An expedition has set up camp in a forest, where there is no electricity or running water. In order to take showers, they pump water from a nearby creek using a pump with an electric motor driven by an automobile battery. The pump uses a smooth water hose with an inner diameter of 25 mm and a total length of 25 m. The shower head is at an elevation 2.5 m above the free surface of the creek and the flow rate is controlled by a ball valve. The maximum electric power that can be provided by the battery to the pump is 36 W and the hydraulic efficiency of the pump may be taken as 65%. Compute the maximum water flow rate that will be possible for this shower.

Contributed by Stavros Tavoularis, Department of Mechanical Engineering, University of Ottawa, Ottawa, Canada. Image from Jungle-Avonturencamping de Belten.