A centrifugal pump having an impeller diameter of \(1 \mathrm{~m}\) is to be constructed so that it will supply a head rise of \(200 \mathrm{~m}\) at a flowrate of \(4.1 \mathrm{~m}^{3} / \mathrm{s}\) of water when operating at a speed of \(1200 \mathrm{rpm}\). To study the characteristics of this pump, a \(1 / 5\) scale, geometrically similar model operated at the same speed is to be tested in the laboratory. Determine the required model discharge and head rise. Assume that both model and prototype operate with the same efficiency (and therefore the same flow coefficient).