A pump is used to pump water from an open tank to a closed tank under pressure of $25$ kPa as shown in the figure below. The lengths of the pipe on the suction side and the discharge side are $3$ m and $40$ m respectively. The pipe diameter is $75$ mm and the pipe material is drawn copper on both the suction and discharge sides. The performance curves for the pump are on the next page.

Fitting are as follows:

$($a$)$ Determine the friction factor based on a flow rate of $\backslash (10\backslash$mathrm$\{$~L$\}/\backslash$mathrm$\{$s$\}\backslash ).(4$ Marks$)$

$($b$)$ Determine the system head equation in terms of flow rate in Litres per second. $(7$ Marks$)$

$($c$)$ The flow rate, power, and efficiency at the duty point. $(4$ Marks$)$

$($d$)$ Determine the net positive suction head available $($NPSHA$)$ and check for cavitation at the flow rate calculated in part $($c$).$ Use the same friction factor calculated in part $($a$).(5$ Marks$)$