---
title: "Effect of urbanization on UH and storm runoff"
subject: "Engineering Hydrology"
chapter: 5
key: "semester_5/engineering_hydrology:urbanization-uh-peak-increase"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/urbanization-uh-peak-increase
site: BCT Engineering
---

# Effect of urbanization on UH and storm runoff

Engineering Hydrology · Chapter 5: Hydrograph Analysis

- Asked in: 2069 Chaitra, 14 marks; 2067 Shrawan (old course), 16 marks (asked 2 times)
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/urbanization-uh-peak-increase
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-5

## Question

A 1 hour unit hydrograph of a small catchment is triangular with peak value of 3.6 m$^3$/s occurring at 2 hours from the start and a base time of 6 hours. Following urbanization over a period of two decades, the infiltration index $\phi$ has decreased from 0.7 cm/h to 0.4 cm/h. Also one hour unit hydrograph has now peak of 6.0 m$^3$/s at 1 hour from start and time of base is 4 hours. If a design storm has intensities of 4 cm/hour and 3 cm/h for two consecutive one hour intervals,

a) Estimate the percentage increase in the peak storm runoff due to urbanization.
b) The volume of flood runoff due to urbanization.

## Short answer

Effective rainfall computed with φ indices, DRH by superposition of 1-h UH triangles. Peak increases from 17.19 to 30.00 m³/s (74.5%). Flood runoff volume after urbanization: 2.68×10⁵ m³, an increase of about 5.0×10⁴ m³ (23% over pre-urban 2.18×10⁵ m³).

## Answer

**Method:** effective rainfall (ER) is rainfall minus $\phi$ loss for each hour; the DRH is found by superposition of the 1-h unit hydrographs.

#### Unit hydrographs (hourly ordinates, triangles)

| t (h) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Before: peak 3.6 at 2 h, base 6 h (m$^3$/s) | 0 | 1.8 | 3.6 | 2.7 | 1.8 | 0.9 | 0 |
| After: peak 6.0 at 1 h, base 4 h (m$^3$/s) | 0 | 6.0 | 4.0 | 2.0 | 0 | 0 | 0 |

(Before: rising limb 0 to 3.6 in 2 h; falling limb 3.6 to 0 in 4 h. After: rising 0 to 6.0 in 1 h; falling 6.0 to 0 in 3 h.)

#### Effective rainfall
Storm intensities: 4 cm/h in hour 1 and 3 cm/h in hour 2.

| | Before ($\phi=0.7$) | After ($\phi=0.4$) |
|---|---|---|
| Hour 1 ER | 4 - 0.7 = 3.3 cm | 4 - 0.4 = 3.6 cm |
| Hour 2 ER | 3 - 0.7 = 2.3 cm | 3 - 0.4 = 2.6 cm |

#### Storm hydrograph $Q(t) = P_1\,u(t) + P_2\,u(t-1)$

| t (h) | Before (m$^3$/s) | After (m$^3$/s) |
|---|---|---|
| 1 | 3.3(1.8) = 5.94 | 3.6(6.0) = 21.60 |
| 2 | 3.3(3.6)+2.3(1.8) = 16.02 | 3.6(4.0)+2.6(6.0) = 30.00 |
| 3 | 3.3(2.7)+2.3(3.6) = 17.19 | 3.6(2.0)+2.6(4.0) = 17.60 |
| 4 | 3.3(1.8)+2.3(2.7) = 12.15 | 0+2.6(2.0) = 5.20 |
| 5 | 3.3(0.9)+2.3(1.8) = 7.11 | 0 |
| 6 | 2.3(0.9) = 2.07 | 0 |
| Peak | **17.19** at 3 h | **30.00** at 2 h |

#### (a) Increase in peak
$$
\text{Increase}=\frac{30.00-17.19}{17.19}\times100 = 74.5\ \%
$$

#### (b) Volume of flood runoff
$$
V = \Delta t\sum Q = 3600\times\sum Q
$$
- Before: $\sum Q = 60.48$ m$^3$/s, $V = 217\,728$ m$^3$ (this equals 5.6 cm over the 3.888 km$^2$ catchment area implied by its unit hydrograph).
- After urbanization: $\sum Q = 74.40$ m$^3$/s, $V = 267\,840$ m$^3$ (6.2 cm over 4.32 km$^2$ implied by its unit hydrograph).

**Answer: (a) Peak increases by about 74.5 % (17.19 to 30.00 m$^3$/s). (b) The flood runoff volume after urbanization is about 2.68 x 10$^5$ m$^3$, an increase of about 50 100 m$^3$ (23 %) over the pre-urban 2.18 x 10$^5$ m$^3$.**

## Check yourself

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

1. With phi = 0.4 cm/h after urbanization and storm intensities 4 and 3 cm/h, the effective rainfall of the two hours is:
   A. 3.3 cm and 2.3 cm
   B. 3.6 cm and 2.6 cm
   C. 4.4 cm and 3.4 cm
   D. 3.6 cm and 3.0 cm
   Answer: B. ER = intensity - phi for each hour: 4-0.4 = 3.6 cm and 3-0.4 = 2.6 cm. (Key point: Effective rainfall)

2. For two consecutive one-hour effective rainfalls P1 and P2 and 1-h UH u(t), the storm hydrograph is:
   A. Q(t) = P1 u(t) + P2 u(t-1)
   B. Q(t) = (P1+P2) u(t)
   C. Q(t) = P1 u(t) - P2 u(t-1)
   D. Q(t) = P1 P2 u(t)
   Answer: A. Each pulse gives a scaled UH; the second one is lagged by 1 h and the responses add. (Key point: Superposition formula)

3. The post-urban peak is 30.0 m^3/s and the pre-urban peak is 17.19 m^3/s. The percentage increase is about:
   A. 42.7 %
   B. 57.3 %
   C. 74.5 %
   D. 174.5 %
   Answer: C. (30.00 - 17.19)/17.19 x 100 = 74.5 %, measured relative to the original peak. (Key point: Peak after urbanization)

4. The flood runoff volume from the hydrograph ordinates (hourly) is found by:
   A. Peak discharge x 3600
   B. Sum of ordinates x 3600 s
   C. Average of ordinates x basin area
   D. Sum of ordinates divided by 3600
   Answer: B. V = Delta t x sum Q = 3600 x sum Q, since ordinates are at 1 h intervals. (Key point: Runoff volume)

## Related in Engineering Hydrology

- [Derive UH from storm, peak flow from two storms](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Auh-from-storm-then-peak-two) — Engineering Hydrology, chapter 5
- [Derive 4-hr UH from triangular direct runoff hydrograph](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Atriangular-dro-4hr-uh) — Engineering Hydrology, chapter 5
- [Flood hydrograph from 4-h UH, 50 m3/s base](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aflood-hydrograph-4h-uh-3-5) — Engineering Hydrology, chapter 5, asked 2×
- [Total rainfall, runoff and peak discharge with phi-index](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aphi-index-50ha-2-5) — Engineering Hydrology, chapter 3
- [Construct 3-h UH and flood hydrograph, 524.88 ha](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Auh-3h-triangular-524-88ha) — Engineering Hydrology, chapter 5
- [2-h UH by S-curve from storm hydrograph](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ascurve-2h-uh-4successive-hrs) — Engineering Hydrology, chapter 5

## Related in other subjects

- [Storm water from a 45 ha catchment](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Astorm-water-catchment-surfaces) — Sanitary Engineering, chapter 2