 # Delta Duty Relationship | Derivation & Numerical | Delta | Duty | Base Period

The 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 a given crop by a supply of 1 cumec 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,

D=Duty in hectare cumec

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 between 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 for 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.

### iv. Relationship Among Delta, Duty & Base Period ( Delta Duty Relationship)

Let us consider a crop having a base period of 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 irrigated 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