A proposed micro$-$hydropower scheme will supply power to a small village off the coast of Nepal. Figure Q$4\mathrm{.}1$ shows the long$-$term flow duration curve $($FDC$)$ for a section of the river flowing through the village. The net head available at the site is $40$m$.$ The overall efficiency of the system under consideration is $85\%.$ Water use is prioritised for irrigation all year round at a rate of $250$ l$/$s$.$ Base your estimation on the mean potential flow $($Q$30).$ The proposed hydropower scheme will provide power to local residents in the village. They request a lighting demand, estimated at $750$ kWh per person annually. The population of the village is $1825.$ Also, there is a power demand for a number of small businesses of $25$ kW for $8$ hours per day all year round. They would also like to provide $100$ kWh each day to support the operation of small mills. The government has announced an incentive to encourage hydropower generation schemes within remote communities. This comprises of a grant of either $2\mathrm{.}5$ cents for every kWh output per year or $20$ cents for every KWh of the annual excess power $($whichever is greater$).$ This is guaranteed for $30$ years. Assume an interest rate of $5\%.$

a$)$ Using the flow duration Curve in Figure Q$4\mathrm{.}1,$ calculate the available flowrate in this river for hydropower and the corresponding power output $($kW$).$ Establish whether the daily demand can be met.

b$)$ Table Q$4\mathrm{.}1$ summaries three possible hydro power systems together with estimated capital and operation and maintenance costs. Using the results from part $($a$)$ evaluate the feasibility of each scheme by calculating each of the following:

$($i$)$ Plant Factor

$($ii$)$ Capacity Factor

$($iii$)$ Annual Power output $($kWhr$/$year$)$

$($iv$)$ Cost per kW installed

$($v$)$ Annual excess power

$($vi$)$ Net present value of the above hydropower options

Show a sample of your calculations and provide a brief comment on each answer.