Q$8$: Water at $20C$ flows through a centrifugal pump at the rate of $4000\frac{L}{m}in.$ The impeller has an inner radius of $50$ mm $,$ an outer radius of $100$ mm $,$ and a width of $75$ mm $,$ and it rotates at $1800$ rpm $.$ The blades of the impeller have a blade angle of $30$ at the inflow surface and a blade angle of $20$ at the outflow surface. Carry out detailed calculations to find: $($a$)$ the head delivered to the fluid; $($b$)$ the difference in pressure between the outflow and inflow if head losses were neglected and the inflow and outflow pipes were at the same elevation and of the same diameter; and $($c$)$ the inflow blade angle that would cause the inflow velocity to be normal to the inflow surface. $($d$)$ Under the normal inflow condition, what would be the difference in pressure between the outflow and inflow if head losses were neglected?