b$)$ A pump whose characteristics are shown in Figure $3$ when operating at $450$ rpm is used to pump water from reservoir $A$ to reservoir $B$ through a $24-$indiameter pipe $)$ of length $170ft.$ neglecting minor losses, find the flow rate and the corresponding head for the following conditions.

i$.$ Reservoir water$-$surface elevations are identical.

$(3\mathrm{.}5$ marks$)$

ii$.$ The water surface in Reservoir B is $20ft$ higher than that in Reservoir A$.$

$(3\mathrm{.}5$ marks$)$

Figure $3$ pump characteristic curve