$1.$ A site is being considered for hydropower development. $10$ years of flow rate date, in ft$3/$s as a

function of time, are given in the file Flow Data on canvas.

a$.$ Is it technically possible to establish a hydropower plant at this site with a constant

discharge rate of $60$ m$3/$s$?$ One way to visualize available flow is a $$discharge curve$.$ This is

constructed by ordering discharge from highest to lowest and plotting the result against

their position in the ordered time series. When visualized this way, the x$-$axis is called the

$$exceedance$($i$.$e$.,$ the percentage of time the flow rate is more than or equal to some

value$).$

b$.$ Construct a discharge curve, in m$3/$s$,$ for this site. This has implicates for the trade$-$off

between power rating and capacity factor. c$)$ Assuming net head and water$-$to$-$wire

efficiency is constant, how much greater would the design power output of a hydropower

plant with a design discharge equal to $50\%$ exceedance be than one equal to $80\%$

exceedance?