$1.)$ A pump is used to move water between two tanks as shown on the next page. The pump is to move a minimum of $\backslash (30000\backslash$mathrm$\{$~L$\}/\backslash$mathrm$\{$hr$\}\backslash ).$ to the upper tank that holds $600000$ L $.$

a$.)$ There are two isolation gate valves and a swing check $($globe$)$ valve in the $300$ m long commercial steel pipeline at the pump. Select a standard size for the pipe based on a maximum frictional head loss of $\backslash (10\backslash \%\backslash )$ of the static head.

b$.)$ Select a suitable pump speed, assuming that the pump will be chosen from the pump characteristic curve shown on the next page. Your selection should be based on the full tank. Give the operating point for the pump $($full tank$).$

c$.)$ If the electric motor driving this pump has an efficiency of $\backslash (85\backslash \%\backslash )$ and electricity costs $\backslash (6\backslash$phi $\backslash )$ per kilowatt$-$hour, what is the cost of filling the upper tank. $($A reasonable answer can be obtained by assuming the pump is pumping to a half full tank.$)$ Consider the efficiency of the pump as well.

d$.)$ If the size of the impeller is increased by a factor of $1\mathrm{.}20,$ what would the flow rate and power costs be $($half$-$full tank$)?$

e$.)$ If two pumps in parallel are used, what would the flow rate be$?$ Assume changes to the system are minimal.