--- title: "Duty and head discharge, 4000 ha channel" subject: "Irrigation and Drainage Engineering" chapter: 2 key: "semester_6/irrigation_and_drainage_engineering:duty-head-discharge-4000ha-70pct" source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/duty-head-discharge-4000ha-70pct site: BCT Engineering --- # Duty and head discharge, 4000 ha channel Irrigation and Drainage Engineering · Chapter 2: Irrigation Water Requirements - Asked in: 2078 Poush, 6 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/duty-head-discharge-4000ha-70pct - Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-2 ## Question The command area of a channel is 4000 hectares. The intensity of irrigation of a crop is 70%. The crop requires 60 cm of water in 15 days, when the effective rainfall is recorded as 15 cm during that period. Find: (i) The duty at the head of field. (ii) The duty at the head of channel (iii) The head discharge at the head of channel. Assume total losses as 15%. ## Short answer Net irrigation depth is 45 cm. Duty at field head is 288 ha/cumec, at channel head (after 15% losses) is 244.8 ha/cumec. Head discharge required is 11.44 m³/s. ## Answer **Given:** CCA = 4000 ha, intensity = 70%, crop water need = 60 cm in $B=15$ days, effective rainfall = 15 cm, total losses = 15%. **Area irrigated:** $A = 0.70\times 4000 = 2800$ ha. **Net depth from irrigation (delta at the field)** $$ \Delta = 60 - 15 = 45\ \text{cm} = 0.45\ \text{m} $$ **(i) Duty at the head of the field** $$ D_{field} = \frac{8.64\,B}{\Delta} = \frac{8.64\times 15}{0.45} = 288.0\ \text{ha/cumec} $$ **(ii) Duty at the head of the channel.** Losses of 15% reduce the area served per cumec: $$ D_{head} = 288.0\times(1-0.15) = 244.8\ \text{ha/cumec} $$ **(iii) Head discharge of the channel** $$ Q = \frac{A}{D_{head}} = \frac{2800}{244.8} = 11.44\ \text{cumec} $$ **Answer: (i) 288 ha/cumec; (ii) 244.8 ha/cumec; (iii) 11.44 cumec.** ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. The crop needs 60 cm and effective rainfall is 15 cm. What delta does irrigation have to supply? A. 45 cm B. 75 cm C. 60 cm D. 15 cm Answer: A. Rainfall meets part of the need, so delta = 60 - 15 = 45 cm = 0.45 m. (Key point: Net irrigation depth) 2. Which expression gives the duty at the field head and its value? A. D = 8.64 delta / B = 25.9 ha/cumec B. D = 8.64 B / delta = 288 ha/cumec C. D = 8.64 B delta = 58 ha/cumec D. D = B / delta = 33 ha/cumec Answer: B. With B = 15 days and delta = 0.45 m, D = 8.64 x 15/0.45 = 288 ha/cumec. (Key point: Duty at field head) 3. How do the 15% losses change the duty at the head of the channel? A. Duty increases to 288/0.85 = 338.8 B. Duty stays 288 C. Duty decreases to 288 x 0.85 = 244.8 ha/cumec D. Duty becomes 288 - 15 = 273 Answer: C. Losses mean more discharge is needed at the head per hectare, so the area served per cumec falls. (Key point: Duty at channel head) 4. The irrigated area is 70% of 4000 ha. What is the head discharge? A. 4000/244.8 = 16.3 cumec B. 2800/288 = 9.72 cumec C. 4000/288 = 13.9 cumec D. 2800/244.8 = 11.44 cumec Answer: D. Q = A/D_head using the actual irrigated area of 2800 ha. (Key point: Head discharge) ## Related in Irrigation and Drainage Engineering - [Duty and minor discharge, wheat 400 ha](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Aminor-wheat-400ha-duty-discharge) — Irrigation and Drainage Engineering, chapter 2 - [Command area, crop rotation, necessity](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acommand-area-crop-rotation) — Irrigation and Drainage Engineering, chapter 1 - [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 - [Field channel discharge for gram and wheat](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Afield-channel-gram-wheat-2000ha) — Irrigation and Drainage Engineering, chapter 2 - [Outlet discharge: wheat and rice, 10000 ha](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Akor-outlet-discharge-wheat-rice-10000ha) — Irrigation and Drainage Engineering, chapter 2 - [Reservoir capacity with intensity table](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Areservoir-capacity-40000ha-table-78p) — Irrigation and Drainage Engineering, chapter 2 ## Related in other subjects - [Settling basin 60 m³/s, 0.15 mm, head 300 m](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Asettling-basin-60cumec-300m-015mm-turbulence) — Hydropower Engineering, chapter 5, asked 2× - [MOC numerical: discharge and head at P (30 cm pipe)](https://www.bctengineer.com/question.md?key=semester_8%2Fcomputational_techniques_in_civil_engineering%3Amoc-pipe-discharge-head-pc-30cm) — Computational Techniques in Civil Engineering, chapter 6 - [Settling basin 60 m³/s, 0.15 mm, head 100 m](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Asettling-basin-60cumec-head-100m-015mm) — Hydropower Engineering, chapter 5 - [Channel earthwork and land area, 50 cm fall](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Achannel-land-acquisition-h) — Estimating and Costing, chapter 6, asked 2×