2.7. Delta-Duty Relationship

Let us consider a crop with base period ‘B' days. Let, 1 m³/s of water is applied to this crop on the field for 'B' days.

The volume of water applied to the crop during 'B' days,

       V = 1 m³/s X B days [: volume = flow x time] 

= 1 m³/s x B X 24 X 60 X 60 sec 

= 86400 B   m3

 By definition of duty, 1 m³/s water supplied for 'B' days irrigate ‘D' hectares of land,

 i.e. ' V ' m³ of water irrigates ' D ' hectares of land.

We know, Area (A) = D hectares = D x 10⁴ m²

So, depth of water applied on this land

 \( = \frac{Volume}{Area} = \frac{86400 B}{D \times 10^4 } = \frac{8.64 B}{D} meters \)

Here total depth of water is called Delta (Δ) Hence, 

 \( Δ = \frac{8.64 B}{D} meters \)