Q$\mathrm{.}1[$a$]1$:$2$ model of a turbine is operated at $600$ rpm under a net head of $15$ m $.$ The brake power of the model is $300$ kW under a discharge of $\backslash (2\mathrm{.}3\backslash$mathrm$\{$~m$\}^\{3\}/\backslash$mathrm$\{$s$\}\backslash ).$ The prototype is to work under net head of $90$ m $.$ compute the $($i$)$ specific speed of the model, $($ii$)$ overall efficiency of the model, $($iii$)$ overall efficiency of the prototype, and $($iv$)$ brake power of the prototype.