It is required that a pump be designed such that it delivers $0\mathrm{.}6$ m$3/$s of water with a pressure increase of $270$ kPa.

a$-$What is the expected flow produced by a model $1/3$the size of the prototype?

b$-$What is the expected pressure increase produced by a model $1/3$the size of the prototype?

c$-$If the model produces a power output of $200$ kWkW$,$ what would be the power output of the prototype?