$ hours of peak

time?

b$)$ How much electricity is consumed for pumping water from LW to the SCD during the $12$

hours of the off$-$peak time?

c$)$ Calculate the economic gain$/$loss per annum $($ignoring any other costs such as capital and

maintenance costs$).$