---
title: "Basin area from 4-h unit hydrograph ordinates"
subject: "Engineering Hydrology"
chapter: 5
key: "semester_5/engineering_hydrology:area-of-basin-from-4h-uh"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/area-of-basin-from-4h-uh
site: BCT Engineering
---

# Basin area from 4-h unit hydrograph ordinates

Engineering Hydrology · Chapter 5: Hydrograph Analysis

- Asked in: 2072 Chaitra, 6 marks
- Video: [Unit Hydrograph Solved Problems | Engineering Hydrology](https://www.youtube.com/watch?v=nnuaxfeMvew) — APSEd
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/area-of-basin-from-4h-uh
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-5

## Question

Given below are ordinates of a 4 h unit hydrograph of a basin in m$^3$/s at one hour intervals.

4, 25, 44, 60, 70, 61, 52, 45, 38, 32, 27, 22, 18, 14, 11, 8, 6, 4, 2, 1

What is the area of the basin?

## Short answer

Sum of ordinates is 544 m³/s, volume = 544 × 3600 = 1.9584×10⁶ m³. Basin area = volume / 0.01 m = 195.8 km².

## Answer

A unit hydrograph represents **1 cm of direct runoff** from the whole basin. So the volume under the UH equals area × 1 cm.

#### Step 1: Volume under the UH
The ordinates are at 1 h intervals, so the volume is the sum of the ordinates × 1 h (3600 s).

$$
\sum Q = 4+25+44+60+70+61+52+45+38+32+27+22+18+14+11+8+6+4+2+1 = 544 \text{ m}^3/\text{s}
$$

$$
V = 544 \times 3600 = 1,958,400 \text{ m}^3
$$

#### Step 2: Area
$$
A = \frac{V}{\text{runoff depth}} = \frac{1,958,400}{0.01} = 195,840,000 \text{ m}^2 = 195.8 \text{ km}^2
$$

**Answer: Area of basin ≈ 195.8 km²** (the hourly ordinates are summed directly; the first and last ordinates are small, so a trapezoidal correction would change the result by less than 1 %).

## Check yourself

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

1. The volume under a UH equals:
   A. Area x 1 cm
   B. Peak x area
   C. Area x 4 cm
   D. Sum Q
   Answer: A. A UH is the response to 1 cm of runoff over the basin. (Key point: UH principle)

2. With ordinates at 1 h interval summing to 544 m^3/s, the volume is:
   A. 544 x 3600 = 1,958,400 m^3
   B. 544 x 4 x 3600
   C. 544 / 3600
   D. 544 x 1000
   Answer: A. Volume = sum Q x 3600 s. (Key point: Volume)

3. The basin area is:
   A. 195.8 km^2
   B. 783 km^2
   C. 19.6 km^2
   D. 1958 km^2
   Answer: A. A = 1,958,400/0.01 = 195.84 x 10^6 m^2 = 195.8 km^2. (Key point: Area)

## Related in Engineering Hydrology

- [2-hr UH from figure: area, flood, Tc, two storms](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Auh-2hr-figure-four-parts) — Engineering Hydrology, chapter 5
- [2-hr UH and flood hydrograph from storm](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Auh-2h-from-4h-three-storms) — Engineering Hydrology, chapter 5
- [Clark IUH, 128 km2 basin](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aiuh-128km2) — Engineering Hydrology, chapter 7
- [Intensity-duration graph from mass curve ordinates](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aintensity-duration-15-180min) — Engineering Hydrology, chapter 2
- [Flood hydrograph from 6-h UH, three storms](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Auh-6h-three-storms-30cumec) — Engineering Hydrology, chapter 5
- [S-curve: 2-hr hydrograph from 4-hr UH](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ascurve-4hr-to-2hr-12-5) — Engineering Hydrology, chapter 5

## Related in other subjects

- [Conductor selection, 100 MW 70 km 132 kV](https://www.bctengineer.com/question.md?key=semester_8%2Ftransmission_and_distribution_system_design%3Aconductor-selection-100mw-70km-132kv) — Transmission and Distribution System Design, chapter 4
- [AVL tree for 52, 65, 72, 15, 11, 32, 20](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Aavl-build-52-65-72) — Data Structure and Algorithm, chapter 6
- [Radix sort on 32, 45, 60, 83, ...](https://www.bctengineer.com/question.md?key=semester_4%2Fdata_structure_and_algorithm%3Aradix-sort-32-45-60) — Data Structure and Algorithm, chapter 7
- [Subnet 202.70.91.0/24 for 25, 16, 29, 11](https://www.bctengineer.com/question.md?key=semester_7%2Fcomputer_networks_and_security%3Asubnetting-202-70-91) — Computer Networks and Security, chapter 4, asked 2×