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

Table of Contents

**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,

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**

Read Also: Duty in Irrigation |