Question five

a$.$ A centrifugal water pump operating at its optimum efficiency delivers $2\mathrm{.}30\frac{m^3}{s}$ over a height of $20$ m $.$ The pump has a $360$ mm diameter impeller and rotates at $300$rad$\frac{s}{sec}.$ Compute the specific speed of the pump in terms of the discharge. $(12$ marks$)$

b$.$ The impeller of the pump in $($a$)$ above has a diameter of $360$ mm $.$ Determine the diameter of the pump that is geometrically similar that can deliver one half of the water discharge at the same head. $(8$ marks$)$