Question $3$: ONLY HAVE TO ANSWER PART $($C$)$ PLZ

You are asked to size the pump for a large scale pumped hydro$-$electric storage system. The

system is to pump water from a lake to a man$-$made reservoir on a mountain, $350m$ above the

lake. It should be capable of delivering volumetric flow rates up to $100\frac{m^3}{s}$ and you can

assume there is no frictional head loss in the pipeline $($i$.$e$.$ no major or minor losses$).$ A

dimensional analysis yields the following PI groups where $P$ is pressure; $Q^{}$ is volumetric flow

rate; $$ is fluid density; $$ is rotational speed; and $D$ is diamter:

$\frac{O}{\frac{P}{{}^2{D}^2},\frac{(Q^{})}{D^3}}$

A novel impellor design $($i$.$e$.$ the rotating part of the pump$)$ is being proposed but the

relationship between PI groups is unknown. It was decided to conduct some laboratory

experiments on a small scale model of the impellor which is $0\mathrm{.}3m$ in diameter. These

experiments were conducted at various rotational speeds and with three different working

fluids while pressure rise across the pump and volumetric flow rate were measured. The

results are indicated in the table below.

Use the data$-$provided to graphically illustrate the relationship betwe

and comment on the significance of the resulting graph.

$($b$)$ Determine the diameter of pump required for the hydro$-$

described at the start of this question if it is noted that large scalf

required are typically limited to a maximup rotational

of $300-$revolutic

per

$9$

$($c$)$ Determine the maximum height a $4\mathrm{.}9m$ diameter pump would be able to pump water to$,$

given a rotational speed of $300$ revolutions per minute and flow rates of $($i$)10\frac{m^3}{s}$ and $($ii$)$

$30\frac{m^3}{s}$