1. WATER RESOURCES ENGINEERING-I CLASS ROOM LECTURES
GNITC
GURU NANAK INSTITUTIONS TECHNICAL CAMPUS
DEPARTMENT OF CIVIL ENGINEERING
WATER RESOURCES ENGINEERING-I
CLASS ROOM LECTURES By
Dr. M. K. Mohan B.E,M.E,Ph.D,MISTE,MISCA,
Professor of Civil Engineering &
Member of Illuminati of IBC, Cambridge, England
WRE I – UNIT-II
August, 2015

2. JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD R13 Syllabus
(A50122) WATER RESOURCES ENGINEERING - I
UNIT II
Distribution of Runoff - Hydrograph Analysis Flood Hydrograph – effective Rainfall - base flow separation – Direct Runoff Hydrograph- Unit Hydrograph, definition, and limitations of applications of Unit hydrograph, derivation of Unit Hydrograph, from Direct Runoff Hydrograph and vice versa - S-hydrograph, Synthetic Unit Hydrograph.

3. INSTRUCTIONAL OBJECTIVE
By the end of this unit, the student shall be able to know about Hydrograph analysis, factors affecting flood hydrograph, components of hydrograph, methods of separation of base flow, flow depletion curve, types of hydrographs and how to obtain them like storm hydrograph, direct runoff hydrograph, unit hydrograph, s-curve hydrograph and Synthetic unit hydrograph

4. A hydrograph is a plot of discharge vs time.
HYDROGRAPH ANALYSIS
A hydrograph is a plot of discharge vs time.
It is a graph showing variations of discharge with time, at a particular point of stream.
It shows the time distribution of total runoff at the point of measurement
This runoff includes surface runoff, sub surface runoff and ground water runoff.
The hydrograph can be regarded as an integral expression of the physiographic and climatic characteristics that govern the relationship between rainfall and runoff.
These factors affecting the hydrograph at a place being complex and inter-related, a basin may not produce two exact hydrographs with two similar precipitations as input nor can two basins of same catchment area produce the same flood hydrographs with similar precipitation.

5. HYDROGRAPH ANALYSIS
Since a hydrograph is generated from runoff due to precipitation resulting from either an isolated storm or a series of consecutive storms (complex storm), it is also known as storm hydrograph.
The hydrograph resulting from an isolated storm is called single peaked hydrograph.
The hydrograph resulting from a complex storm is called multi-peaked hydrograph.
Isolated storm: When subsequent storm does not occur before the runoff of previous storm ceases, that storm is called isolated storm.
Complex storm: When subsequent storm occurs before the runoff of the previous storm ceases, such combined storms are called complex storms.

6. COMPONENTS OF A SINGLE PEAKED HYDROGRAPH
There are 3 essential components of a single peaked hydrograph resulting from an isolated storm
The rising limb
The peak or crest element
The recession limb
Point A is starting point of flood hydrograph or the beginning of excess rainfall
Point B is point of inflection on rising limb (shape of curve changes from concave upwards to convex upwards)
Point P is the peak or crest point
Point C is the point of inflection on the recession limb (shape of curve changes from convex upwards to concave upwards)
Point D is the end point of the hydrograph

7. COMPONENTS OF A SINGLE PEAKED HYDROGRAPH

8. COMPONENTS OF A SINGLE PEAKED HYDROGRAPH
The Rising Limb (AB) :
The rising limb (AB) is the ascending portion of the hydrograph corresponding to the increase of discharge due to gradual formation of storage over channels existing in the area and the watershed surface.
In the early periods of a storm, there are initial losses and infiltration losses and hence the discharge rises slowly.
As the time increases, the initial losses and infiltration losses decreases, as a result more and more water from faraway parts reach the basin outlet.
The shape of the rising limb is controlled by the characteristics of the basin and duration, intensity and uniformity of the rain.
Rising curve is concave due to greater losses due to interception, surface detention, evaporation and infiltration.

9. COMPONENTS OF A SINGLE PEAKED HYDROGRAPH
The Peak or Crest Segment (BPC) :
This includes the part of the hydrograph from the inflection point (B) on the rising limb to the inflection point (C) on the recession limb.
Crest segment is one of the most important component of hydrograph because it indicates the peak flow rate.
Peak represents the arrival of flow at the outlet from all parts of the basin. For large catchments, the peak flow point (P) occurs after the cessation of rainfall.
Lag time, the time interval between centre of mass of rainfall to the peak is controlled by characteristics of both the basin as well as the storm.
The end of the crest segment, i.e. the inflection point ‘C’ marks the time when direct runoff from over land flow into the stream outlet ceases.
The point of inflection ‘C’ represents the condition of maximum detention storage.

10. COMPONENTS OF A SINGLE PEAKED HYDROGRAPH
The Recession Limb (CD) :
The recession limb extends from the point of inflection (point C) of the crest segment, to the point ‘D’(the point of commencement of natural ground water flow)
The recession limb indicates delayed runoff from surface detention, channel storage, interflow and ground water flow.
Since depletion of this detention storage takes place after the cessation of rainfall, the shape of recession limb depends only on basin characteristics and independent of storm characteristics.

11. The Recession Curve The Recession Curve:
The recession curve can be considered as a rate of discharge resulting from the draining off process.
The discharge at any time interval (t days) after the point of inflection C is given by

12. Some Basic Definitions
Effective rainfall duration tre:
It is the net duration of precipitation during which rainfall rates are more than infiltration rates.
2. Lag time or Basin lag (tl):
It is the time interval between the centre of mass of net rainfall (or rainfall excess) and the centre of mass of runoff hydrograph.
More commonly, it is the time lapse between the centre of mass of net rainfall and peak of hydrograph.
3. Time to peak (tp):
It is the time interval between the starting of the rising limb (A) to the peak (P) of the hydrograph.

13. Some Basic Definitions
4. Time base of hydrograph (tb):
It is the time from which direct runoff begin to the time when it stops.
In other words, the time from the beginning point (A) to the end point (D) of the direct runoff.
5. Recession time (tr):
It is the duration of the direct runoff after the end of effective rainfall duration

14. Some Basic Definitions
6. Time of concentration (tc): The time of concentration (tc) is defined in two ways.
In terms of physical characteristics of the watershed, it is defined as the travel time of a water particle from the hydraulically most remote point in the basin to the outflow location.
However, based on rainfall and hydrograph characteristics, it is taken as the time from the end of the net rainfall to the point of inflection ‘C’ of the falling limb of the hydrograph.
The time of concentration (tc) can be calculated using the following formula.

15. Some Basic Definitions
6. Recession time (Tr):
It is the duration of direct runoff after the end of the effective rainfall duration. Thus, it is the difference in time between the end of effective rainfall and lowest point (D) of the recession limb.
7. Time base of hydrograph (Tb):
It is the time from which direct runoff begins to the time when it stops.
In other words, it is the time from the beginning point (A) to the end point (D) of the direct runoff.

16. Identification of End Point ‘D’ on the Hydrograph
The first point ‘A’ on the hydrograph, which represents the beginning of direct runoff, can be easily identified in view of sharp change in the runoff rate at that point.
But point D which marks the end of direct runoff cannot be easily located.
The point D occurs at a time interval of N days after the peak point P.
An empirical equation for the time interval (N days) from the peak (P) to the point (D) is given below.

17. Separation of Base flow
There are 3 popular methods of separation of base flow and direct runoff in a single peaked storm hydrograph.
They are
1. Straight line method
2. Two lines method
3. Curves extension method

18. Base flow Separation - Straight line method
This is a simplest method.
Points A & D are joined together to form a straight line.
The area below this line indicates base flow.

19. Base flow separation - Two lines method
This is most widely used method in which the base flow is separated from direct runoff by two lines.
The first line AE is obtained by extending the base flow curve, existing prior to the commencement of surface runoff, till it intersects a vertical line drawn from the peak (P) in a point (E).
Points E & D are joined by a straight line.
4. The area below AED represents base flow.

20. Base flow Separation - Curves extension method
Extend the base flow curve on recession side backward till it intersects a vertical line through point of inflection ‘C’ in point ‘F’.
D1F is the curve extended backwards.
Points A & F are joined by an arbitrary smooth curve
Therefore, the area below AFD1 represent base flow.
This method is preferred where the stream and ground water table are hydraulically connected and flow from ground water storage reaches the stream quickly.
The surface runoff hydrograph obtained after base flow separation is known as direct runoff hydrograph.

21. Actual Base Flow or Depletion Curve
The base flow or depletion curve AED or AD or AFD1 determined above are theoretical and may not represent actual conditions at site.
Actual contribution of ground water is shown by dotted line
When water level before the storm is low, there is flow from ground water to stream. When the water level is high after storm flow takes place from stream to ground water.

22. Computation of Direct Runoff Hydrograph from Storm Hydrograph
Procedure:
Find the ordinates of storm hydrograph, representing total discharge ‘Q’ at a given time interval, say t hrs.
Separate the base flow by two lines method
Find the ordinates of base flow at the same time interval
Find the ordinates of direct runoff by subtracting the ordinates of base flow from total discharge ordinates.
The direct runoff in depth of water (in cm) is found from the expression given below:

23. COMPUTATION OF ORDINATES OF DIRECT RUNOFF HYDROGRAPH FROM THE GIVEN ORDINATES OF STORM HYDROGRAPH

24. Unit Hydrograph
A unit hydrograph shows the temporal change of discharge per unit of runoff.
In other words, how the flow of a stream will be affected over time by the addition of one unit of runoff.
The unit hydrograph is a useful tool in the process of predicting the impact of precipitation on stream flow.
When 1 cm of rainfall excess occurs for a unit duration uniformly distributed over a catchment area, then the resulting hydrograph is known as Unit Hydrograph
Unit duration refers to the continuous time period during which one unit of excess rainfall occurred.
For example, if a unit hydrograph results from a 3 hrs unit rainfall duration, it is known as a 3-hr unit hydrograph meaning thereby a hydrograph produced by surface runoff from a storm lasting for 3 hrs and yielding rainfall excess of 1 cm.

25. Unit Hydrograph
The Concept of unit hydrograph was first given by L.K. Sherman (1932)
Unit duration may vary from
One day for large catchments
Few hours - for small catchments
L. K. Sherman suggested the following values of unit time duration
Catchment Area Unit time duration (hrs)
>2500 km – 24
250 – 2500 km , 8, or 12
50 – 250 km
Small areas /3 to ¼ of tc
Base period T is the total time of the flood hydrograph.
The direct runoff of any duration unit hydrograph will always be 1 cm.

26. Assumptions of Unit Hydrograph Theory
The effective rainfall is uniformly distributed with in its duration of specified period of time
The effective rainfall is uniformly distributed through out the whole area of the drainage basin
The base or time duration of the hydrograph of direct runoff due to an effective rainfall of unit duration is constant
The ordinates of direct runoff of common base time are directly proportional to the total amount of direct runoff represented by each hydrograph
For a given catchment area, the hydrograph of runoff due to a given period of rainfall reflects all the combined physical characteristics of the basin.

27. SUGGESTED VALUES OF UNIT DURATION

28. Construction of Unit Hydrograph
From the ordinates of storm hydrograph, deduct the ordinates of base flow to get the ordinates of direct runoff hydrograph.
From the ordinates of direct runoff hydrograph, compute direct runoff in cm.
Calculate the ordinates of unit hydrograph by using the relation

29. Derivation of Unit Hydrograph from Flood Hydrograph

30. Derivation of Flood Hydrograph from Unit Hydrograph

31. Computation of ordinates of Unit Hydrograph from the ordinates of Storm Hydrograph
Ordinates of DRH can be obtained by subtracting the ordinates of base flow from the ordinates of direct runoff hydrograph.
Col 5 = Col 3 – Col 4
2. Ordinates of UH can be obtained by dividing the ordinates of direct runoff hydrograph by direct runoff in cm.
Col 6 = Col 5 / DRO in cm

32. Construction of Flood Hydrograph resulting from three consecutive storms

33. Construction of Flood Hydrograph resulting from three consecutive storms

34. Example Problem: Construction of Flood Hydrograph resulting from three consecutive storms

35. Example Problem: Construction of Flood Hydrograph resulting from three consecutive storms
Col 4 = Col 2 x 0.75
Col 5 = Col 2 x 6
Col 6 = Col 2 x 3
Col 7 = Col 4 + Col 5 + Col 6
Col 9 = Col 7 + Col 8

36. S- Hydrograph or Summation Hydrograph
S-hydrograph is a hydrograph that is produced by a continuous effective rainfall at a constant rate for indefinite period.
It is a continuous rising curve in the form of ‘S’ till equilibrium is reached.
The equilibrium discharge for a S-hydrograph is given by
Qo(cumecs) = A V = A (in m2) Ro(in m/s)
(when A is given in sq km and Ro is given in cm/hr)
Qo = (A x 1000 x 1000) Ro / 100 x 3600
= A Ro
Where A = Catchment area in sq km
Ro = Uniform rainfall rate or Rainfall intensity in cm/hr

37. S-hydrograph

38. Construction of S-hydrograph
The s-hydrograph is constructed by adding together a number of unit hydrographs of unit time duration (To) spaced at unit time duration (To).

39. Construction of S-hydrograph from the ordinates of 6-hr unit hydrograph
Column 2 represents ordinates of 6-hr unit hydrograph.
The ordinates of successive unit hydrographs are to be entered in columns 3 to 8 each lagged by 6 hrs.
Column 9 gives the ordinates of s-hydrograph which is obtained by summing up columns from 2 to 8.

40. Construction of S-hydrograph by Off-set ordinate method
Column 3 represents ordinates of 6-hr unit hydrograph
Column4 represents off- set ordinates lagged by 6 hrs.
Column 5 represents ordinates of s-hydrograph.
Column 4 and column 5 are to be populated simultaneously Row by Row (2 rows at a time since UH is of 6 hrs duration )
Column 5 = column 3 + column 4 (row by row)
Rows 1 and 2 of column 5 are to be carry forwarded to rows 3 and 4 of column 4 and rows and 3 and 4 of carry forwarded to rows 5 and 6 of column 4 and so on .

41. Construction of UH of longer duration from a given UH of shorter duration by Principle of Superposition
According to principle of superposition, the ordinates of a 6 hr UH can be obtained by adding the ordinates of 3 successive 2-hr unit hydrographs (each lagged by 2 hrs) and dividing the sum by 3 (sum of 3 unit hydrographs represent 3 cm excess rainfall and dividing it by 3 represents 1 cm excess rainfall)
Ordinates of 6 hr UH =
(Ordinates of 2 hr UH + Ordinates of 2 hr UH lagged by 2 hrs + Ordinates of 2 hr UH lagged by another 2 hrs) / 3

42. Example Problem:
Construction of 6 hr UH from a given 2 hr UH by Principle of Superposition

43. Example Problem:
Construction of 6 hr UH from a given 2 hr UH by Principle of Superposition

44. Construction of UH of shorter duration from a given UH of longer duration by S-hydrograph method.
If the ordinates of 6 hr (To) UH are available, then S-hydrograph can be constructed by off-set ordinate method.
In order to get the ordinates of 3 hr (to)UH, an off-set S-curve ordinates are to be found lagged by 3 hrs duration.
Subtracting the off-set(3hr) s-curve ordinates from original s-curve ordinates gives ∆y.
The ordinates of 3 hr UH can be obtained by multiplying ∆y ordinates with To/to.

45. Example Problem: Construction of 3 hr UH from a given 6 hr UH using S-hydrograph method

46. Synthetic Unit Hydrograph (SUH)
In case of ungauged catchments, the stream flow data is not available.
In such cases, the unit hydrographs are derived by relating the selected basin characteristics to the unit hydrograph shape.
The resulting hydrograph, derived from basin characteristic relationships is known as Synthetic Unit Hydrograph.
The Synthetic Unit Hydrograph developed by Synder (1938), is one of the most popular method.

47. Standard Duration (T) and Non-Standard Duratin (T1)of
Synder’s Synthetic Unit Hydrograph
Synder gave formulae for Peak Discharge (Qp), Basin Lag (tL)and Base time (Tb)for a Standard Duration (T) of Unit hydrograph resulting from a standard duration of effective rainfall.
The standard duration (T) of Synder’s Synthetic Unit Hydrograph is given by the formula
However, in case, if the data or unit hydrograph of meteorologically similar catchment is given for non-standard duration (T1) only, then the formulae for Peak discharge, Basin lag and Base time will have to be modified as Qp1, tL1, Tb1

48. Synder’s Synthetic Unit Hydrograph
Synder studied the data of catchments of Appalachian Highlands in Eastern United States and developed empirical equations for Synthetic Unit Hydrograph.
Synder selected three parameters of unit hydrograph
i. base width or time base Tb
ii. Peak discharge Qp
iii. Basin lag TL

49. Synthetic Unit Hydrograph

50. Peak Discharge for Standard Duration

51. Basin Lag for Standard Duration
The basin lag time tL is given by the following formula
Where, tL = basin lag in hours
Ct = a coefficient
= 1.35 to 1.65 for Appalachian catchments,
= 0.3 to 0.6 for other catchments
(Ct value depends on units and drainage basin characteristics like topography, stream density, channel slopes and channel storage)
L = distance from station to catchment boundary measured along the main stream line
LC= distance along the main stream from gauging station to a point on the main stream which is nearest to the centroid of the basin in km.

52. Time base (Tb) for Standard Duration
For large catchments, the base time (Tb) of the synthetic unit hydrograph is given by
Tb = tL
For small catchments, the bas time (Tb) of the synthetic unit hydrograph is taken as 5 times the time to peak (tp)
A catchment is large or small can be decided by the following three parameters viz. 1) Catchment area 2) W50 and 3) W75

53. Synthetic Unit Hydrograph for 50% and 75% of Peak Discharge
Widths W50 and W75 of
Synthetic Unit Hydrograph
for 50% and 75% of Peak Discharge
The width of synthetic unit hydrograph for 50% W50 of discharge is given by the following formula
Where qP is the peak discharge per unit catchment area.
The width of synthetic unit hydrograph for 50% W75 of discharge is given by the following formula

54. Modified Formulae for Non-standard Duration(T1)
The modified basin lag time tL1 for non-standard duration T1 is given by
The modified peak discharge Qp1 for non-standard duration T1 is given by
The modified time base Tb1 for non-standard duration T1 for large catchments is given by
The modified time base Tb1 for non-standard duration T1 for small catchments is given by

55. FOR SYNDER’S METHOD OF SUH
EXAMPLE PROBLEM 1
FOR SYNDER’S METHOD OF SUH

56. EXAMPLE PROBLEM 1 solution

57. EXAMPLE PROBLEM 1 solution contd…

58. EXAMPLE PROBLEM 1 solution contd…

59. FOR SYNDER’S METHOD OF SUH
EXAMPLE PROBLEM 2
FOR SYNDER’S METHOD OF SUH

60. EXAMPLE PROBLEM 2 solution

61. EXAMPLE PROBLEM 2 solution contd…

62. EXAMPLE PROBLEM 2 solution contd…

63. EXAMPLE PROBLEM 2 solution contd…

64. Ordinates of Flood Hydrograph (cumecs) Ordinates of Base flow (cumecs)
ASSIGNMENT-2 QUESTIONS
1.With the help of a neat sketch, explain the various component parts of single peaked storm hydrograph.
2. Explain with the help of sketches, the three methods of base line separation.
3. Derive the ordinates of unit hydrograph from the following flood hydrograph data. Take the area of the catchment as 25 sq.km.
Date
Time
(hour)
Ordinates of Flood Hydrograph (cumecs)
Ordinates of Base flow (cumecs)
12 Aug
06.00 6
08.00 8
10.00 10
5.5
12.00 16 5
14.00 28
4.5
16.00 42 4
18.00 60
3.5
20.00 80 3
22.00
110
2.5
13 Aug
24.00
100
02.00 90
04.00 68 56 45

65. ASSIGNMENT-2 QUESTIONS
12.00 35 4
14.00 26
16.00 18
4.5
18.00 11
20.00 9
5.5
22.00 8
14 Aug
24.00 7
02.00 6
6.0
4. Find the ordinates of flood hydrograph using the ordinates of unit hydrograph given below for a single storm resulting from an excess rainfall of 8 cm.
Date
Time (hour)
Ordinates of Unit hydrograph (cumecs)
Ordinates of base flow (cumecs)
12 Aug
06.00 4
09.00
0.12
3.5
12.00
0.35
3.0
15.00
0.88
2.5
18.00
1.5
2.0
21.00
2.8
24.00
1.8
03.00
1.85
2.1
1.53
2.4
1.26
2.7
0.84
0.50
3.3
3.6
3.8
4.0

66. ASSIGNMENT-2 QUESTIONS
5. Find the ordinates of a storm hydrograph resulting from a 3 hr storm with rainfall of 2 cm, 6.75 cm, and 3.75 cm during subsequent 3 hr intervals. The ordinates of 3 hr unit hydrograph are given in the following table. Assume an initial loss of 5 mm, infiltration index of 2.5 mm/hr and base flow of 10 cumecs.
Date
Time (hours)
Ordinates of 3-hr unit hydrograph (cumecs)
15 Aug 03 06
110 09
365 12
500 15
390 18
310 21
250 24
235
175
130 95 65 40 22 10

67. ASSIGNMENT-2 QUESTIONS
6. Compute the ordinates of s-hydrograph from the 6-hr unit hydrograph data given below using offset ordinate method.
S.No.
Time (hours)
Ordinates of 6-hr unit hydrograph (cumecs) 1 2 3 9 6 20 4 35 5 12 49 15 43 7 18 8 21 28 24 22 10 27 17 11 30 33 13 36 14 39 42

68. ASSIGNMENT-2 QUESTIONS
7. The ordinates of a 2-hr unit hydrograph are given below. Derive a 6-hr unit hydrograph for the same catchment.
Time (hours)
Ordinates of 2-hr unit hydrograph (cumecs) 1 2
2.7 3 5 4 8
9.8 6 9 7
7.5
6.3
5.0 10
4.0 11
2.9 12
2.1 13
1.3 14
0.5 15

69. ASSIGNMENT-2 QUESTIONS
8. The ordinates of 6-hr unit hydrograph are given below. Derive the ordinates of 9-hr unit hydrograph for the same catchment.
Time (hours)
Ordinates of 6-hr unit hydrograph (cumecs) 3 9 6 20 35 12 49 15 43 18 21 28 24 22 27 17 30 33 36 39 42

70. TEXT BOOKS
1. Engineering Hydrology by Jayaram Reddy, Laxmi publications pvt. Ltd., New Delhi
2. Irrigation and water power engineering by Punmia & Lal, Laxmi publications pvt. Ltd., New Delhi

71. REFERENCE BOOKS
1. Elementary hydrology by V.P.Singh, PHI publications.
2. Irrigation and Water Resources & Water Power by P.N.Modi, Standard Book House.
3. Water resources engineering –I by Dr. G.Venkata Ramana, academic publishing company.
4. Irrigation Water Management by D.K. Majundar, Printice Hall of India.
5. Irrigation and hydraulic structures by S.K.Garg
6.Applied hydrology by Ven Te Chow, David R.Maidment larry W. Mays Tata Mc. Graw Hill
7. Introduction to hydrology by Warren Viessvann, Jr, Garyl. Lewis, PHI.

72. Have a Good Luck.
THANK YOU.