Chapter 2

CHAPTER 2:
HYDROLOGY IN RELATION TO SOIL
EROSION
Mengistu Zantet (MSc in Hydraulic Engineering )
Lecturer @ Hydraulic and Water Resources Engineering department
Mizan Tepi university
Email: mengistu.zantet@gmail.com
P.O.Box: 260
Tepi, Ethiopia
7/15/2021
mengistu.zantet@gmail.com
. lecturer @Hydraulic and Water
Resources Engineering Department
Mizan Tepi University 1

Brainstorming
What is hydrology?
Why we need to study hydrology?
What is a hydrologic cycle?
Components of hydrologic cycle
World water quantities
Application in Engineering
Hydrological Data and its Sources
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Mizan Tepi University

2.1 General
In the context of soil erosion the
hydrological event more sound is the
run-off besides precipitation, water
infiltration and other processes and
conditions of the hydrologic cycle.
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Cont..
The portion of precipitation which appears in the
surface streams of either perennial or intermittent
nature is called runoff. OR
Runoff:
 Gravity movement of water from a watershed
through a surface channel.
 Output from a watershed in a given unit of
time.
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Units of runoff are normally expressed as:
Volume per unit of time: cumec (m3s-
1) and
In Depth form equivalent: mm/day (or
month or year)
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Runoff images
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2.2. Components of Runoff
According to the source from which the flow
is derived, the total runoff is visualized to
consist of
Surface runoff -Flow above the soil
Subsurface runoff -Flow at the upper crusts of the
soil that returns to the surface
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1.Surface runoff
The precipitation falling on the water surface is called
channel precipitation and it immediately becomes the
stream flow.
The rest of the precipitation falling on the land surface,
after satisfying the infiltration demand, is temporarily
detained on the ground surface and
 when sufficient depth is built up it travels over the
ground surface towards the stream channel – overland
flow.
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Surface runoff:
That part of the total runoff which travels over the
ground surface to reach a stream channel and then
through the channel to reach the basin outlet.
it is the combination of the overland flow and
the channel precipitation
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Surface runoff
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2.Subsurface runoff/Interflow
Water which infiltrates the soil surface and then
moves laterally through the upper soil horizons
towards the stream channels above the main
groundwater table is known as the interflow.
There may be several levels of interflow, depending
on the texture and characteristics of the soils.
It is also known as subsurface runoff, subsurface
stream flow, storm seepage, and secondary base
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2.Subsurface runoff/Interflow
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3. Groundwater Flow:
 Rainfall that infiltrates the catchment surface,
percolates through the soil layer to the underlying
groundwater and will eventually reach the main
stream channels.
 The slow movement of the flow through the soil may
lead to delays in the stream flow occurrence.
(Several days, weeks or years)
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Groundwater Flow:
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Runoff Classification
Runoff is categorized based on the time delay
between the precipitation and runoff.
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Direct runoff
The direct runoff or quick flow is that part of RO which
enters the stream promptly and is equal to the sum of
surface RO and rapid interflow.
This clearly represents the major RO contribution
during storm periods and is also the major contribution
to most floods.
Precipitation excess is that part of total precipitation
which contributes directly to the surface runoff
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Base flow
–The base flow is defined as the sustained or
fair-weathered RO and it is composed of GW
RO and delayed interflow.
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2.3 Factors affecting runoff
1)The climatic factors
include
 Intensity of rainfall
 Duration of rainfall
 Areal distribution of rainfall
 Direction of storm movement
 Antecedent precipitation
 Other climatic factors that
affect evapotranspiration
2) The physiographic factors
are
 Land use
 Type of soil
 Area of the basin
 Shape of the basin
 Slope
 Storage characteristics of
the basin
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1)The climatic factors
Intensity of rainfall, Ip
RO α Ip because an intense RF occurs in a
short time and the evp. and infiltration losses are
relatively small.
 For Ip exceeding the infiltration capacity, the
RO increases with increase in intensity.
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Intensity of rainfall
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Duration of rainfall
If RF occurs over a long period, the runoff is large
because the RO is proportional to the total RF.
Moreover, the infiltration capacity decreases with
time.
 Under favorable conditions the infiltrated water may
even raise the water table to the ground surface
reducing the infiltration to zero leading to serious flood.
 As a consequence, rains of long duration may
produce high rates of RO even though Ip is relatively
mild.
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It is pertinent here to consider the duration
of rainfall in conjunction with concentration
time of the basin tc,
It is defined as the time taken by a rain drop
falling on the remotest point of the basin to
reach the basin outlet.
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Duration of rainfall
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As duration increase runoff increase

If the duration of RF, tr >= tc the whole of the
basin is likely to contribute to RO >> so that
the potential RO rate is maximum.
• On the other hand, if tr < tc the potential RO
will be lower than the maximum because only
part of the basin will be contributing to RO
before RF ceases.
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RF distribution over the basin
Uniform areal distribution >> rare in nature.
-Some portion receive RF << average RF over the
basin while the remaining portion receive RF which is
> the average of the basin.
-A large areal extent of the RF over the catchment
produces large RO.
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RF distribution
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Heavy RFs in the lower portions of the basin
will produce a RO hydrograph with a rapid rise
and nearly peak discharge,
while heavy RF in the upper portions will
reverse the hydrograph trend with a slow rise
and late peak.
If uniform over the entire basin __ a long and
slow increase in the hydrograph.
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Direction of storm movement
If a storm striking a long and narrow basin is
moving in an u/s direction the RO contributed by the
lower tributaries would have been already drained
out by the time the RO from the middle and upper
tributaries reaches the basin outlet >> less peak
discharge would be observed in this case.
When storm moves d/s the runoff peaks from the
individual tributaries are more likely to arrive at the
basin outlet at approximately the same time>>with
the result the runoff peak will be many times more than in
the case of storm moving upstream.
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Direction of storm movement
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Antecedent precipitation
soil moisture at the time of occurrence of storm
would greatly influence the RO peak resulting from
that storm.
Even very intense rains falling in late summer,
when the soil moisture is at its least, rarely produce
high discharges because most of the water enters
the soil moisture under the existing high infiltration
capacity rates and is held there.
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Antecedent precipitation
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Moisture high runoff
Dry less runoff

2) Physiographic factors
• Land use:
 the manner in which a land is being used is called land use.
Rain over a thick forest or vegetated area produces less
RO because of large interception, transpiration and
infiltration losses.
In urban areas, the losses are less and the RO is more
because of paved areas (no infiltration).
In non forested areas the infiltration, interception and
evaporation and transpiration losses are less and
therefore high RO rates are expected.
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Land use:
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Urban
area
High
run off
Vegetation
area
Less runoff

Type of soil
 The type of soil has direct influence on its
infiltration capacity rate and consequently it also
affects the runoff.
 Light textured soils (sandy soils) consists of
coarser soil particles and has large pore spaces
 rapid absorption of water  less runoff
potential.
 Heavy textured soil (clay soils) have fine soil
particles  small pore spaces  little absorption
of water  huge runoff volume.
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Type of soil
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Clay soil high runoff
Sandy soil less runoff

Area of the basin
 The area of the basin increases as the outlet point
shifts downstream.
 Area of the basin affects the peak flow and minimum
flow in different ways.
 If all other factors including depth and intensity of
rainfall remain constant in all instances, the total runoff
expressed as depth in cm over the basin will be same
for all the basins irrespective of their size.
 The total runoff expressed as volume will be more in
the case of large basins associated with higher peak
discharges.
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Area of the basin
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Large area high runoff
Small area less runoff

Shape of the catchment
In approximately square or circular drainage basins
the tributaries often tend to become together and
join the main stream near the center of the area.
Consequently, the separate runoff peaks generated
by heavy rainfall in the individual tributaries are
likely to reach the main stream in approximately the
same locality and at approximately the same time,
there by resulting in a large and rapid increase in
the runoff.
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Shape of the catchment
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On the other hand, if the basin is long and narrow the
tributaries will tend to be relatively short and are
more likely to join the main stream at intervals along
its length.
 This means that after a heavy rainfall over the area
the runoff peaks of the lower tributaries would have
left the catchment before the peaks of the upstream
tributaries have reached the basin outlet.
Elongated catchments are thus less subjected to
high runoff peaks (see Fig. below).
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A catchment area with a carrot-shape has peak
flow occurring earlier than the catchment of other
type
The is because a larger catchment area in the
latter case is contributing at the basin outlet.
Depending on the shape, sometimes a catchment
may have a multi-peak runoff pattern , even
though all the three catchments may have the
same area and characteristics.
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Slope
 The slope of the catchment area is an
important factor as it decides the relative
importance of infiltration, interflow and
overland flow..
 A catchments having extensive flat area
gives rise to low peaks and less runoff
whereas a catchment with steep slope
produces high peak flood
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Slope
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Steep slope ,high runoff
Flat land less runoff

Rate of infiltration from a flat catchment is more
which affects the velocity of overland flow.
Therefore, the time of arrival of peak at the outlet is
late and so is the total time of runoff for such flat
shaped catchment. The basin slope plays an
important role in urban hydrology where catchment is
usually small. For a high intensity and long duration
storm, the effect may be less pronounced.
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Activity 2.1
What is the Effects of surface runoff??
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2.4 Determination of Runoff
•Determination of accurate runoff rate or
volume from the watershed is a difficult
task, because runoff is dependant upon
several factors related to watershed and
atmosphere, prediction of whom is not so
easy
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Some common runoff estimation methods
are given below:
1) Rainfall-Runoff Correlation
2) Empirical Methods
3) Rational Method
4) Curve Number Method (runoff volume
estimation)
5) Infiltration Indices method
6) Hydrograph Method
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2.3.1.Rainfall-Runoff Correlation
• The relation between rainfall and the resulting runoff is quit
complex and is influenced by a host of factors relating to the
catchments and climate.
• Further, there is the problem of paucity of data which forces
one to adopt simple correlations for the adequate estimation
of runoff.
• One of the most common methods is to correlate runoff, R
with rainfall, P values.
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Rainfall-Runoff Correlation
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• Plotting of R values against P and drawing a best
fit line can adopted for very rough estimates.
• A better method is to fit a linear regression line
between R and P and to accept the result if the
correlation coefficient is nearer unity.
• The equation for straight-line regression between
runoff R and rainfall P is R = aP + b
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and the values of the coefficients a and b are
given by
The value of r lies between 0 and 1 as R have
only positive correlation with P.
See Example on subermanya page 163
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• A value of 0.6 < r < 1.0 indicates good
correlation. Further it should be noted that R  0.
• For large catchment, it is found advantageous to
have an exponential relationship as
In logarithmic form
and the coefficients
m and ln  determined by using the method
indicated earlier.
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2.3.2. Computation of Runoff using
empirical formulae
With a keen sense of observation in the region of
their activity, many engineers of the past have
developed empirical runoff estimation formulae.
However, these are applicable only to the region in
which they have been developed.
Empirical formulas can be classified in different
ways depending upon the basis adopted.
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• But they be considered under the following heads for the
purpose of present discussion
• Formulae that take area of the basin only into
consideration
• Formulae that take one or more basin parameters apart
from area and also rainfall characteristics into
consideration
• These formulae are essentially rainfall-runoff relations
with additional third or fourth parameters to account for
climatic or catchment characteristics.
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Some of the important formulae are
1) Runoff Coefficient Method
• This method involves the estimation of runoff by
multiplying the runoff coefficient to the rainfall
depth of the area. It is given by
R = C  P
where, R = runoff, cm
C = Runoff coefficient, and P = Rainfall depth, cm
• Runoff coefficient depends on factors affecting
runoff.
• The values of runoff coefficient for different land
use conditions are given in the Tab. Below.
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Table 2.1: Values of Runoff Coefficient (C)
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2) Formulae based on Area of the basin
• There are several regression equation for predicting the
runoff rate from the drainage basins.
• The form of equation is given as under.
• where = Peak flow for a given recurrence interval, (m3/s)
• n,C = are constants, known as regression constants
• A = Drainage area, (km2)
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• Dicken's Formula:
• Admasu's Formaula (1989):
• Seleshi (2001):
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3) Khosla`s formula
• R = P – 4.811 T
• Rm = Pm – Lm
Lm = 0.48 Tm for Tm >4.5 °C
For Tm < 4.5 0C
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Where,
R = annual runoff in mm
P = annual rainfall in mm
T = mean temperature in °C
Rm = monthly runoff in cm and Rm  0
Pm = monthly rainfall in cm
Lm = monthly loss in cm
Tm = mean monthly temperature of the catchment in
°C.
• Khosla’s formula is indirectly based on the water-
balance concept and the mean monthly catchments
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Example:
• For a given catchment, the mean monthly
rainfall and temperatures are given.
Calculate the annual runoff and annual
runoff coefficient by Khosla`s formula.
Solution
In Khosla`s formula (Eq. 8)
Rm = Pm – Lm
If the loss Lm is higher than Pm then Rm is taken
to be zero.
The value of Rm calculated by Eq. are
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Annual runoff = Total = 17.1 + 15.1 + 2.6 = 34.8 cm3
65

2.4.3. Rational Method
•Among various types of empirical relations, rational formula
is the most rational method of calculating peak discharge for
small catchments.
•In this method, it is assumed that the maximum flood flow is
produced by a certain rainfall which lasts for a time equal to or
greater than the period of concentration time.
•This concentration time is the time required for the surface
runoff from the remotest part of the catchments area to reach
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Dr REZAUR, R.B.
66

• When the storm continues beyond concentration
time every part of the catchments would be
contributing to the runoff at outlet and therefore it
represents conditions of peak runoff.
• The runoff rate corresponding to this condition is
given by
where A is the area of the catchment,
I is the intensity of rainfall and
C a runoff coefficient to account for th
abstractions from the rainfall.
• In this equation, if A and I are substituted in units of
acres and inches/h, the runoff is obtained in ft3/s
without requiring any conversation factor.
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• where
• Qp = peak discharge (m3/s),
• C = runoff coefficient,
• I= the mean intensity of precipitation
(mm/h) for a duration equal to tc and an
exceedence probability P, and
• A = drainage area in (km)2.
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Runoff coefficient
• is the ratio of peak runoff rate to the rainfall
intensity.
• Its values are assigned on the basis of land use
and soil type (Tab. 1).
• When the watershed has different features
regarding land use and soil types, then weighted
value of runoff coefficient is determined.
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For example: Let, if a watershed area is
divided into five sub-parts on the basis of
soil type and land use practice adopted,
having the area a1, a2, a3, a4 and a5 and the
value of runoff coefficient is C1, C2, C3, C4,
and C5, respectively for the five sub-
watersheds, Then the value of weighted
runoff coefficient (C) is given by:
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Table: Values of C as a function of land use, topography and
soil type for use in rational Method
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Example 2
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Compute the value of weighted runoff coefficient of
watershed from the following data regarding
watershed characteristics.
72

Solution:
• Using the weighted runoff coefficient formula
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Example 3
An engineer is required to design a drainage system
for an airport with an area of 2.5 km2 for 50 years
return period. The 50-year rainfall intensity in that
region is given by:
where I is intensity in cm/h and t is duration in
minutes.
If the concentration time for the area is estimated as
50 minutes, what is discharge that must be used to
design the system?
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Solution
Concentration time tc = 50 min
Intensity of rainfall for this duration =
Since the airport is fully paved, it may be
considered impervious and the runoff coefficient
C may be taken as unity.
• Therefore
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Example 4
A culvert is proposed across stream drainage an area
of 185 ha. The catchment has a slope of 0.004 and
the length of travel for water is 1150 m. Estimate the
25-year discharge if the rainfall intensity is given by
where I is in mm/h, Tr is in years and t is in minutes.
Assume a runoff coefficient of 0.35.
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Solution:
• L = 1150 m, S = 0.004
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Example 5
• Calculate the time of concentration of 306 ha land
of watershed, if the maximum length of drainage
course is 350 m and effective slope of water
course is about 4 m/ 100 m.
• Solution:
• Given that, L = 350 m, S = 4/ 100
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Since the above relationship does not give
the accurate estimate for the small watershed
smaller than 5 sq. km.
 Haan et al (1982) proposed another
relationship.
He justified that, small watersheds are mainly
dominated by overland flow rather than channel
flow.
Incorporating this effect, he formulated the
following equation for computing the time of
concentration which is basically the addition of
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where, L0 = length of overland flow, m
n = Manning’s roughness coefficient (Tab.)
S0 = Slope along the flow path, m/m
Table 6.3: Value of Manning's Roughness Coefficient
(n)
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To find intensity of rainfall I at a place, any of the
following formulae can be used depending on their
suitability.
Table 6.4: Equations for Computation of Maximum
Intensity of a Storm
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If there is no self-recording rain gauge, then the
following formula can be used to obtain the
maximum intensity of the storm that is likely to
occur during an interval of any one hour within the
storm duration.
where I is the maximum intensity of rainfall in
mm/h, F the total rainfall of the storm in mm and t
is the duration of the storm in h.
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Assumption of rational Method
1. Rainfall occurs with a uniform intensity for the
duration at least equal to the time of concentration of
the catchments area, and
2. The rainfall intensity is uniformly distributed
throughout the catchments.
If the above two assumptions are satisfied for any
storm, then the relationship between rainfall and runoff
produced by the catchment, may be presented in the
graphical form, shown in the Fig., which indicates that,
any specified storm having uniform intensity, if
occurred for the duration greater than time of
concentration, the rate of runoff yield is less than the
peak value, because rainfall intensity is reduced for
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• Similarly, a storm occurring for the duration less
than Tc, the resulting runoff would also be less than
the peak value, as in this condition, all parts of
watershed are not able to yield the discharge to the
outlet, simultaneously.
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Example 6:
An outlet is to be designed for a small town covering 12 km2,
of which road area is 30 %, residential area is 50 % and the
rest is industrial area. The slope of the catchment is 0.005 and
the maximum length of the town measured on the map is 1.6
km. From depth duration analysis for the catchment, the
following information are obtained.
Rainfall duration (min) 30 40
50
Rainfall depth (mm) 30 40 44
Compute the peak discharge from this town
Solution
Time of concentration can be calculated from Kirpich
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Rainfall for tc = 45 min is computed by
interpolating data given in the problem.
i.e. 40 45 50
40 ? 44 using interpolation
 d = 42 mm and tc=45 min then ,I=56
mm/h
From Table 5.2, C for road is 0.8, for residential
area is 0.40 and for industrial area is 0.20.
= 0.24 + 0.20 + 0.04 = 0.48
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Limitation of Rational Formula
1. The formula is applicable to small catchments. The
watershed can be maximum up to 50 km2.
2. Duration of rainfall intensity should be more than the
time of concentration of the basin.
3. It gives the peak of the hydrograph but does not provide
the complete hydrograph.
4. It plots a straight-line relation between Qp and I with
intercept zero whereas nature does not follow such a simple
equation.
5. Rainfall intensity must be constant over the entire
watershed during the time of concentration.
6. Coefficient C is assumed to be same for all storms which
means the losses are constant for all storms.
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2.5 SCS Curve Number Method
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3.Hydrograph analysis
A hydrograph is the graphical representation of
the instantaneous discharge of a stream plotted with
time (see Fig. 3.1).
The hydrograph has two main components, a
broad band near the time axis representing base
flow contributed from groundwater, and the
remaining area above the base flow, the surface
runoff, which is produced by the storm.
The peak of the hydrograph is reached after the
effective rainfall has reached its maximum.
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• The time difference between the maximum
effective rainfall intensity and the maximum
runoff is called the time lag.
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Depending upon the unit of time involved, we
have:
i. Annual Hydrograph:
Showing the variation of daily or weekly or 10 daily
mean flows over a year
ii. Monthly Hydrograph:
Showing the variation of daily mean flows over a
month
iii. Seasonal Hydrograph:
Showing the Variation of the discharge in a particular
season, e.g. monsoon or dry season.
iv. Flood Hydrograph or Hydrograph:
A hydrograph that shows stream flows in a watershed
during the occurrence of storms.
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Applications of annual and seasonal
hydrographs are
calculating the surface water potential of stream,
reservoir studies and
drought studies.
Flood hydrographs are essential in analysing
stream characteristics associated with floods.
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A study of the annual hydrographs of streams
enables one to classify streams into three
classes as
perennial,
 intermittent and
 ephemeral.
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The following basic assumptions are inherent
in this model (Chow et.al., 1988):
The excess rainfall has a constant intensity within the
effective duration.
The excess rainfall is uniformly distributed throughout
the whole catchment area.
The base time of the direct runoff resulting from an
excess rainfall of given duration is constant, irrespective
of the rain intensity.
The ordinates of all hydrographs of a common time base
(or the direct runoff hydrographs produced by effective
rainfalls of the same duration) are directly proportional to
the total amount of direct runoff represented by each
hydrograph.
For a given catchments, the hydrograph resulting from a
given excess rainfall reflects the unchanging
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Separation of Base Flow and Runoff
• As mentioned earlier, a hydrograph consists of 3
sources – surface runoff, interflow and base flow.
• In most cases, it is not easy to estimate the actual
amount of base flow that contributes to the watershed.
• Therefore, one way to do this is to assume and
separate the base flow components from the
hydrograph.
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• There are 3 methods of base flow separation:
1) Method 1: Straight line method
2) Method 2: Fixed Base Method:
3) Method 3: Variable Slope Method
• The surface runoff hydrograph obtained after the
base flow separation is called ‘Direct Runoff
Hydrograph’ (DRH).
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Method 1: Straight line method
Straight line method joining the beginning of the
direct runoff to a point on the recession limb
representing the end of the direct runoff.
Point A represents the beginning of the excess
rainfall (direct runoff), by looking sharp change of
runoff.
• But point B, end of the direct runoff is difficult to
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• Therefore, point B is estimated by using,
N = 0.83 A 0.2
where, A is the watershed area (km2) and N
(days) is measured from Qpeak.
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Method 2: Fixed Base Method
• This method projects the initial base flow curve
from point A to C, which lies directly below the peak
rate of flow. Later, point C is joined to point B by a
straight line.
•
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Method 3: Variable Slope Method
• The base flow recession curve after the depletion
of the flood water is extended backwards till it
intersects the ordinate at the point of inflection, Pi
. Points A and F are joined by arbitrary smooth
curve while points F and E are joined by a
straight line.
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EFFECTIVE RAINFALL
• Effective Rainfall Hyetograph (ERH) is defined
by subtracting the initial losses and infiltration
losses from a hyetograph of the rainfall.
• ERH is also known as hyetograph of rainfall
excess or supra rainfall.
Calculation for Total Amount of ER
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DRH (unit of m3/s) and ERH (unit of cm/h) represent the
same total quantity of runoff even though both are in
different units.
BUT, it is necessary to make DRH and ERH having the
same units, how can we do this?
How to make ER=DR?
HYETOGRAPH – ERH HYDROGRAPH - DRH
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UNIT HYDROGRAPH (UH)
•The DRH hydrograph that results from 1
cm (or inch) of rainfall excess, occurring
uniformly over the basin at a uniform rate
during a specified duration of time.
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EXERCISE#1
Given below are the ordinates of a 6h unit
hydrograph for a catchment. Calculate the
ordinates of the DRH due to a rainfall excess of
3.5 cm occurring in 6h.
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Exercise#2
• Given is the following cumulative rainfall and
total runoff from a catchment of size 104 km2
Required: the derivation of the unit hydrograph of appropriate duration
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the end
7/15/2021

Chapter 2

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Chapter 2