---
title: "Most efficient of three distributaries"
subject: "Irrigation and Drainage Engineering"
chapter: 2
key: "semester_6/irrigation_and_drainage_engineering:compare-three-distributaries-efficiency"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/compare-three-distributaries-efficiency
site: BCT Engineering
---

# Most efficient of three distributaries

Irrigation and Drainage Engineering · Chapter 2: Irrigation Water Requirements

- Asked in: 2072 Asoj, 5 marks
- 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/compare-three-distributaries-efficiency
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-2

## Question

Three distributaries are used for irrigation. The details are given below. Find which one is more efficient.

| | Distributary-1 | Distributary-2 | Distributary-3 |
|---|---|---|---|
| Discharge | 15 m³/s | 20 m³/s | 25 m³/s |
| C.C.A | 15,000 ha | 25,000 ha | 30,000 ha |
| Intensity of irrigation | 60% | 80% | 50% |
| Base period | 200 days (cotton crop) | 120 days (wheat crop) | 365 days (sugarcane) |

## Short answer

Efficiency is measured by duty (A/Q). Distributary-2 has the highest duty of 1000 ha/cumec (area 20000 ha, Q 20 cumec). Distributaries-1 and -3 both have 600 ha/cumec. Therefore, Distributary-2 is most efficient.

## Answer

**Idea.** The efficiency of a distributary in using water is measured by its **duty**: the area irrigated per cumec of discharge during the base period. A higher duty means more area irrigated with the same water.

**Step 1: Area irrigated** $= \text{CCA}\times\text{intensity}$. **Step 2: Duty** $D = A/Q$. **Step 3: Delta** $\Delta = 8.64B/D$ (m).

| | Area irrigated = CCA x intensity (ha) | Q (cumec) | Duty = A/Q (ha/cumec) | Delta = 8.64B/D (m) |
|---|---|---|---|---|
| Distributary-1 | 9,000 | 15 | 600 | 2.880 |
| Distributary-2 | 20,000 | 20 | 1000 | 1.037 |
| Distributary-3 | 15,000 | 25 | 600 | 5.256 |

Sample calculation (Distributary-2): $A = 25000\times0.80 = 20000$ ha, $D = 20000/20 = 1000$ ha/cumec, $\Delta = 8.64\times120/1000 = 1.037$ m.

**Comparison:** duty is 600, 1000 and 600 ha/cumec respectively.

**Answer: Distributary-2 is the most efficient** (highest duty, 1000 ha/cumec; lowest water per hectare). Distributary-1 and -3 have the same duty, but their delta is high because cotton and sugarcane are long-base-period, high-water crops. The comparison is approximate, as the crops differ.

## Check yourself

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

1. What measure is used to compare how efficiently the distributaries use water?
   A. Duty: area irrigated per cumec of discharge
   B. Discharge alone
   C. Command area alone
   D. Base period alone
   Answer: A. Higher duty means more area irrigated per unit of flow. (Key point: Efficiency measure)

2. How is the area irrigated by each distributary found?
   A. CCA / intensity
   B. CCA x intensity of irrigation
   C. Discharge x base period
   D. CCA x base period
   Answer: B. E.g. Distributary-2: 25000 x 0.80 = 20000 ha. (Key point: Area irrigated)

3. Duties are 600, 1000 and 600 ha/cumec. Which is most efficient and why?
   A. Distributary-3, because it has the largest discharge
   B. Distributary-1, because it has the lowest discharge
   C. Distributary-2, because it has the highest duty and lowest delta
   D. All are equal
   Answer: C. Distributary-2 irrigates 20000 ha with 20 cumec = 1000 ha/cumec and delta 1.04 m. (Key point: Most efficient)

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