---
title: "Drainage rate (mm/day), initial 55 mm"
subject: "Irrigation and Drainage Engineering"
chapter: 9
key: "semester_6/irrigation_and_drainage_engineering:drainage-rate-mmday-bunded-55mm"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/drainage-rate-mmday-bunded-55mm
site: BCT Engineering
---

# Drainage rate (mm/day), initial 55 mm

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

- Asked in: 2076 Bhadra, 7 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/drainage-rate-mmday-bunded-55mm
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-9

## Question

Determine drainage rate in mm/day required to meet the following conditions for healthy growth of rice in bunded field of plain area in Nepal. Initial water level in field = 55 mm; Maximum water level is 400 mm which may persist for up to 1 day; Depth of excess of 250 mm may persist for up to 2 days; No rainfall follows the design rainfall for several days; Design 3 days rainfall is 400 mm; Neglect ET and deep percolation losses.

## Answer

Rice tolerates standing water only within limits of depth and duration, so the drainage rate is chosen such that the field water level during and after the design storm stays within these limits. The field is a bunded rice field in the plains (Terai).

#### Given data and assumptions
- Initial depth $h_0$ = 55 mm; design 3-day rainfall $R$ = 400 mm, falling uniformly, so the rain rate $r = R/3$ = 133.3 mm/day
- Maximum depth 400 mm may persist for 1 day; depth above 250 mm may persist for 2 days
- ET and deep percolation neglected (safe side); drainage $D$ (mm/day) starts with the rain and is constant

#### Water level history
During the storm the level rises at $(r-D)$ per day, and after it the level falls at $D$ per day:

$$
\begin{aligned} h_{peak} &= h_0 + R - 3D \\ t_1 &= \frac{h_e-h_0}{r-D} \quad (\text{time to reach } h_e) \\ t_2 &= \frac{h_{peak}-h_e}{D} \quad (\text{time to fall back to } h_e) \\ T_e &= (3-t_1)+t_2 \le 2 \end{aligned}
$$

The duration condition above 250 mm governs. Trial values:

| D (mm/day) | Peak level (mm) | Time above limit (days) |
|---|---|---|
| 40 | 335 | 3.04 |
| 45 | 320 | 2.35 |
| 47.9 | 311 | 2.00 |
| 50 | 305 | 1.76 |
| 55 | 290 | 1.24 |

Solving $T_e$ = 2 days gives $D$ = 47.9 mm/day. Then:
- $h_{peak}$ = 55 + 400 − 3 × 47.9 = 311 mm, which is below 400 mm, so the 400 mm level is never reached and the 1-day limit is satisfied
- $t_1$ = 2.28 days, $t_2$ = 1.28 days, $T_e$ = (3 − 2.28) + 1.28 = 2.00 days

Conversion: 1 mm/day = 10 m³/ha/day = 0.1157 l/s/ha, so

$$
D = 47.9\times\frac{10}{86.4} = 5.54\ \text{l/s/ha}
$$

**Answer: drainage rate ≈ 47.9 mm/day** (≈ 5.5 l/s/ha); adopt 48 mm/day.

## Check yourself

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

1. How is the drainage rate chosen for rice in a bunded field?
   A. So that, after the design storm, the water level stays within the permitted depth and duration limits
   B. So that all the rainfall is removed on the same day it falls
   C. So that the field is kept completely dry at all times
   D. So that it equals the evapotranspiration rate
   Answer: A. Rice tolerates standing water only up to limits of depth and duration, so D is found so the level history respects both limits. (Key point: Idea of design)

2. With constant drainage D starting with the rain, what is the peak level at the end of the 3-day storm?
   A. h0 + R
   B. h0 + R - 3D
   C. h0 + R - D
   D. R - 3D
   Answer: B. Rain adds R in total while drainage removes D per day for 3 days, so peak = h0 + R - 3D. (Key point: Peak water level)

3. Which condition governs the design here?
   A. Time above 400 mm must not exceed 1 day
   B. The initial depth of 55 mm must be restored in 1 day
   C. Time above 250 mm must not exceed 2 days
   D. Deep percolation must be balanced
   Answer: C. The duration above 250 mm governs; the 400 mm limit is not even reached (peak is 311 mm). (Key point: Governing condition)

4. What drainage rate satisfies the 2-day limit above 250 mm?
   A. 40 mm/day
   B. 55 mm/day
   C. 133.3 mm/day
   D. 47.9 mm/day
   Answer: D. At D = 47.9 mm/day, Te = (3 - 2.28) + 1.28 = 2.00 days; 40 mm/day gives 3.04 days (too long). (Key point: Result)

## Close variants set in other exams

- [Drainage rate (l/s/ha) for bunded rice fields](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Adrainage-rate-lsha-bunded-rice-70bh) — Irrigation and Drainage Engineering, chapter 9, asked 3×

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