---
title: "Unit hydrograph, assumptions and limitations"
subject: "Engineering Hydrology"
chapter: 5
key: "semester_5/engineering_hydrology:uh-assumptions-limits"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/uh-assumptions-limits
site: BCT Engineering
---

# Unit hydrograph, assumptions and limitations

Engineering Hydrology · Chapter 5: Hydrograph Analysis

- Asked in: 2079 Bhadra, 2+4 marks; 2074 Asoj, 2+2 marks (asked 2 times)
- Video: [Unit Hydrograph Theory & Assumption in Detail | Unit Hydrograph Basics| Unit Hydrograph Concept| UH](https://www.youtube.com/watch?v=6xB3BZoxczA) — Professor Nidhi Trivedi
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/uh-assumptions-limits
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-5

## Question

What is Unit hydrograph? What are assumptions and limitations of UH?

## Short answer

A unit hydrograph is the direct runoff hydrograph from 1 cm of effective rainfall uniformly over a basin in a specified duration. Assumptions: uniform intensity and distribution, constant base time, linearity, superposition. Limitations: basin size 25–5000 km², non-uniform rain, not for snowmelt or regulated basins, needs S-curve for different durations.

## Answer

#### Unit hydrograph (UH)
A **unit hydrograph** (Sherman, 1932) is the direct runoff hydrograph resulting from **1 unit (1 cm or 1 mm) of effective rainfall** falling uniformly over the whole basin at a uniform rate during a specified duration $D$. It is written as the $D$-hour unit hydrograph.

```text
 Q |      /\
   |     /  \
   |    /    \___
   |___/         \____
   +------------------- t
   |<-- Tb (base) --->|
```

#### Assumptions
1. **Constant intensity:** effective rainfall is uniform in intensity over the duration $D$.
2. **Uniform distribution:** effective rainfall is uniformly spread over the whole drainage area.
3. **Constant base time:** the base time of the direct runoff hydrograph is the same for all storms of equal duration, whatever the intensity.
4. **Linearity (proportionality):** ordinates of DRH due to the same duration are directly proportional to the effective rainfall depth; for twice the rain, ordinates are doubled.
5. **Superposition (time invariance):** the hydrographs of successive rain periods can be added; the catchment response does not change with time.
6. All characteristics of the catchment are reflected in the shape of the UH.

#### Limitations
1. Applies to catchments of about 25 to 5000 km$^2$; very small (< 25 km$^2$) or very large basins (> 5000 km$^2$) violate the assumptions.
2. Not valid when rainfall is not uniform in space or time, or storms move across the basin.
3. Not suitable for snowmelt-dominated or heavily regulated basins, or basins with large storage (lakes, reservoirs).
4. Cannot handle effective rainfall of different durations without S-curve conversion.
5. Real catchment behaviour is not exactly linear; UH from small storms may differ from that of large floods.
6. Needs reliable rainfall and streamflow records; an ungauged basin needs synthetic methods.
7. Derived UH is valid only for that point on the stream.

## Check yourself

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

1. A D-hour unit hydrograph is the direct runoff hydrograph produced by:
   A. 1 cm of total rainfall over the basin in any time
   B. 1 cm of effective rainfall falling uniformly over the basin at a uniform rate during D hours
   C. 1 cm of effective rainfall falling in one hour only
   D. The peak discharge of a storm divided by the basin area
   Answer: B. A UH is the DRH from 1 unit of effective (not total) rainfall, uniformly distributed in space and over the specified duration D. (Key point: Definition of UH)

2. According to the linearity (proportionality) assumption, if the effective rainfall of the same duration is doubled, then:
   A. The base time doubles
   B. The DRH ordinates double while the base time stays the same
   C. The peak doubles and occurs twice as late
   D. The ordinates stay the same but the base time halves
   Answer: B. Ordinates are directly proportional to effective rainfall depth, while base time is assumed constant for equal-duration storms. (Key point: Linearity assumption)

3. Which assumption says storms of equal duration but different intensity give DRHs of the same length?
   A. Superposition
   B. Uniform distribution
   C. Constant base time
   D. Time invariance of loss
   Answer: C. Constant base time means the base length of the DRH is the same for all storms of equal duration. (Key point: Constant base time)

4. Which basin is NOT suited to the unit hydrograph method?
   A. A 500 km^2 gauged basin with uniform rain
   B. A 1000 km^2 basin with a long record
   C. A basin with large lakes/reservoirs or snowmelt-dominated flow
   D. A 100 km^2 basin with reliable rainfall data
   Answer: C. UH assumes linear response; heavy storage, regulation or snowmelt violate it. Applicability is also about 25-5000 km^2. (Key point: Limitations of UH)

## Related in Engineering Hydrology

- [Unit hydrograph, assumptions, base flow separation](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Auh-assumptions-baseflow-methods) — Engineering Hydrology, chapter 5
- [Unit hydrograph and UH for multiple storms](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Auh-define-multiple-storm) — Engineering Hydrology, chapter 5, asked 2×
- [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
- [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
- [S-hydrograph from rectangular 1-hr UH](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Ascurve-rectangular-1hr-uh) — Engineering Hydrology, chapter 5
- [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