Irrigation Set Run Time

An irrigation is measured the way rain is measured: as a depth spread over the ground. That choice is not arbitrary and it is worth understanding before the arithmetic, because a depth is the only figure that lets a centre pivot, a drip line and a thunderstorm be compared with one another. A volume divided by an area reduces to a length, so "25 mm of water" and "250 m³ per hectare" are the same statement written in two currencies.

The identity behind that is exact. One hectare is 10,000 m² by definition, so 1 mm of depth over it is $0.001 \times 10{,}000 = 10$ m³, which is 10,000 litres. Nothing measured enters the conversion, so it holds to as many figures as anyone cares to write. To run 25 mm onto 4 ha therefore means putting $25 \times 4 \times 10 = 1{,}000$ m³ of water on the ground, and at 50 L/s — that is 0.05 m³/s — the set takes $1{,}000 / 0.05 = 20{,}000$ seconds, or 5.56 hours.

The imperial half of the identity is the number North American scheduling is actually built on. An acre is 43,560 ft², an inch is a twelfth of a foot, so an acre-inch is 3,630 ft³. A cubic foot is 1,728 in³ and a US gallon is 231 in³ exactly, which makes a cubic foot 7.4805 gallons and an acre-inch 27,154 US gallons. Once that figure is memorised, most irrigation arithmetic can be done on the tailgate: an inch on ten acres at 500 gpm is $271{,}542 / 500 = 543$ minutes, a little over nine hours.

Two mistakes account for nearly all the errors in this calculation. The first is using the pump's nameplate flow instead of what is actually arriving at the set — worn nozzles, a partly closed valve and friction in a long lateral all take their share, and the honest number comes from a flow meter or a bucket and a stopwatch. The second is confusing the depth delivered with the depth stored, which is a separate calculation entirely and the reason application efficiency exists as a term. Run time computed from a gross depth on a system that is 70% efficient waters the crop to 70% of the intention.