---
title: "Principles of IUH development by Clark's method"
subject: "Engineering Hydrology"
chapter: 7
key: "semester_5/engineering_hydrology:clark-iuh-principles"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/clark-iuh-principles
site: BCT Engineering
---

# Principles of IUH development by Clark's method

Engineering Hydrology · Chapter 7: Flow Routing

- Asked in: 2079 Bhadra, 6 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/clark-iuh-principles
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-7

## Question

Explain briefly the basic principles involved in the development of IUH by Clark's method.

## Short answer

Clark's method develops the IUH by first translating excess rainfall via a time-area diagram of isochrones, then routing the translation hydrograph through a linear reservoir at the outlet with storage constant K. The outflow ordinates form the IUH; averaging two successive ordinates gives the unit hydrograph.

## Answer

Clark's method develops the IUH of a catchment by treating the transformation of excess rainfall into runoff as two separate processes.

#### 1. Translation (pure delay, no storage effect)

- The catchment is divided by **isochrones**, lines of equal travel time to the outlet, up to the time of concentration $t_c$.
- The area between consecutive isochrones ($A_i$) gives the **time-area diagram**. Excess rain falling on a strip reaches the outlet after a time equal to its travel time.
- For 1 cm excess rain, the inflow to the outlet from each strip is $I_i = 2.78\,A_i/\Delta t$ (m³/s), which is the translation hydrograph.

#### 2. Attenuation (storage effect)

- All storage of the basin is lumped into **one linear reservoir** at the outlet, with $S = KO$ ($K$ = storage constant, in hours).
- The translation hydrograph is routed through it using continuity $I - O = dS/dt$:
$$
O_2 = C_0 (I_1 + I_2) + C_2 O_1,\quad C_0 = \frac{\Delta t}{2K + \Delta t},\quad C_2 = \frac{2K - \Delta t}{2K + \Delta t}
$$

#### Result

The outflow ordinates form the **IUH**; the average of two successive ordinates, $U_n = (O_n + O_{n-1})/2$, gives the $\Delta t$-hour unit hydrograph.

Basic assumptions: uniform excess rain over the basin, constant travel velocity (fixed isochrones), a single linear reservoir, and $t_c$ and $K$ constant. The parameters $t_c$ and $K$ are obtained from observed hydrographs or regional relations.

## Check yourself

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

1. Clark's method treats excess rainfall to runoff as which two processes?
   A. Translation (pure delay) and attenuation (storage)
   B. Infiltration and percolation
   C. Evaporation and transpiration
   D. Interception and depression storage
   Answer: A. Translation is a delay by isochrones; attenuation is storage in a single linear reservoir. (Key point: Two processes)

2. What does the area between consecutive isochrones represent?
   A. Rainfall volume
   B. Strip area A_i whose rain reaches the outlet after its travel time
   C. Storage constant
   D. Infiltration area
   Answer: B. These strip areas give the time-area diagram and the translation inflow 2.78 A_i/dt. (Key point: Time-area diagram)

3. How is basin storage represented?
   A. Many reservoirs in series
   B. A single linear reservoir at the outlet, S = K O
   C. A constant storage
   D. No storage
   Answer: B. All storage is lumped into one linear reservoir at the outlet. (Key point: Storage representation)

4. Which is an assumption of the method?
   A. Constant travel velocity with fixed isochrones
   B. Rainfall varies strongly across the basin
   C. K changes with discharge
   D. Storage is nonlinear
   Answer: A. The method assumes uniform excess rain, constant velocity, a linear reservoir and constant tc and K. (Key point: Assumptions)

## Related in Engineering Hydrology

- [Clark's 2-h IUH, 110 km2](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aclark-2h-iuh-110km2) — Engineering Hydrology, chapter 7, asked 2×
- [Flood routing and Clark IUH method](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aflood-routing-clark-iuh) — Engineering Hydrology, chapter 7
- [Clark IUH, 180 km2 basin](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aiuh-180km2) — Engineering Hydrology, chapter 7, asked 2×
- [Clark IUH, 172 km2](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aiuh-172km2) — Engineering Hydrology, chapter 7, asked 2×
- [Clark IUH, 128 km2 basin](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aiuh-128km2) — Engineering Hydrology, chapter 7
- [Clark IUH, 157 km2 basin](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Aiuh-157km2) — Engineering Hydrology, chapter 7

## Related in other subjects

- [Principles of levelling; reciprocal levelling](https://www.bctengineer.com/question.md?key=semester_3%2Fsurveying_i%3Aprinciples-leveling-and-reciprocal) — Surveying I, chapter 5, asked 2×
- [Activities in OO system development](https://www.bctengineer.com/question.md?key=semester_6%2Fobject_oriented_analysis_and_design%3Aactivities-oo-system-development) — Object Oriented Analysis and Design, chapter 1
- [Principles of mix design; factors not in DOE](https://www.bctengineer.com/question.md?key=semester_5%2Fconcrete_technology_and_masonry_structure%3Amix-design-principles-doe-omitted) — Concrete Technology and Masonry Structure, chapter 3
- [Testing principles and testability](https://www.bctengineer.com/question.md?key=semester_5%2Fsoftware_engineering%3Atesting-principles) — Software Engineering, chapter 8