Water must be pumped from ground level to the top of a building. The building is \(30 \mathrm{~m}\) tall. We wish to compare the work required to pump water at three different average velocities: \(1 \mathrm{~m} / \mathrm{s}, 5 \mathrm{~m} / \mathrm{s}\) and \(10 \mathrm{~m} / \mathrm{s}\). The diameter of the pipe through which the water flows is \(6 \mathrm{~cm}\) and the roughness of the pipe, \(\varepsilon=2 \times 10^{-4}(\mathrm{~m})\). The length of the piping is \(50 \mathrm{~m}\). At which velocity is the pumping most efficient? Calculate the ratio of flow rate/work required in order to do this.