---
title: "Duty and delta relationship"
subject: "Irrigation and Drainage Engineering"
chapter: 2
key: "semester_6/irrigation_and_drainage_engineering:duty-delta-relationship"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/duty-delta-relationship
site: BCT Engineering
---

# Duty and delta relationship

Irrigation and Drainage Engineering · Chapter 2: Irrigation Water Requirements

- Asked in: 2080 Chaitra, 3 marks; 2066 Bhadra (old course), 4 marks; 2062 Baisakh (old course), 4 marks (asked 3 times)
- Video: [Duty, Delta and Base Period | Irrigation Engineering](https://www.youtube.com/watch?v=FZv1vrBVQvE) — APSEd
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/duty-delta-relationship
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-2

## Question

Explain the terms duty and delta and derive the relationship between them.

## Short answer

Duty is the area (ha) irrigated by a continuous flow of 1 cumec during the base period; delta is total water depth (m) needed. They relate as Δ = 8.64 B / D (m), with B in days and D in ha/cumec; example: wheat with 120 days and D=1800 ha/cumec gives Δ=0.576 m.

## Answer

#### Duty ($D$)
The area of land (in hectares) that can be irrigated by supplying one cumec ($1\ m^3/s$) of water continuously throughout the base period of the crop. Unit: ha/cumec. Duty depends on the point of measurement (field, outlet, canal head).

#### Delta ($\Delta$)
The total depth of water (in m or cm) required by a crop over its base period if the water is spread over the land. Unit: m.

#### Base period ($B$)
The time in days from the first watering to the last watering of the crop before harvest.

#### Relationship between duty and delta
Take 1 cumec flowing for $B$ days.

$$
\begin{aligned}
\text{Volume of water} &= 1 \times B \times 86400\ \text{m}^3\\
\text{Area irrigated} &= D\ \text{ha} = D\times 10^4\ \text{m}^2\\
\Delta &= \frac{\text{Volume}}{\text{Area}}=\frac{86400\,B}{10^4\,D}
\end{aligned}
$$

$$
\Delta = \frac{8.64\,B}{D}\ \text{(m)}
$$

with $B$ in days and $D$ in ha/cumec. Hence a crop with a high delta has a low duty, and vice versa.

**Example:** wheat with $B=120$ days and $D=1800$ ha/cumec gives $\Delta = 8.64\times120/1800 = 0.576$ m.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Duty is:
   A. Depth of water per crop
   B. Days between waterings
   C. Hectares irrigated per cumec over the base period
   D. Cumecs per hectare per day
   Answer: C. Unit ha/cumec. (Key point: Duty definition)

2. Delta in metres is:
   A. D / 8.64 B
   B. 86400 B x D
   C. B / 8.64 D
   D. 8.64 B / D
   Answer: D. Volume 86400 B over area 10^4 D. (Key point: Relationship)

3. A crop with high delta has:
   A. Low duty
   B. High duty
   C. Same duty
   D. Zero base period
   Answer: A. Delta inversely proportional to duty. (Key point: Inverse)

4. B=120 days, D=1800 ha/cumec gives delta:
   A. 5.76 m
   B. 0.576 m
   C. 0.0576 m
   D. 1.8 m
   Answer: B. 8.64 x 120 / 1800 = 0.576. (Key point: Example)

## Related in Irrigation and Drainage Engineering

- [Duty, delta, base period, crop period](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Adefine-duty-delta-base-crop-period) — Irrigation and Drainage Engineering, chapter 2

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