Custom $1,$ practical: Consider the image for problem $5-91$ in the text. The flow rate through the system is $20\frac{f{t}^3}{(s)}$ of $70F$ water. The entrance to the pipe from the reservoir is sharp$-$edged. The pipe is made of cast iron and has a diameter of $2$ ft $,$ and all fittings used flanged connections. There is a fully open gate valve in the dam before the turbine. The elbows shown are short radius elbows. The total length of the pipe is $50$ ft $,$ after which the exit at the end of the pipe has a $30$ gradual expansion to a diameter of $8$ ft before the fluid is discharged to the atmosphere.

If the turbine has an efficiency of $85\%,$ how much power is it producing?

Repeat the analysis with $1\mathrm{.}5-$ft diameter pipe, expanded to $6-ft$ at the end before the fluid exits.

Do some internet searching to fynd the cost of cast iron pipe and fittings for $1\mathrm{.}5$ ft and $2$ ft diameters. What are these costs? Cite your source$($s$).$

How much more would the $2$ ft diameter system cost than the $1\mathrm{.}5$ ft diameter system?

If the power produced can be sold to the power company at a rate of $$\frac{0\mathrm{.}07}{k}Wh,$ how long will it take to recoup the extra cost of using the larger pipes?