Farmers often depend on elevated water storage tanks to supply water

Farmers often depend on elevated water storage tanks to supply water for irrigation using gravity and pipes. The tanks are filled using a pump that draws water up from a source through a pipe. The pumps used are rated for their ability to move water through systems of pipes of certain sizes and designs. In the United States, this rating is expressed in either pounds per square inch (psi) or vertical feet. (Note that, in a vertical column of water, the pressure at the bottom is about 0.43 psi per vertical foot in the column.) That is, a pump rated for x feet can operate a pumping system of up to x total vertical feet. For example, the total vertical feet of a pumping system of the type above is the sum of

- the vertical distance of the pipe between the surface of the water source and the pump;

- the vertical distance of the pipe between the pump and the top of the elevated tank; and

- the resistance from friction when water moves through the pipes, which is increased by angled pipes and smaller diameter pipes, expressed in vertical feet as a measure of the pump’s resultant loss in capability.

A farmer in the United States is constructing a pumping system with an elevated water tank to support a gravity-fed irrigation system. The farmer has the following in place:

- the irrigation system, which requires at least 10 pounds per square inch (psi) of pressure at its inlet to operate;

- a pump that can draw 50 gallons of water per minute from the water source and that has a rating of 58 vertical feet—meaning it can operate a pumping system having up to 58 total vertical feet; and

- an 8-foot-tall water tank with a 10,500 gallon capacity.

The farmer has yet to choose the diameter of the irrigation pipes. The diagram specifies the heights and lengths the farmer has in place. Those not specified have yet to be determined. The systems sit on level ground approximately 1 foot above the surface of the water source.