In this article we will discuss about:- 1. Introduction to Unit Hydrograph 2. Assumptions in the Theory of Unit Hydrograph 3. Construction 4. To Develop Storm Hydrograph 5. Use 6. Limitations.
Introduction to Unit Hydrograph:
The basis of unit hydrograph is that if two identical rainfalls occur on a drainage basin having identical conditions prior to the rains, the hydrograph of run-off from the two storms would be expected to be same.
In actual conditions two identical storms are rare to occur. Most of the practical storms vary in duration, amount, and distribution of rainfall.
A unit hydrograph is a hydrograph of a rainfall of a specified duration and areal pattern, resulting in a run-off of 1 cm. In other words, the total volume of water contained in this run-off hydrograph will be equal to 1 cm depth of water on the catchment. The specified duration is such that the hydrographs of any other storms of like durations are assumed to have the same shape but with ordinates of flow in proportion to the run-off volumes.
This specified duration is known as unit duration and the storm of this specified duration is called unit storm. Various storms of varying intensities and having different volumes of run-off, but a particular unit duration, will have the same shape of their run-off hydrographs.
Different unit hydrographs for different unit duration can be prepared. A particular unit hydrograph when once prepared for a particular unit duration can be utilised for evaluating the run-off hydrographs of other storms of the like durations.
The number of unit hydrographs for a given basin is theoretically infinite, since there may be one for every possible rainfall duration, and for every possible distribution pattern in the basin. Practically only a certain limited number of hydrographs can be used for a given basin. It is a common practice to ignore variations in rainfall distribution within a basin.
This is reasonable for small catchments, but for large catchments, this assumption is not valid because these variations are usually too large to be ignored. Some catchments are so large that a storm covers only a small portion of the basin.
Unit hydrograph cannot give precise results and should not be used for areas larger than 8000 sq km. The number of unit durations is also reduced to keep only a limited number of unit hydrographs for a basin.
Assumptions in the Theory of Unit Hydrograph:
The assumptions considered in the theory of unit hydrographs are:
1. The rainfall is uniformly distributed within the specified duration.
2. The rainfall is uniformly distributed in the whole of the catchment area.
3. The base or time duration of the hydrograph of direct run-off due to an effective rainfall of unit duration is constant.
4. The ordinates of direct run-off of common base time are directly proportional to the total amount of direct run-off represented by each hydrograph.
5. For a given basis the hydrograph of run-off due to a given period of rainfall reflects all the combined physical characteristics for the catchment.
Construction of Unit Hydrograph:
The unit hydrograph method is used for determination of the maximum flood discharge of a stream and also for developing a flood hydrograph corresponding to any anticipated rainfall. For this a unit hydrograph of suitable unit duration is derived from an observed hydrograph of the drainage basis under consideration. Using the unit hydrograph, the flood hydrograph corresponding to any rainfall of the same unit duration can be obtained.
The following steps are used to derive a unit hydrograph:
1. Choose a hydrograph resulting from an isolated, intense, short-duration rainfall of nearly uniform distribution over the entire drainage basis as well as within its duration.
2. To obtain direct run-off deduct the base flow from the total run off represented by the hydrograph.
3. Draw a series of ordinates at some uniform time interval for the entire hydrograph.
4. From these ordinates of the hydrograph obtain the ordinates of direct run-off by deducting the corresponding ordinates of base-flow.
5. Compute the volume of direct run-off which is equal to (∑R x t x 3600) m3. Where ∑R is the sum of the direct run-off ordinates in cumecs and t is the time interval in hours between the successive ordinates.
6. Divide the volume of direct run-off by the area of the drainage basis to obtain the equivalent depth of direct run-off as follows:
Direct run-off depth = [(∑R x t x 3600) / (A x 106)] m
= (0.30 ∑R x t) / A cm.
7. By dividing each of the ordinates of direct run-off by the depth of direct run-off, obtain the ordinates of the unit hydrograph. By joining the tops of these ordinates by a smooth curve a unit hydrography is obtained. The unit duration of the obtained unit hydrograph is same as that of effective rain-fall corresponding to which the resulting hydrograph has been used for driving the unit-hydrograph.
To Develop Storm Hydrograph from Unit Hydrograph:
The unit hydrograph of specified unit duration can be easily used to develop the hydrograph of storms of the same duration. The total volume of run-off (in cm) resulting from a storm when divided by 1 cm will give the multiplying factor i.e. the factor by which the ordinates of the unit hydrograph must be multiplied in order to obtain the ordinates of storm hydrograph of the same duration.
The following example illustrates the method by which storm hydrograph is developed from unit hydrograph of the same duration:
Example:
Date, time, ordinates of unit hydrograph and base flow are given as follows. Determine the ordinates of direct run-off and total discharge ordinates. Rainfall excess is 10 cm. Time of duration is 6 hrs.
Use of Unit Hydrograph of Specific Duration to Evaluate the Storms Hydrograph of Longer Duration:
The unit hydrograph of a specified duration can be used to evaluate the hydrograph of storms of longer durations. If a unit hydrograph of say 3 hours duration is given, it can be used to evaluate the hydrograph of 6 hours, 9 hours to 12 hours duration. This is accomplished by dividing the storm in to a number of storm hydrographs, each of 3 hours duration.
Ordinates of different hydrographs are computed separately and then added to get the final storm hydrograph. But care should be taken to see that the hydrograph of each subsequent part of the storm will start at a lag time of each part i.e. 3 hours as shown in Fig. 6.22.
In Fig. 6.22 a 3 hours unit hydrograph is available and it is required to compute the flood hydrograph for a rainfall lasting 9 hours. With variable intensities of rainfall. The rainfall intensity rates are n1 cm/3 hr for the first of 3 hours, n2 cm/3 hr for the second 3 hours and n3 cm/3 hr for the last 3 hours. The storm is divided into three parts and flood hydrograph of each point are found separately and added to get the final flood hydrograph as shown in Fig. 6.22.
Example:
Illustrates the development of storm hydrograph from a 2 hours storm with 3 6.4 and 5.4 cm intensities of rainfall during subsequent intervals of 2 hours. Find the ordinates of a storm hydrograph resulting from a 2 hours storm with rainfall 3.0, 6.4 and 5.4 cm during subsequent intervals of 2 hours.
The ordinates of unit hydrograph of 2 hours are given as follows:
Assume initial loss of 6 mm, infiltration index as 2 mm/hr and Base Flow 10 cumecs. Solution:
1. Rainfall excess during first 2 hours
= 30-2×2-6 = 20 mm = 2 cm.
2. Rainfall excess during second 2 hours
= 64-2 x 2 = 60mm = 6.0cm.
3. Rainfall excess during the last 2 hours
= 54-2 x 2 = 50 min = 5 cm.
Rainfall excess as ratio of unit rainfall of 1 cm during subsequent 2 hours intervals are 2 cm, 6 cm and 5 cm. The example has been solved in tabular form as follows. The computations of run-off due to 2 cm rainfall excess will start from 2 A.M. The computations of run-off due 6 cm and 5 cm rainfall excesses will start at 4 A.M. and 6 A.M. respectively. See Fig. 6.23.
Limitations of Unit Hydrographs:
A tolerance of about 25% of the adopted unit hydrograph duration is generally accepted, without serious errors. Thus a 4 hours unit hydrograph might be applied for storms of 3 hours to 5 hours effective duration.
Large variation in the rainfall intensity during the unit period may considerably affect the accuracy of the unit hydrograph approach. Errors due to this reason can be reduced by using unit hydrographs for relatively short time periods. The short period of unit hydrographs can be used to develop the hydrograph resulting from a long rain of varying intensity.
Experience has shown that the best unit period is about one fourth of the basin lag i.e. the time from the centre of mass of rainfall to the peak of the hydrograph. In general it has been found that the period of unit storm should always be less than the period of rise (probably half or so).
Sometimes the unit hydrographs having a similar range in durations are averaged to obtain an average unit hydrograph. An average unit hydrograph is, preferred to a single storm unit hydrograph since the averaging tends to minimise the errors in data.