Kumaran a/l gopalan
151014455
group 2
#include <stdio.h>
int calculate();
int print_star ,print_plus;
main()
cfw_
printf("*",print_plus);
calculate();
int calculate()
cfw_
printf("\n+\n",print_plus);
#include <stdio.h>
int print_richard;
main()
cfw_
int
Unit hydrograph
Example Problem
Convert the following 2hr UH to a 3hr UH using the Scurve method
Time (hr)
2hr UH ordinate (cfs)
0
0
Solution
1
75
Make a spreadsheet with the 2hr
2
250
UH ordinates, then copy them in
3
300
the next column lagged by D
Module 4
Lecture 2: Kinematic overland flow
routing
Kinematic overland flow routing
For the conditions of kinematic flow, and with no appreciable backwater effect,
the discharge can be described as a function of area only, for all x and t;
Q= Am
.4.5
wher
Module 6
Lecture 4: Derivation of momentum equation
(contd.)
2D Saint Venant Equations
Obtained from Reynolds NavierStokes equations by depthaveraging.
Suitable for flow over a dyke, through the breach, over the floodplain.
Assumptions: hydrostatic pr
Module 8
Lecture 3: Markov chain
Markov Chains
A Markov chain is a stochastic process having the property that the value of
the process Xt at time t, depends only on its value at time t1, Xt1 and not on
the sequence Xt2, Xt3, , X0 that the process pas
Module 7
Lecture 5: Commonly used distributions in
hydrology
Normal Distribution
Normal Distribution:
2
1
x
f ( x )=
exp 1
2
2
f(x)
 x +
 +
>0
x=
+

x
Also, called Saminion Distributon; Bell shaped Distribution
Most popular distribution in an
Lecture 2
Philosophy of mathematical models of
watershed hydrology (contd.)
Watershed Modeling Methodology
I. Goal
time
Hydrologic
Model
flow
Watershed
Precipitation
The goal considered here is to simulate the shape of a hydrograph given a
known input (Eg
Module 3
Lecture 3: Hydrograph analysis
Hydrograph analysis
A hydrograph is a continuous plot of instantaneous discharge v/s time. It
results from a combination of physiographic and meteorological conditions in
a watershed and represents the integrated e
Module 7
Lecture 3: Measures of central tendency
and dispersion
Measures of Central Tendency
Mean:
E(x) = =
+
x f ( x )dx,
for parameter estimate
n
Arithmatic Mean ( x ) =
x
i =1
i
.for sample estimate
Mode:
Most frequently occuring value
f
f
= 0&
<0
1)
Module 5
Lecture 2: Level pool routing and modified
Puls method
Hydrologic flow routing
1. Level Pool Routing
When a reservoir has a horizontal water surface elevation, the storage function is a
function of its water surface elevation or depth in the pool
Module 5
Lecture 4: Hydraulic routing
Hydraulic/Distributed flow routing
Flow is calculated as a function of space and time throughout the system
Hydraulic methods use continuity and momentum equation along with the
equation of motion of unsteady flow (
Module 4
Lecture 3: Kinematic channel modeling
Kinematic channel modeling
Representative of collectors or stream channels
Triangular
Rectangular
Trapezoidal
Circular
These are completely characterized by slope, length, crosssectional
dimensions, sh
Module 1
Lecture 2: Weather and hydrologic cycle
(contd.)
Hydrology
Hydor + logos (Both are Greek words)
Hydor means water and logos means study.
Hydrology is a science which deals with the occurrence, circulation and
distribution of water of the earth an
Module 8
Lecture 5: Reliability analysis
Reliability
It is defined as the probability of nonfailure, ps, at which the resistance of the
system exceeds the load;
ps = P( L R)
where P() denotes the probability.
The failure probability, pf , is the compli
Module 9
5 Lectures
Hydrologic Simulation Models
Prof. Subhankar Karmakar
IIT Bombay
Objectives of this module is to investigate on various
hydrologic simulation models and the steps in watershed
modeling along with applications and limitations of major
h
Module 1
Lecture 3: Hydrologic losses
Hydrologic losses
In engineering hydrology, runoff is the main area of interest. So, evaporation
and transpiration phases are treated as losses.
If precipitation not available for surface runoff is considered as los
Example Problem
V is wind velocity with a pdf f(v) = 1/10; 0 v 10. The pressure at point is
given by = 0.003 v 2 . Find the expected value of pressure.
Soln :
f(v) =
1
; 0 v 10; = 0.003 v 2
10
E() = ?
+
E() =
g( )d, given = 0.003 v 2 or d = 0.006 vdv
giv
Module 9
Lecture 4: MIKE models
MIKE Models
a)
Flood Management
b)
MIKE 11 For Analyzing Open Channel Flow
MIKE 21 For Analyzing surface complicated overflow
River Basin Management
c)
Hydrological Cycle
d)
MIKE BASIN
MIKE SHE
Urban Drainage
MOUSE For Anal
Module 9
Lecture 5: Urban Flood Risk Mapping using
MOUSE, MIKE 21 and MIKE FLOOD
MOUSE Model
MIKE FLOOD
Set up
Validation
Preparation
GIS
Rainfall
Analysis
Set up
Coupling
Preprocessing for MOUSE
MIKE21 Model
Set up
Validation
Run Model
Check the result a
Module 6
Lecture 3: Derivation of momentum
equation
Velocity Distribution in an Open Channel Flow
Isovels
100
80
60
60
40
(a)
(b)
Diagrammatic representation of (a) Isovels and (b) Velocity profile in an open
channel flow
Module 6
Gradually Varied Flow
Hy
Module 6
Lecture 5: Energy equation and numerical
problems
Energy in Gradually Varied
Open channel flow
In a closed conduit there can be a pressure gradient that drives the flow.
An open channel has atmospheric pressure at the surface.
The HGL (Hydraul
Module 5
Lecture 3: Channel routing methods
Hydrologic flow routing
2. Channel Routing
In very long channels the entire flood wave also travels a considerable distance
resulting in a time redistribution and time of translation as well. Thus, in a
river, t
Example Problem
Channel width (rectangular) = 2m, Depth = 1m, Q = 3.0 m3/s, Height above
datum = 2m. Compute specific and total energy
Ans: A = b*y = 2.0*1.0 = 2 m2
Specific energy =
Total energy =
Q2
E = y+
32
E =1+
2gA2
2 * 9.81 * 2 2
Datum height + spe
Module 8
Lecture 2: Markov process and
Thomas Fierring model
First Order, Stationary Markov Process
Many hydrologic time series exhibit significant serial correlation.
Value of the random variable under consideration, X at one time period (say, t+1)
is co
Module 7
Lecture 2: Statistical Moments
Introduction
Measures of Central Tendency:
Mean,
Arithmetic average (for sample),
Mode,
Median
Measures of Spread or Distribution:
Range [(xmaxxmin)],
Relative Range [=(range/mean)],
Variance,
Standard deviation
Module 3
Lecture 6: Synthetic unit hydrograph
Synthetic Unit Hydrograph
In India, only a small number of streams are gauged (i.e., stream flows due
to single and multiple storms, are measured)
There are many drainage basins (catchments) for which no strea
Example Problem 1
If in a sample there are 95% nonzero values, calculate X10 .
Solution:
1
P [ X x10 ] = =0.1
10
1
0
1
F( x10 ) = 0.1 = .9 0.9 = 0.9 5 + 0.9 5F * ( x10 )
k =0.95 =P [ X 0 ] ,
F = 0.895 = P [ X x10  X 0 ] given x 0
(x)
*
*
2
If F ( x ) fo
Example Problem
Find the storm hydrograph for the following data using time area method.
Given rainfall excess ordinate at time is 0.5 in./hr
D
A
B
C
D
C
Area (ac)
100 200 300 100
B
Time to gage G (hr)
1
2
3
4
A
Time area histogram method uses
Qn = RiA1 +