$(15\%)$ A water pump with impeller diameter $60cm$ is to be designed to move $0\mathrm{.}5\frac{m^3}{s}$ when running at $800rpm.$ Testing is performed on a $1$:$5$ scale model running at $2500rpm$ using air $(20C)$ as the fluid. Please answer the following questions:

$($a$)$ For similar conditions $($neglecting Reynolds number effects$),$ what will be the model flow rate?

$($b$)$ If the model draws $75W,$ what will be the power requirement of the prototype?