# Delta Duty Relationship | Derivation & Numerical

**Relationship between Delta, Duty, Base Period is given below after definitions.**

**i. Duty**

The duty of water is the relationship between the volume of water and the area of land it matures. It may be defined as the area of land (in hectares) irrigated for full growth of given crop by a supply of 1 m3lsec of water continuously during the entire base period of the crop. Duty of water is generally expressed in hectare cumecs and is denoted by letter `D `mathematically,

D=A/Q

Where,

A=Area in hectares

Q=Discharge in m3/s

Duty can also be expressed as

D=8.44 B/Δ

**ii. Delta**

Each crop requires a certain amount of water after a fixed interval of time, throughout its period of growth. The depth of water required every time varies 5 to 10 cm depending upon the type of crops, climate & soil. The time interval between two consecutive watering is called the frequency of irrigation or rotation period. The depth of irrigation water required by a crop during its entire period of maturation is called delta. It is usually expressed In cms and is denoted by Δ.

**iii. Base Period**

The time between the first watering of a crop at the time of its sowing to its last watering before harvesting is called the base period. It is denoted by B.

**Relationship Among Delta, Duty & Base Period**

Let us consider a crop having base period B days. Assume that 1 cumec of water is supplied to this crop for B days to provide delta Δ m depth of water.

Now the volume of water supplied by unit discharge to this crop during B days is given by:

V=Q (m³/s)*B (days)

V= 1*24*60*60*B m³

**V=8.64*10000 m³ …(1)**

Also, the volume of water applied to the field can be calculated as:

V=Area of land irrigates by unit discharge*depth of water applied

V=D(ham)*Δ (m)

**V=D *A*10000(m³) ….(2)**

From Eqn(1) and (2), we get

8.864*10000=D*Δ*10000

**D=8.64*B/Δ**

**Example**

Calculate delta based on the following data

Base peroid=110 days

Duty=1400ha/cumec

Delta=?

solution,

Δ =8.64*110/1400

Δ=0.68m

Δ =68cm

Read Also: Duty in Irrigation |