---
title: "Days inundated above 200 mm at 3 l/s/ha"
subject: "Irrigation and Drainage Engineering"
chapter: 9
key: "semester_6/irrigation_and_drainage_engineering:inundation-days-drainage-3lsha"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/inundation-days-drainage-3lsha
site: BCT Engineering
---

# Days inundated above 200 mm at 3 l/s/ha

Irrigation and Drainage Engineering · Chapter 9: Water Logging and Drainage

- Asked in: 2073 Bhadra, 4+2 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/inundation-days-drainage-3lsha
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-9

## Question

How many days the field will be inundated above 200 mm depth if a drainage rate of 3 l/s per ha is maintained by constructing internal drainage system? Will such system cause the depth to exceed 300 mm?

## Answer

A drainage rate of 3 l/s/ha is a fixed removal rate. The field is inundated above 200 mm for as long as the water level exceeds 200 mm, so the level history is traced for the design storm.

#### Data (from the standard problem this question follows)
Initial depth $h_0$ = 40 mm; maximum yearly 3-day rainfall 300 mm with a growth factor of 1.5 for the 10-year return period, so the design 3-day rainfall $R$ = 1.5 × 300 = 450 mm (150 mm/day); ET and deep percolation neglected.

$$
D = 3\ \text{l/s/ha} = 3\times\frac{86.4}{10} = 25.92\ \text{mm/day}
$$

(1 l/s/ha = 86.4 m³/ha/day = 8.64 mm/day.)

#### Rise during rain
Net rise = 150 − 25.92 = 124.08 mm/day. Time to reach 200 mm:

$$
t_1 = \frac{200-40}{124.08} = 1.29\ \text{days}
$$

Peak at the end of day 3:

$$
h_{peak} = 40 + 450 - 3\times25.92 = 412.2\ \text{mm}
$$

#### Fall after rain
Time to fall from 412.2 mm to 200 mm:

$$
t_2 = \frac{412.2-200}{25.92} = 8.19\ \text{days}
$$

| Stage | Depth (mm) | Time (days) |
|---|---|---|
| Start | 40 | 0 |
| Reaches 200 mm | 200 | 1.29 |
| Reaches 300 mm | 300 | 2.10 |
| Peak (rain stops) | 412 | 3.00 |
| Back to 300 mm | 300 | 7.33 |
| Back to 200 mm | 200 | 11.19 |

Duration above 200 mm = (3 − 1.29) + 8.19 = **9.90 days** (permitted: 3 days).

#### Will the depth exceed 300 mm?
Yes. The maximum depth is 412 mm, which is more than 300 mm, and the level stays above 300 mm for (3 − 2.10) + 4.33 = 5.23 days, against the permitted 1 day. So a drainage rate of 3 l/s/ha is inadequate; about 7.0 l/s/ha (60.6 mm/day) is needed to meet both limits.

If the 300 mm rainfall were used directly, without the growth factor, the peak would be 262 mm and the field would stay above 200 mm for 3.24 days.

**Answer: about 9.9 days above 200 mm; yes, the depth rises to about 412 mm, exceeding 300 mm for about 5.2 days.**

## Check yourself

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

1. What is 3 l/s/ha in mm/day?
   A. 2.592 mm/day
   B. 25.92 mm/day
   C. 259.2 mm/day
   D. 3 mm/day
   Answer: B. 1 l/s/ha = 86.4 m3/ha/day = 8.64 mm/day, so 3 l/s/ha = 25.92 mm/day. (Key point: Unit conversion)

2. How is the time to reach 200 mm computed during the storm?
   A. t1 = 200/100 = 2 days
   B. t1 = (200 - 40)/100 = 1.6 days
   C. t1 = (200 - 40)/(100 - 25.92) = 2.16 days
   D. t1 = (200 - 40)/25.92 = 6.2 days
   Answer: C. Level rises at the net rate rain minus drainage = 74.08 mm/day from 40 mm to 200 mm. (Key point: Rise during rain)

3. How long is the field above 200 mm?
   A. About 3.24 days = (3 - 2.16) + 2.40
   B. About 2.16 days
   C. About 5.40 days
   D. About 2.40 days
   Answer: A. Time above 200 mm counts from reaching 200 mm (day 2.16) to the fall back to 200 mm (day 5.40) = 3.24 days. (Key point: Days above 200 mm)

4. Does the depth exceed 300 mm?
   A. Yes, the peak is 340 mm
   B. Yes, the peak is 412 mm for the 300 mm storm
   C. No, because the peak equals 200 mm
   D. No, the peak is 40 + 300 - 3 x 25.92 = 262 mm
   Answer: D. With the 300 mm storm the peak is 262 mm, below 300 mm. (Key point: 300 mm check)

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