$1.$ The results in TABLE Q$1$ were obtained from a test on a centrifugal pump running at constant speed. The working fluid was water.

TABLE Q$1$

Flow rate Q $($m$^3$ h$-1)0481216202428$

Total head H $($m$)16\mathrm{.}316\mathrm{.}516\mathrm{.}515\mathrm{.}814\mathrm{.}51294\mathrm{.}9$

Overall efficiency $\backslash$eta $(\%)038627680\mathrm{.}5807050$

Two of these pumps are connected in parallel, with common suction and delivery pipes, to provide a static lift of $5$ m$.$ The friction and other losses external to the pumps is $4\mathrm{.}5$ x $10-3$ Q$2$ m$,$ where Q is the delivery of water in m$3$ min$-1.$

$($a$)$ Using APPENDIX A$,$ calculate and tabulate the flow rates, pump heads, and efficiencies for the two pumps in parallel using the single pump data shown.

$(4$ marks$)$

$($b$)$ Using APPENDIX A$,$ calculate and tabulate the system head for the actual system.

$(4$ marks$)$

$($c$)$ Use the graph provided in APPENDIX B $($FIGURE Q$1)$ to plot the $\text{'}2$ pump' and the system head characteristics; estimate the $\text{'}2$ pump' delivery, head and pump efficiency.

$(4$ marks$)$

$($d$)$ Calculate the total shaft power required to drive the pumps.

$(4$ marks$)$

$($e$)$ If one of the pumps is removed from the installation, what will be the delivery and power consumption for the remaining pump?

$(4$ marks$)$

$($f$)$ What percentage increase in friction losses would be required to reduce the flow to $35$ m$3$ min$-1$ with $2$ pumps in parallel? Briefly explain how this might be achieved in practice.