## What are Hydrology and Hydrograph?

Hydrology is the science which deals with the study of water on the earth’s surface. The word Hydrograph is derived from the word hydro which means water. Hydrograph is basically a graph in which the discharge is plotted against the time interval at a specific point in a river or other channel. In a hydrograph, the discharge is plotted along the y-axis and time interval is plotted along the x-axis. Hydrograph is used to estimate the runoff. The variations in discharges with the change in time is shown by a hydrograph. It was revealed that the total discharge at an outlet increases with time by a kinematic wave model.

## Components of Hydrograph

### Rising limb

As the rainfall continues more and more flow from distant parts reach the basin outlet and thus the runoff increases with the increase in time. In the hydrograph fig. given above the point from A to B represents the rising limb.

### Crest segment

The crest segment is one of the most important parts of the hydrograph and it represents the highest point in a hydrograph. In the above figure, point C represents the crest segment of the hydrograph.

### Recession limb or falling limb

As the rainfall decreases or stops the discharge into the basin outlet decreases thus the flow in the stream or river decreases. The recession limb extends from the point where the hydrograph starts decreasing at the end of the crest segment to the beginning of the natural groundwater flow. In the above figure points- 11 to 6, represent the falling limb.

- The rising limb and crest segment of the hydrograph depends both on catchment factors and storm factors.
- For calculating the rising limb of 1D flow for isochrone indication Hec-1 approach is recommended.
- The recession limb is independent of the storm factor and depends only on the catchment factor.

### Basin lag time

Basin lag time is the difference between the peak of the storm event and the peak of the discharge.

## Unit Hydrograph

- A unit hydrograph may be defined as the direct runoff hydrograph produced by a rainstorm of a specified storm duration which results in a runoff with a depth of 1 cm spread over the entire catchment area or land use as the drainage basin. It may also be defined as the DRH (Direct Run-off Hydrograph) resulting from one unit depth (usually 1cm) of constant rainfall intensity occurring uniformly over the catchment basin for a specified storm duration. The runoff volume under the hydrograph represents 1 cm and hence it is called unit hydrograph.
- Here the distribution of storm is considered to be uniform all over the catchment area and the runoff is constant which is equal to 1 cm.
- Ordinate of the unit hydrograph is the ratio of ordinate of direct runoff hydrograph to the runoff depth multiplied by 1 cm. Mathematically, ordinate of unit hydrograph = $\frac{OrdinateofDRH}{Runoffcm}\times 1cm$
- It can be used to determine the volume of direct runoff of any storm occurring in the catchment.
- Unit hydrograph (UHG) is also a direct runoff hydrograph (DRH), but the runoff in the unit hydrograph is 1 cm which remains constant but it is not constant for direct runoff hydrograph.
- Unit hydrograph was proposed by L.K Sherman in 1932. L.K Sherman's theory of unit hydrograph: L.K Sherman proposed that if two or more rainfalls of similar characteristics feed a drainage basin the hydrograph obtained from each of the rain would be similar.
- General dimensionless unit hydrograph is also a way of formulating synthetic unit hydrograph. The procedure is based on the succession of several linear reservoirs. It has two parameters, the courant number C and N the number of linear reservoirs, once C and N are chosen a dimensionless unit hydrograph is obtained. The succession of linear reservoirs may be made dimensionless without hesitation.
- If the effective rainfall has a continuous variation in time, the ordinate of hydrograph at moment ‘t’ in (n-m) is expressed as a function of unit hydrograph by Duhamel integral of convolution.

## Derivation of unit Hydrograph

Unit hydrograph from an isolated storm may be prepared as:

- Select a unit period of intense rainfall/storm duration from the past records.
- Separate the groundwater flow/base flow
- Determine the volume of direct runoff

**Direct runoff ordinate= Total ordinates of the hydrograph – base flow ordinates.**

- Determine the effective rainfall

Effective rainfall = $\frac{Volumeofdirectrunoff}{areaofwatershed}$

- Calculate the ordinates of unit hydrograph

Ordinate of unit hydrograph = $\frac{Ordinatesofdirectrunoff}{effectiverainfall}$

## Assumptions of unit Hydrograph

The basic assumptions of unit hydrograph are:

- Time invariance: The runoff produced from a given drainage basin due to a given effective rainfall shall always be the same irrespective of the time of when it occurred.
- Linear response: The direct runoff response to the rainfall excess is assumed to be linear.
- Effective rainfall is assumed to be uniformly distributed over the entire land use as the drainage basin. With the physical characteristics of the basin remaining constant the hydrograph of similar rainfalls has similar shapes to a considerable degree.
- The physical characteristics of a drainage basin are reflected by the hydrograph of a given base period.
- Unit hydrograph method is applicable for small basins small enough not to cause major changes in hydrograph shape. It cannot give reliable results for basin exceeding about 500 sq. km and are also not used for small basin having are lesser than 2 sq. km
- The ordinates of flow are proportional to the volume of runoff for all storms of a given duration on the assumption that the time base of all the hydrographs resulting from storms of a given duration is constant.

## Estimation of direct runoff by using direct runoff Hydrograph

- Volume of runoff = area of runoff
- Depth of runoff = $\frac{Volumeofrunoff}{catchmentarea}$

If direct runoff hydrograph is triangular in shape, then

- Volume of runoff = area of runoff

Volume of runoff = $\frac{1}{2}\times Q\times dt$

- Depth of runoff = $\frac{volumeofrunoff}{catchmentarea}$

If the direct runoff hydrograph is trapezoidal in shape, then

1) Volume of runoff = area of runoff

$Volumeofrunoff=\left(\frac{dt1+dt2}{2}\right)\times Q$

- Depth of runoff = $\frac{Volumeofrunoff}{catchmentarea}$

## Construction of unit Hydrograph from Storm Hydrograph

1) Volume of runoff = area of runoff

2) Depth of runoff = $\frac{Volumeofrunoff}{catchmentarea}$

3) Catchment Area = $\frac{Volumeofrunoff}{depthofrunoff}$

## S-Curve

The hydrograph that results from an infinite series of runoff increments of 1 cm/h is called s-curve. It is a continuously rising curve that ultimately attains a constant value after a time equal to the base of the unit hydrograph minus one unit duration. S-curve is also known as summation hydrograph. S-curve is used for converting a given hydrograph to either a shorter or longer duration.

## Context and Applications

A unit hydrograph is very important for the establishment of the relationship between Effective Rainfall hyetograph and direct rainfall hydrograph. Design Storm is the criteria used in context to strength or capacity. It is used in the design of hydraulic structures like a dam considering the design storm and storm gutters on streets are constructed large enough to hold flood water which again is calculated using design storm. Also, Estimates the peak discharges which may also serve as a warning for flood disasters in case of heavy runoff. The Hydrologic Modelling System (HEC-HMS) is software for hydrologic analysis and designed to stimulate the complete process of hydrology for dendritic watershed systems.

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for

- Bachelors of Technology (Civil Engineering)
- Bachelors in Technology (Mechanical Engineering)
- Bachelors in Science in Physics
- Masters in Science in Physics

## Practice Problems

1. A 4 hours unit hydrograph for the basin can be approximate as a triangle with a base period of 48 hours and a peak of ordinate $300\frac{{m}^{3}}{s}$. What is the area of the catchment basin in $k{m}^{2}$?

Solution: Given, $B=48h$

$Q=300\frac{{m}^{3}}{s}$

$\mathrm{Volume}\mathrm{of}\mathrm{runoff}=\mathrm{area}\mathrm{of}\mathrm{runoff}$

$=\frac{1}{2}\times Q\times \mathrm{dt}$

$=\frac{1}{2}\times 48h\times 300\frac{{m}^{3}}{s}$

$=25.9\times {10}^{6}{m}^{3}$

$Areaofcatchment=\frac{Volumeofrunoff}{depthofrunoff}$

$=\frac{25.9\times {10}^{6}{m}^{3}}{1c{m}^{3}}$

$=25.9\times 100\times {10}^{6}{m}^{2}\phantom{\rule{0ex}{0ex}}=2590k{m}^{2}$

2. Given below are the ordinates of a 6h unit hydrograph for a catchment. Calculate the ordinates of the DRH due to rainfall excess of 3.5 cm occurring in 6h.

Time interval (h) | 0 | 3 | 6 | 9 | 12 | 15 |

Unit hydrograph ordinates $\left(\frac{{m}^{3}}{s}\right)$ | 0 | 25 | 50 | 85 | 125 | 160 |

Solution.

Time interval (h) | Ordinates of 6-h UH $\left(\frac{{m}^{3}}{s}\right)$ | Ordinates of 3.5 cm DRH $\left(\frac{{m}^{3}}{s}\right)$ |

0 | 0 | 0 |

3 | 25 | 87.5 |

6 | 50 | 175.0 |

9 | 58 | 297.5 |

12 | 125 | 437.5 |

15 | 160 | 560 |

Here, the ordinate of 3.5 cm DRH for the time interval 3 = $ordinateofUH\times effectiverainfall$

$=25\times 3.5$

$=87.5$

Similarly calculate the DRH for other time intervals.

## Practice Problems

1. The science of Hydrology deals with which of the following?

- Rainwater
- River
- Seawater
- Surface and groundwater

Answer- d

Explanation: Hydrology is the science which deals with the study of water on the earth’s surface.

2. What causes the surface runoff?

- Initial rain
- Residual rain
- Rain in the net supply interval
- All of the above

Answer- c

Explanation: Surface runoff occurs after the soil has been saturated to an extend where the water can flow freely over the surface with minimum infiltration.

3. What is the Hydrograph representing one cm of runoff from a rainfall of some unit duration and specified distribution known as?

- Hyetograph
- Flood hydrograph
- Unit hydrograph
- None of these

Answer- c

Explanation: Unit hydrograph is a DRH (Direct Runoff Hydrograph) resulting from one unit depth (usually 1cm) of constant rainfall intensity occurring uniformly over the catchment basin for a specified storm duration

4. What is run-off measured in?

- $\frac{{m}^{3}}{s}$
- $\frac{{m}^{3}}{min}$
- $\frac{c{m}^{3}}{h}$
- None of these

Answer- a

Explanation: Runoff = discharge/time

5. Hydrograph is a physical representation of

- Surface runoff
- Groundwater flow
- Rainfall
- None of these

Answer- d

Explanation: It is a graphical representation of discharge against time.

**Related Concept**s

- Methods of base flow separation

1) Straight-line method

2) Fix base method

3) Variable slope method

- Effective rainfall hyetograph
- Runoff
- Arithmetic mean method
- Thiessen Polygon method
- Isohyet method.

### Want more help with your civil engineering homework?

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.

### Search. Solve. Succeed!

Study smarter access to millions of step-by step textbook solutions, our Q&A library, and AI powered Math Solver. Plus, you get 30 questions to ask an expert each month.

## Unit Hydrograph Homework Questions from Fellow Students

Browse our recently answered Unit Hydrograph homework questions.

### Search. Solve. Succeed!

Study smarter access to millions of step-by step textbook solutions, our Q&A library, and AI powered Math Solver. Plus, you get 30 questions to ask an expert each month.