Question $1$

$($a$)$ It can be shown from dimensional analysis that friction factor and Reynolds number are the governing dimensionless parameters for pipe flow problems, with a drag coefficient used to characterise losses in valves and fittings. Use the information in the schematic below along with relevant correlations from the supplementary information section at the end of this exam paper to predict elevation, $z_1,$ of the left hand side reservoir required to achieve a flow rate of $1\mathrm{.}5$ litres per second. Take pipe roughness as $0\mathrm{.}5$ mm $.$

$10$

$($b$)$ Taking the same pipe network as shown above, determine the flow rate that would result if the water level in the left reservoir, $z_1,$ was instead equal to $4\mathrm{.}1$ m $.$

$[14]$

$($c$)$ Now assume the water level in the left reservoir, $z_1,$ is equal to that in the right reservoir, $z_2.$ Write out an equation that describes the system curve and explain in detail how one would go about selecting an appropriate pump and its rotational speed to achieve a desired flow rate of $10$ litres per second between the reservoirs. Use an appropriate graph to aid with you explanation.

$9$

$[$Total $33]$