Duty and delta relationship

Duty ($D$)

The area of land (in hectares) that can be irrigated by supplying one cumec ($1\ m^3/s$) of water continuously throughout the base period of the crop. Unit: ha/cumec. Duty depends on the point of measurement (field, outlet, canal head).

Delta ($\Delta$)

The total depth of water (in m or cm) required by a crop over its base period if the water is spread over the land. Unit: m.

Base period ($B$)

The time in days from the first watering to the last watering of the crop before harvest.

Relationship between duty and delta

Take 1 cumec flowing for $B$ days.

$$\begin{aligned} \text{Volume of water} &= 1 \times B \times 86400\ \text{m}^3\\ \text{Area irrigated} &= D\ \text{ha} = D\times 10^4\ \text{m}^2\\ \Delta &= \frac{\text{Volume}}{\text{Area}}=\frac{86400\,B}{10^4\,D} \end{aligned}$$ $$\Delta = \frac{8.64\,B}{D}\ \text{(m)}$$

with $B$ in days and $D$ in ha/cumec. Hence a crop with a high delta has a low duty, and vice versa.

Example: wheat with $B=120$ days and $D=1800$ ha/cumec gives $\Delta = 8.64\times120/1800 = 0.576$ m.