Duty & Delta & The Canal's Promise to the Crop

Duty is the area of land a unit discharge can irrigate over the whole base period of a crop — expressed in hectares per cumec (ha/cumec). A higher duty means one cumec of canal water serves more land, so the same headworks can command a larger area. It is one of the central design figures in canal irrigation.

Delta is the total depth of water a crop needs over its base period, usually given in metres or millimetres. If you imagine all the water supplied to a field spread evenly over its surface, the depth of that layer is the delta. Each crop has a typical delta — rice is high, while wheat and pulses are much lower.

They are linked through the base period: Δ = 8.64 × B ÷ D, where Δ is delta in metres, B is the base period in days and D is the duty in ha/cumec. The constant 8.64 comes from converting one cumec flowing for one day into a depth over one hectare. So as duty rises, delta falls for the same base period.

The base period is the number of days between the first and last watering of a crop in a season — essentially how long the crop is drawing irrigation. It appears directly in the duty–delta relation, so using the correct base period for your crop is essential to getting a sensible delta or duty.

It lets engineers size canals and command areas. Knowing the duty fixes how much area a given discharge can serve; knowing the delta fixes how much depth of water each hectare needs. Together they connect the canal capacity at the head to the total area that can be reliably irrigated downstream.

One cumec is one cubic metre per second. Over one day that is 86,400 m³. Spread over one hectare (10,000 m²) that depth is 8.64 metres, and over the base period of B days it becomes 8.64 × B metres per hectare. Dividing by the duty (ha served per cumec) gives the delta per hectare.

For a fixed base period, yes — a higher duty spreads the same cumec over more land, so each hectare receives a smaller depth, i.e. a smaller delta. That is why low-water crops like wheat and pulses have high duties, while heavy-water crops like rice have low duties and large deltas.

Yes. The relation rearranges to D = 8.64 × B ÷ Δ. If you know the crop's delta and base period you can find the duty the canal must achieve, which then tells you the command area a given discharge will cover. This tool reports both so you can design from either end.

The duty–delta relation is a clean engineering identity, so the maths is exact. The judgement lies in choosing realistic delta, duty and base-period values for your crop, soil and climate, and in allowing for conveyance losses between the head and the field — outlet duty is lower than field duty because of these losses.