Irrigation System Capacity

System capacity is the sizing question: how much water must arrive at the field, continuously, for the crop to never go short in the worst week of the year? Everything downstream — well yield, pump curve, mainline diameter, the electrical service — follows from this one number, and it is the one number that cannot be fixed later without digging.

The calculation multiplies the area by the peak daily crop use to get a demand, then inflates it twice. The first inflation is application efficiency: water that runs off, drifts away or drains past the roots was pumped but never used, so the pump must supply the crop's need divided by the fraction that lands usefully. The second is the operating fraction, because a system that runs 18 hours a day has to move a day's water in three-quarters of a day. Twenty hectares at a peak use of 7 mm/day needs $0.007 \times 200{,}000 = 1{,}400$ m³ daily; at 85% efficiency that is 1,647 m³ pumped; spread over 18 hours it is 91.5 m³/h, or about 25.4 L/s.

In North American units the same logic produces the rule of thumb everybody quotes. Forty acres at a quarter-inch a day is 10 acre-inches, which is 271,543 gallons; at 80% efficiency that is 339,429 gallons, and over 18 hours it is 314 gpm — call it 7.9 gpm per acre. The familiar "5 gpm per acre" figure is the same calculation with a humid-climate peak use and a higher efficiency, which is exactly why it should never be carried into a drier region without redoing the arithmetic.

Two design cautions belong with this equation. The operating fraction should leave room for a breakdown: sizing at 24 hours a day means the first failed contactor during peak demand puts the crop into deficit, and the standard allowance is 20 to 22 hours rather than 24. And peak use is not average use — a season-average ET figure will undersize the system by a third or more, because the whole point of the exercise is the fortnight in July when the crop is at full canopy under a clear sky. Where capacity genuinely cannot meet the peak, the design decision is deliberate deficit irrigation timed to miss the crop's most sensitive growth stage, which is a legitimate strategy and a bad accident.