Question $1.$

Three identical centrifugal pumps operating in parallel are used to draw water from

a large sump to a large tank. The difference in the water levels in the sump and in

the tank is $15m.$ The hydraulic frictional losses $(m$ of water$)$ in the pipeline system

curve is given by $h_L=0\mathrm{.}15Q^2$ where $Q$ is the flow in the pipeline measured in $\frac{m^3}{m}in.$

The performance characteristics of each pump running at $1450$ RPM is given below.

The impeller diameter is $30cm.$

$($a$)$ What is the operating discharge, head and efficiency of each pump when all

three pumps are running at $1450$ RPM$?$

$($b$)$ Each pump is set on a level foundation above the sump water level. What is

the maximum height above the sump water level before cavitation sets in$?$ The

vapour pressure of water is $0\mathrm{.}32m$ of water.

$($c$)$ One of the pumps failed and the other two pumps will have run in parallel at a

new speed so that the same combined $(3$ pumps$)$ operational head and discharge

can be achieved. What is the new speed which each of the remaining pumps have to

be operated?

What are the new operating head, discharge and efficiency of each pump at the new

speed?

For plotting, use the following scale:

Horizontal axis for $Q$:$1cm=1\frac{m^3}{m}in$

Vertical axis for $H$ and NPSH: $2cm=10m$

Vertical axis for efficiency: $1cm=10\%$

$H=30(m),Q=3\mathrm{.}3\frac{m^3}{m}in$;$<mn>4</mn><mn>.</mn><mn>1</mn><mn>8</mn><mi>(</mi><mi>m</mi><mi>)</mi>$;$2175RPM$;$18\mathrm{.}5(m),3\mathrm{.}89\frac{m^3}{m}in$;$63\%$;$38\mathrm{.}5(kW)$