The Irrigation Problem

This article has students imagine a linear irrigation system to uniformly spray water on a rectangular field where the irrigation device moves across the field at a constant rate in a linear fashion.

The linear irrigation system consists of a long water pipe, generally set on wheels that keep it above the level of the plants. Nozzles are placed periodically along the pipe, and each sprays water in a circular region. The entire system moves slowly down the field, watering the plants beneath as it moves. You have 1000 feet of pipe and 20 nozzles available. You have enough pumps to keep up the pressure on each of the nozzles so they deliver a uniform spray to a circular region 50 feet in radius. how far apart should the nozzles be placed to produce the most uniform distribution of water on a field 1000 feet wide?