FLOOD

1
FLOOD

• Mrinmoy Majumder
• www.baipatra.ws

2
Definition

• High stage in river when the river overflows and
  inundates the adjoining area
• Flood peak and frequency of the peak is an
  important consideration in hydraulic design
• Magnitude and time of the flood varies with
  change in watershed characteristics
• Peak flood depends on rainfall, discharge or
  watershed area and type
• Magnitude of flood can be estimated in
• Rational method
• Empirical method
• Unit hydrograph technique
• Flood frequency studies

3
Rational Method

• Assumptions
• Area of watershed must be less than 50 Sq.Km
• Rainfall continues beyond time of concentration
• Catchment is homogeneous
• The equation for peak flood, according to
  rational method
• Qp C A i
• Qp is the peak discharge, C is coefficient of
  runoff (runoff/rainfall), i is rainfall intensity
  which depends on time of concentration and
  exceedance probability, A is drainage area in
  Sq.Km

4
Time of Concentration

• Rainfall intensity is found to be a function of
  time of concentration (tc) and an exceedance
  probability P
• tc can be expressed as

tp CtL(LLca/(S)1/2)n where, C is a
constant, L is the distance from farthest point
of the catchment to basin divide,Lca is the
distance of gage from centroid of the watershed,S
is slope between farthest point and outlet,n is
the mannings constant
tc 0.01947L0.77S-0.385 where, time of
concentration (minutes),L is maximum length from
farthest point to outlet and S is slope of
catchment(from highest point to lowest point)
5
Rainfall Intensity

• The rainfall intensity is thus represented by
• itc,p KTx/(tca)m

K,a,x and m are constants which can be collected
from frequency duration curves
6
Empirical Formula

• Regional formula
• Based on correlation
• Between flow(Qp) and catchment properties
• Almost all use area(A)
• Neglects flood frequency
• The reason why empirical formulas are all
  regional and gives approximate results when
  applied to other regions

7
Dickens Formula

• Qp CDA3/4

CD Dickens Formula with value between 6 - 30
8
Ryves Formula

• Qp CRA2/3

CR Ryves Formula with value between 6.8 10.2
9
Inglis Formula

• Qp (124A)/(A10.4)1/2

For Western Ghats in Maharashtra
10
Fullers Formula

• QTp (CfA0.8)/(10.8logT)

For USA,T return period, Cf is a constant 0.18
1.88.
11
Baird and Mcillwraith(1951)

• Qmp (3025A)/(278A)0.78

From maximum rrecorded floods throughout the world
12
Flood Frequency Analysis

• P m/(N1)
• T 1/P

Prn nCrPrqn-r T 1/P
Where P is the probability of an extreme event
and T is the return period of that event. Prn is
the occurrence of the event for r times in n
successive years m is the rank of the event with
respect to other events of the year or decade or
greater time span. N total number of events in
the dataset C combination of n and r and q 1-P
13
Plotting Position Formula

• Probability values can be used to determine the
  position of the event in a probability curve.
  From which both exceedance and non-exceedance
  probability of the event can be estimated.

14
General Equation of Hydrologic Frequency
Analysis(Chow,1951)

• xT x K.s

Where xT is the value of the flood in T return
period x is the mean and s is the standard
deviation K f (T, frequency distribution)
frequency factor
15
Gumbels Method
If f(x) is probability density function,then,Gumbe
ls distribution is given by
Where the distribution has  mode a,  mean a?ß (
where ?0.5772156649... is Euler's constant),
and variance ?ß2p2
16
Gumbels Distribution Explained

• There are essentially three types of
  Fisher-Tippett extreme value distributions.
• The most common is the type I distribution, which
  are sometimes referred to as Gumbel types or just
  Gumbel distributions.
• The term "Gumbel distribution" is used to refer
  to the distribution corresponding to a minimum
  extreme value distribution (i.e., the
  distribution of the minimum  ).
• The Gumbel distribution has a location
  parameter a  and scale parameter  ß

17
Normal Distribution
18
LogNormal Distribution
19
Pearson Distribution
20
Log-Pearson Distribution