# Delta Duty Relationship : Derivation & Numerical

Table of Contents

**The relationship between Delta, Duty, and Base Period is given below with 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 the 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 { B days = 24*60*60 Seconds & Q = 1 m³/s }

V=8.64*10000 B m³ …(1)

The volume of water applied to the field can also be calculated as:

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

V=D(ham)*Δ (m)

V=D *Δ*10000(m³) ….(2)

From Eqn 1 & 2 , we get

8.864*10000*B= 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 |

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