A village with a need for a simple irrigation system propose

A village with a need for a simple irrigation system proposes to have a collectio pool for rain water and then a simple human-powered pump mounted to a stationary bicycle frame to deliver the water to crops during dry times. If the required lift is 2.5 m and the total loss in the line is 1.8 m, determine what flow rate, in liters per minute, is possible with a person producing 125 W by pedaling assuming the pumping station to be 65 percent efficient.

Solution

h = 1.8 m and H = 2.5 m

The work requied to be done against gravity (per unit time) = volume flow rate x density of water xg x H

The energy lost (per unit time) = volume flow rate x density of water x g x h

The total work requied to be done (per unit time) = volume flow rate x density of water x g x (H + h)

The power given by person = P

The useful power = 0.65 P = 81.25 watt

This useful power provides the work required to pull water up. So,

volume flow rate = 1.928 Lt/sec