Fluid Mechanics

For a high$-$flow site with a head of $45$ ft$,$ it is desired to design a single $7-$ft$-$diameter turbine that develops $4000$ bhp at a speed of $360$ r$/$min and $88\%$ efficiency. It is decided first to test a geometrically similar model of diameter $1$ ft$,$ running at $1180$ r$/$min$.$ For water, take $=1\mathrm{.}94$ slug$/$ft$3.$

a$)$ What is the appropriate head for the model test?

b$)$ What is the appropriate flow rate for the model test?

c$)$ Estimate the power expected to be delivered by the model turbine.