---
title: "Maximum rainfall intensity for 1, 3, 5 hr"
subject: "Engineering Hydrology"
chapter: 2
key: "semester_5/engineering_hydrology:max-intensity-1-3-5hr-7am"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/max-intensity-1-3-5hr-7am
site: BCT Engineering
---

# Maximum rainfall intensity for 1, 3, 5 hr

Engineering Hydrology · Chapter 2: Precipitation

- Asked in: 2080 Baisakh, 8 marks
- Video: [Maximum Intensity and Depth of Rainfall](https://www.youtube.com/watch?v=T2-4Nn0JZWs) — Revit for Civil Engineers
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/max-intensity-1-3-5hr-7am
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-2

## Question

Calculate the maximum intensity of rainfall for 1 hr, 3 hr and 5 hr with the following data.

| Duration | 7 am | 8 am | 9 am | 10 am | 11 am | 12 am | 1 am | 2 am | 3 am | 4 am | 5 am | 6 am | 7 am | 8 am |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rainfall (mm) | 10 | 8 | 6 | 12 | 5 | 0 | 2 | 5 | 8 | 12 | 7 | 6 | 0 | 0 |

## Short answer

For each duration, sum consecutive hourly rainfalls and divide by duration. Maximum intensities: 12.0 mm/h for 1 h, 9.0 mm/h for 3 h, and 8.2 mm/h for 5 h.

## Answer

The maximum depth for a duration $D$ is the largest sum of $D$ consecutive hourly values; the maximum intensity is that depth divided by $D$. Hourly rainfall (mm) in time order from 7 am: 10, 8, 6, 12, 5, 0, 2, 5, 8, 12, 7, 6, 0, 0 (total 81 mm).

#### 1-hour duration
Largest single hour $= 12$ mm, so $i_{max} = 12/1 = 12$ mm/h.

#### 3-hour duration
Sums of 3 consecutive hours: 24, 26, 23, 17, 7, 7, 15, 25, 27, 25, 13, 6.
Maximum $= 8 + 12 + 7 = 27$ mm, so $i_{max} = 27/3 = 9.0$ mm/h.

#### 5-hour duration
Sums of 5 consecutive hours: 41, 31, 25, 24, 20, 27, 34, 38, 33, 25.
Maximum $= 10+8+6+12+5 = 41$ mm (first five values), so $i_{max} = 41/5 = 8.2$ mm/h.

| Duration | Max depth (mm) | Max intensity (mm/h) |
|---|---|---|
| 1 h | 12 | 12.0 |
| 3 h | 27 | 9.0 |
| 5 h | 41 | 8.2 |

**Answer: Maximum intensities = 12.0 mm/h (1 h), 9.0 mm/h (3 h) and 8.2 mm/h (5 h).**

## Check yourself

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

1. How is the maximum intensity for a duration D found?
   A. Largest single hourly value divided by D
   B. Largest sum of D consecutive hourly values divided by D
   C. Total storm depth divided by D
   D. Average of all hourly values
   Answer: B. Find the largest depth in any D consecutive hours, then divide by D. (Key point: Method)

2. What is the maximum 3-hour intensity?
   A. 8.2 mm/h
   B. 12 mm/h
   C. 9.0 mm/h
   D. 27 mm/h
   Answer: C. Max 3-h depth is 8+12+7 = 27 mm, so intensity = 27/3 = 9.0 mm/h. (Key point: 3-hour result)

3. The maximum 5-hour depth and intensity are:
   A. 41 mm and 8.2 mm/h
   B. 38 mm and 7.6 mm/h
   C. 41 mm and 41 mm/h
   D. 34 mm and 6.8 mm/h
   Answer: A. First five values 10+8+6+12+5 = 41 mm; 41/5 = 8.2 mm/h. (Key point: 5-hour result)

4. How does maximum intensity change as duration increases (12, 9.0, 8.2 mm/h)?
   A. It increases
   B. It stays constant
   C. It decreases
   D. It first rises then falls
   Answer: C. Longer durations average in lower-rain hours, so the maximum average intensity falls. (Key point: Trend with duration)

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