Answer 5—The question is deliberately under specified in order to test your general knowledge and common sense.

There are two aspects of a home shower that require significant amounts of power: heating the water and providing the pressure. Let’s ignore things like lighting and ventilation, which should be trivial in comparison, and are usually available “for free” anyway.

Cold water usually comes into the house at ground temperature, or about 10°C. Domestic water heaters are usually set to heat water to between 50° and 60°C, but most people operate their showers with a mix of hot and cold water for an output temperature close to 40°C. Assume you need to raise the temperature of the water by 30°C.

Modern low-flow showerheads operate at about 2.5 gpm, or roughly 10 liters per minute. This is equivalent to 166.7 cc per second. Therefore, you need 166.7 × 30 × 4.184 = 20924 Joules/sec. (Wats) to heat the water.

A showerhead requires about 30 psi minimum to operate properly, or roughly 20 m of “head.” In other words, the power required to create this pressure is equivalent to pumping the mass of the water 20 m upward in the Earth’s gravity (and allowing it to fall back down to the starting level):

Of course, this analysis completely ignores friction and other pumping losses. A real pump would require considerably more power than this.

Contributor: David Tweed

Published March 2004