What One Person Can Actually Pump: Sustained Power and the Litres-per-Hour Bound by Depth

Hand pumps are frequently described by a flow rate, and that rate is frequently a peak: the delivery achieved in a vigorous short demonstration, by a fresh operator, sometimes at a shallower depth than the one at which the pump will actually serve. This paper computes, from energy rather than from demonstration, the flow one person can sustain. The central stated assumptions are a sustainable mechanical power of 50 W delivered at the handle, an overall pump efficiency of 0.60, and an effective pumping day of 6 hours. On those assumptions the hydraulic power available is 30.0 W, and the sustainable delivery is 1101 litres per hour against a depth of 10 m, 550 litres per hour at 20 m, 367 litres per hour at 30 m, 275 litres per hour at 40 m, and 183 litres per hour at 60 m. Over a 6-hour pumping day those rates give total volumes of 6606 litres from 10 m, 3303 litres from 20 m, 2202 litres from 30 m, and 1651 litres from 40 m. The energy cost of the water is 163.5 joules per litre at 10 m, 490.5 joules per litre at 30 m, and 981.0 joules per litre at 60 m. Three advertised-style claims are then tested by the same arithmetic: a sustained rate of 1500 litres per hour at 20 m would require 136.2 W at the handle, a sustained 2000 litres per hour at 30 m would require 272.5 W, and a sustained 1000 litres per hour at 40 m would require 181.7 W — respectively 2.73, 5.45, and 3.63 times the assumed sustainable power. Those claims do not survive as descriptions of a working day, although the first and third are within brief-effort capability, which is precisely why short demonstrations mislead.