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Table of Contents
                            Preface to the Second Edition
Preface to the First Edition
Contents
Part A-Fundamental Hydrology
	Chapter 1. Introduction
		1.1 World’s Water Resources
		1.2 Water Resources of India
		1.3 Hydrological Study of Tapti Basin (Central India)
		1.4 Hydrology And Hydrologic Cycle
		1.5 Forms of Precipitation
		1.6 Scope of Hydrology
		1.7 Hydrological Data
		1.8 Hydrologic Equation
	Chapter 2. Precipitation
		2.1 Types of Precipitation
		2.2 Measurement of Precipitation
		2.3 Radars
		2.4 Rain-Gauge Density
		2.5. Estimates of Missing Data and Adjustment of Records
		2.6 Mean Areal Depth of Precipitation (Pave)
		2.7 Optimum Rain-Gauge Network Design
		2.8 Depth-Area-Duration (Dad) Curves
		2.9 Graphical Representation of Rainfall
		2.10 Analysis of Rainfall Data
		2.11 Mean And Median
		2.12 Moving Averages Curve
		2.13 Design Storm And PMP
		2.14 Snow Pack And Snow Melt
	Chapter 3. Water Losses
		3.1 Water Losses
		3.2 Evaporation
		3.3 Evaporation Pans
		3.4 Soil Evaporation
		3.5 Unsaturated Flow
		3.6 Transpiration
		3.7 Evapotranspiration
		3.8 Hydrometeorology
		3.9 Infiltration
		3.10 Infiltration Indices
		3.11 Supra Rain Technique
		3.12 Watershed Leakage
		3.13 Water Balance
	Chapter 4. Runoff
		4.1 Components of Stream Flow
		4.2 Catchment Characteristics
		4.3 Mean and Median Elevation
		4.4 Classification of Streams
		4.5 Isochrones
		4.6 Factors Affecting Runoff
		4.7 Estimation of Runoff
	Chapter 5. Hydrographs
		5.1 Hydrograph Components
		5.2 Separation of Streamflow Components
		5.3 Hydrograph Separation
		5.4 Unit Hydrograph
		5.5 Unit Hydrograph From Complex Storms
		5.6 S-Curve Method
		5.7 Bernard’s Distribution Graph
		5.8 Instantaneous Unit Hydrograph
		5.9 Synthetic Unit Hydrographs
		5.10 Transposing Unit Hydrographs
		5.11 Application of Unit Hydrograph
	Chapter 6. Stream Gauging
		6.1 Methods of Measuring Stream Flow
		6.2 Current Meter Gaugings
		6.3 Stage-Discharge-Rating Curve
		6.4 Selection of Site for a Stream Gauging Station
	Chapter 7. Ground Water
		7.1 Types of Aquifers and Formations
		7.2 Confined and Unconfined Aquifers
		7.3 Darcy’s Law
		7.4 Transmissibility
		7.5 Well Hydraulics
		7.6 Specific Capacity
		7.7 Cavity Wells
		7.8 Hydraulics of
 Open Wells
		7.9 Construction of Open Wells
		7.10 Spacing of Wells
	Chapter 8. Floods-Estimation and Control
		8.1 Size of Floods
		8.2 Estimation of Peak Flood
		8.4 Flood Frequency Studies
		8.5 Encounter Probability
		8.6 Methods of Flood Control
		8.7 Soil Conservation Measures
		8.8 Flood Control Economics
		8.9 Flood Forecasting and Warning
	Chapter 9. Flood Routing
		9.1 Reservoir Routing
		9.2 Stream Flow Routing
	Chapter 10. Storage, Pondage and Flow Duration Curves
		10.1 Reservoir Mass Curve and Storage
		10.2 Flow Duration Curves
		10.3 Pondage
	Chapter 11. Reservoir Sedimentation
		11.1 Sediment Movement and Deposition
		11.2 Reduction in Reservoir Capacity
		11.3 Reservoir Sedimentation Control
	Chapter 12. Arid, Semi-Arid and Humid Regions
		12.1 Arid Regions
		12.2 Semi-Arid Regions
		12.3 Humid Regions
Part B-Advanced Topics
	Chapter 13. Linear Regression
		13.1 Fitting Regression Equation
		13.2 Standard Error of Estimate
		13.3 Linear Multiple Regression
		13.4 Coaxial Graphical Correlation of Rainfall Runoff
	Chapter 14. Statistical, and Probability Analysis of Hydrological Data
		14.1 Elements of Statistics
		14.2 Probability of Hydrologic Events
	Chapter 15. Flood Frequency-Probability
 and Stochastic Methods
		15.1 Flood Frequency Methods
		15.2 Stochastic Method
		15.3 Stochastic Modelling by the Partial Duration Series
		15.4 Annual Flood Peaks—River Ganga
		15.5 Regional Flood-Frequency Analysis (RFFA
)
	Chapter 16. Mathematical Models in Hydrology
		16.1 Type of Mathematical Models
		16.2 Methods of Determining IUH
		16.3 Synthetic Stream Flow
		16.4 Flow at Ungauged Sites by Multiple Regression
		16.5 Reservoir Mass Curve
		16.6 Residual Mass Curve
		16.7 Selection of Reservoir Capacity
		16.8 Mathematical Model
	Chapter 17. Instantaneous Unit Hydrograph (IUH)
		17.1 IUH for a Basin
		17.2 Derivation of IUH
		17.3 Other Methods of Derivation of IUH
		17.4 Nash Conceptual Model
		17.5 Clark’s Model
		17.6 Drawing Isochrones and Time-Area Diagram (TAD)
		17.7 Clark’s Method
	Chapter 18. Cloud Seeding
		18.1 Conditions for Cloud Seeding
		18.2 Cloud Seeding Technique
		18.3 Cloud Seeding Operation
		18.4 Recent Case History
Appendices
Selected References
Bibliography
Index
                        
Document Text Contents
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FLOODS-ESTIMATION AND CONTROL 225

When the flood items are tabulated in terms of mean flood, Cv = �. If the annual flood is
x and the mean flood is x , then the annual flood in terms of mean flood is x/x . The coefficient
of variation for annual precipitation data is equal to the standard deviation of the indices of
wetness.

While a small value of Cv indicates that all the floods are nearly of the same magnitude,
a large Cv indicates a range in the magnitude of floods. In other word Cv represents the slope
of the probability curve, and the curve is horizontal if Cv = 0. The actual length of records
available has a very little effect on the value of Cv, i.e., Cv for a 20-yr record varies very little
from that for a 100-yr record.

The coefficient of skew, Cs is seriously affected by the length of record and will be too
small for a short period; Cs is then modified to allow for the period of record (n) by multiplying
by a factor (1 + k/n) where the constant K = 6 to 8.5. If even this adjusted Cs does not give a
curve to fit actual observed data, an arbitrary value of Cs will have to be assumed to fit the
curve for the given annual flood data. From this theoretical curve can then be read off the
probability or the percentage of time, of a flood of any given magnitude occurring, usually,

Cs 2 Cv ...(8.21)
The coefficient of flood indicates the general magnitude of the floods in the particular

stream; hence, it fixes the height of the curve above the base. Using Cf, the mean flood of a
stream, for which no flood data are available, can be got, as

Mean flood = Cf ×
A0.8

2 14.
...(8.22)

The exponent 0.8 is the slope of the line obtained by plotting the mean annual flood
against water-shed area for a number of streams. Almost all observed data till to-date confirm
this value originally obtained by Fuller.

8.5 ENCOUNTER PROBABILITY

Even if a flood of a long recurrence interval is chosen, there is always a possibility that the
flood can be exceeded more then once during the interval. The probability of ‘r’ events occur-
ring in ‘N’ possible events is given by

P(N, r) =
N

r N r
!

! ( ) !�
Pr (1 – P)N–r ...(8.23)

where P = probability of a single event.
If r = 0, the flood will not be exceeded during the ‘N’ years, the useful life of the struc-

ture. Then Eq. (8.23) becomes
Probability of non-exceedance, P(N, 0) = (1 – P)

N ...(8.23 a)
So, the probability that the design flood (T-year flood, annual probability of occurrence

P = 1/T) will be exceeded one or more times during N year (useful life of the structure) is given
by

Probability of exceedance, PEx = 1 – (1 – P)
N ...(8.23 b)

and the percentage risk = PEx × 100 (8.23 c)

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226 HYDROLOGY

Thus, the probability of a 100-year flood will not be exceeded in the next 50 years is

P(N, 0) = 1
1

100

50

�FHG
I
KJ = 0.6 or 60%

or 6 chances in 10; and the probability that the 100-year flood will be exceeded once or more
during the next 50 years is

PEx = 1 – 0.6 = 0.4 or 40%
or 4 chances in 10

As another example, to determine the recurrence interval of a design flood having a
63% risk of being exceeded during a 100-year period

PEx = 1 – (1 – P)
N

0.63 = 1 – (1 – P)100

from which P = 0.01. Hence, T =
1 1

0 01P
=

.
= 100 years.

The percentage probabilities of floods (or rainfall) of different recurrence intervals (T)
to occur in particular periods (N) are given in Table 8.4.

Table 8.4 Probability (%) of T-yr flood to occur in a period of N-years

Period (N-years) Average recurrence interval of flood (T-yr)

5 10 50 100 200

1 20 10 2 1 0.5

5 67 41 10 5 2

10 89 65 18 10 5

25 99.6 93 40 22 12

50 — 99.5 64 40 22

100 — — 87 63 39

200 — — 98 87 63

500 — — — 99.3 92

Partial duration curve method Partial duration curves are plotted showing the flood
discharges against their probable frequency of occurrence in 100 years and not against per-
centage of time as in the annual flood series.

Probable frequency =
m
y

× 100 ...(8.24)

where m = order number or rank of the particular flood in the series of items selected and
arranged in the descending order of magnitude

y = total length of record in years
The number of flood items selected need not be greater than the number of years in

record to simplify the procedure. Gumbel paper should not be used for partial series, which
usually plot better on semi-log paper.

Frequency method may be used for drainage basins of any size. The reliability of the
frequency estimates depends on the length of the observed record rather than the method of
probability analysis. Thus, if a 50-year record is available, a 10-yr flood may be predicted with

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462 HYDROLOGY

Stage-discharge rating curve, 176, 178, 184
adjustment of, 181
extension of, 181

Statistics, elements, 327
mean, median, 43, 44, 327, 328, 331
mode, 328, 331
skew distribution, 328
skewness, 329

coefficient of, 330
variance, 329

Station-year method, 24
Storage capacity, reservoir, 281, 383, 488
Storage coefficient, aquifer, 194

basin, 375, 399
Storm characteristics, correlation of,

depth-duration, 11, 45
intensity-duration, 46
intensity-duration-frequency (IDF), 38, 41, 114
design, 49, 217
track, 9
maximum probable (MPS), 10

Storm maximisation, 10
by moisture charge, 10, 217
by unit hydrograph method, 221

Streams, classification of, 103
effluent, 103
ephemeral, 103
influent, 103
intermittent, 104
perennial, 104

Stream flow components, 96
separation of, 120

Stream flow computation, 171, 185
contracted area method, 172, 186
salt concentration method, 172
slope-area method, 171, 187

Stream gauging, methods of 171
area-velocity method, 172, 176, 179
by current meter, 174, 176
selection of site, 183

Supra-rain technique, 83
curve, 85
Synthetic stream flow, 379
Synthetic unit hydrograph, Snyder’s, 149

Tank irrigation, 109
length of weir, 111
yield for, 109

Tapti basin, 6
hydrological study, 5-12, 36

Thiessen polygon method, 27, 28
Time-area diagram (TAD), 378, 398, 400
Time of concentration, 109, 398

runoff from, 109, 398
Transpiration, 67

ratio, 67
Transmissibility, 196, 199
Trap efficiency, 301-303

Unit hydrograph, 113, 124, 379
application of, 157, 158, 160
alteration of duration, 136
assumptions of, 113
average, 136
derivation of, 124, 129

from complex storms, 130, 132
dimensionless, 156
elements of, 126
instantaneous (IUH), 149, 379, 393, 401
limitations of, 127
matrix method, 135
propositions of, 127
runoff estimation from, 113
SCS method, 157
synthetic (SUH), Snyder’s 149
transposing of, 154

Unit storm, 127
Unsaturated flow, 66

Valley storage, 97, 106
Variance, 327
Velocity measurements, 172
Velocity rods, 172

Water balance, 87, 445
of Krishna river basin, 87

Water bearing formations, 192
Water losses, 60
Watershed leakage, 87

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INDEX 463

Water resources, World’s, 1
of India, 1

Well hydraulics, 196
Cavity wells, 200
Dupuitt’s equations, 196-198
Jacob’s equations, 433-438
Open (dug) wells, 202
Thies equations, 432-438

Well interference, 207
Wells spacing, 207
W-index, 82

Yield (see runoff estimation), 106, 429
for tank, 109
rational method for, 106, 108

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