Delta of a crop and Duty of water and their relation

Delta:

Some quantity of water is required for any crop to come to its maturity. The total quantity of water required for any crop during its base period(B) for its full fledged nourishment when expressed in depth of water(i.e. in 'cm' or in 'inches') is called its Delta. The total quantity of water(i.e. volume of water) is divided by the total irrigated area to obtain Delta of crop of the irrigated area.

     We have talked about base period(B), it is the time period between the first watering of the crop during its sowing to last watering before its harvesting. It is generally expressed in 'days'. 

   The another related term is Crop period. For practical purpose Base period and Crop period are taken as same but they have a little difference. Crop period is the time period between sowing of a crop to its harvesting. In this manner, Crop period is slightly greater than the Base period. 

Duty:

 Duty of a water simply expresses the number of hectare of land that can be irrigated for the full growth of the given crop by supplying 1 cumec water continuously during the entire base period of that crop. It is generally represented by 'D'. Its unit is hectare/cumec. For example, if water flowing at the rate of 1 cumec, runs continuously for B days of the crop matures 100 hectares then Duty of that crop is 100 hectare/cumec to the base of B days.

  Duty varies from point to point. It increases as one moves to downstream from the head of main canal to the head of branches. It is due to the transmission losses in the channels.

Relation between Delta and Duty:

Let a crop of Base period B for which 1 cumec water is supplied continuously for its full growth.

Then the total volume of water supplied during B days for that Crop = (1*B*24*60*60) cubic meter.

By the definition of duty, it is clear that it matures D hectares of land.

Then the total depth of water supplied during base period B = (1*B*24*60*60)/(D*10000)

                                                                                           =8.64B/D meters

We know total depth of water supplied during base period of a crop is Delta.

Then, Delta= 8.64B/D meters.