Sometimes the variation of water viscosity with temperature can be used to achieve dynamic similarity. A model pump delivers \(0.10 \mathrm{~m}^{3} / \mathrm{s}\) of water at \(15^{\circ} \mathrm{C}\) against a head of \(27 \mathrm{~m}\), when operating at \(3600 \mathrm{rpm}\). Determine the water temperature that must be used to obtain dynamically similar operation at \(1800 \mathrm{rpm}\). Estimate the volume flow rate and head produced by the pump at the lower-speed test condition. Comment on the NPSH requirements for the two tests.