An axial-flow pump is required to deliver \(0.75 \mathrm{~m}^{3} / \mathrm{s}\) of water at a head of \(15 \mathrm{~J} / \mathrm{kg}\). The diameter of the rotor is \(0.25 \mathrm{~m}\), and it is to be driven at \(500 \mathrm{rpm}\). The prototype is to be modeled on a small test apparatus having a \(2.25 \mathrm{~kW}, 1000 \mathrm{rpm}\) power supply. For similar performance between the prototype and the model, calculate the head, volume flow rate, and diameter of the model.