Hydrology.pdf

Chapter 5
Drainage Design Manual - 2002 Hydrology

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5.1 DEFINITIONS AND SYMBOLS
Hydrology is generally defined as a science dealing with the interrelationship between
water on and under the earth and in the atmosphere. For the purpose of this manual,
hydrology will deal with estimating flood magnitudes as the result of precipitation. In the
design of highway drainage structures, floods are usually considered in terms of peak
runoff or discharge in cubic meters per second (m
3
/s) and hydrographs as discharge per
time. For structures that are designed to control volume of runoff, like detention storage
facilities, or where flood routing through culverts is used, then the entire discharge
hydrograph will be of interest.
The following are concepts that are important in a hydrologic analysis. These concepts
will be used throughout the remainder of this chapter in dealing with different aspects of
hydrologic studies:
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The soil moisture conditions of the catchment area at the beginning
of a storm. These conditions affect the volume of runoff generated
by a particular storm event. Notably they affect the peak discharge
only in the lower range of flood magnitudes – approx. below the 15-
year event threshold. As floods become more rare, antecedent
moisture has a rapidly decreasing influence on runoff.
'HSUHVVLRQ
6WRUDJH
The natural depressions within a catchment area that store runoff.
Generally after the depression storage is filled, runoff will begin.
)UHTXHQF The number of times a flood of a given magnitude can be expected
to occur on average over a long period of time. Frequency analysis
is the estimation of peak discharges for various recurrence intervals.
Another way to express frequency is with probability. Probability
analysis seeks to define the flood flow with a probability of being
equaled or exceeded in any year.
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A composite of the physical characteristics that influence the flow
of water across the earth's surface, whether natural or channelized. It
affects both the time response of a catchment area and drainage
channel, as well as the channel storage characteristics.
+GURJUDSK A graph of the time distribution of runoff from a catchment area.
+HWRJUDSK A graph of the time distribution of rainfall over a catchment area.
,QILOWUDWLRQ A complex process of allowing runoff to penetrate the ground
surface and flow through the upper soil surface. The infiltration
curve is a graph of the time distribution at which this occurs.

Chapter 5
Hydrology Drainage Design Manual - 2002

,QWHUFHSWLRQ The storage of rainfall on foliage and other intercepting surfaces
during a rainfall event is called interception storage.
/DJ7LPH The time from the centroid of the excess rainfall to the peak of the
hydrograph.
3HDN'LVFKDUJH Sometimes called peak flow. The maximum rate of flow of water
passing a given point during or after a rainfall event.
5DLQIDOO([FHVV The water available to runoff after interception, depression storage
and infiltration have been satisfied.
6WDJH The elevation of the water surface above some elevation datum.
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RQFHQWUDWLRQ
The time it takes a drop of water falling on the most remote point
hydraulically in the catchment area to travel through the catchment
area to the outlet.
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+GURJUDSK
The direct runoff hydrograph resulting from a rainfall event that has
a specific temporal and spatial distribution and which lasts for a unit
duration of time. The ordinates of the unit hydrograph are such that
the volume of direct runoff represented by the area under the
hydrograph is equal to one millimeter of runoff from the catchment
area.
To provide consistency within this chapter, as well as throughout this manual, the
following symbols will be used. These symbols were selected because of their wide use
in hydrologic publications.
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Symbol Definition Units
A Catchment area hectares, sq.km.
BDF Basin development factor %
C Runoff coefficient -
C
f Frequency factor -
CN SCS-runoff curve number -
C
t, C
p Physiographic coefficients -
d Time interval hours
DH Difference in elevation m
I Runoff intensity mm/hr
IA Percentage of impervious area %
I
a Initial abstraction from total rainfall mm
K Frequency factor for a particular return period and skew -
L Lag hours
l Length of mainstream to furthest divide m
L
ca Length along main channel to a point opposite the
catchment area centroid km
M Rank of a flood within a long record -
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n Manning roughness coefficient -
N Number of years of flood record years
P Accumulated rainfall mm
Q Rate of runoff m
3
/s
q Storm runoff during a time interval mm
R Hydraulic radius m
RC Regression constant -
RQ Equivalent rural peak runoff rate m
3
/s
S or Y Ground slope m/m, m/km or %
S Potential maximum retention storage mm
SCS Soil Conservation Service -
SL Main channel slope m/m
S
L Standard deviation of logarithms of peak annual floods -
ST Basin storage factor %
T
B Time base of unit hydrograph hours
t
c or T
c Time of concentration min or hours
T
L Lag time hours
T
r Snyder’s duration of excess rainfall hours
UQ‘ Urban peak runoff rate m
3
/s
V Velocity m/s
X Logarithm of the annual peak -
5.2 HYDROLOGIC DESIGN PRINCIPLES
KDSWHU6WDQGDUGVDQG'HSDUWXUHV from Standards defines the general principles for
hydrological and drainage design in accordance with this manual. The hydrological data
available for Ethiopia is generally limited so the procedures that can be applied are
consequently imprecise. No specific standards or definitive criteria for hydrological
analysis are suitable for recommendation at this time. For standard procedures to be
adopted confidently, storm water runoff coefficients and procedures shall be calibrated.
6859(6
Since hydrologic considerations can influence the selection of a highway corridor and the
alternate routes within the corridor, studies and investigations shall be undertaken at the
Planning Stage (see KDSWHU3ODQQLQJ). Also, special studies and investigations may
be required at sensitive locations. The magnitude and complexity of these studies shall be
commensurate with the importance and magnitude of the project and problems
encountered. Typical data to be included in such surveys or studies are: topographic
maps; aerial photographs; streamflow records; historical highwater elevations; flood
discharges; and locations of hydraulic features such as reservoirs, water projects, and
designated or regulatory floodplain areas.
+'52/2*,$1$/6,6$1'0(7+2'6
A hydrologic analysis is prerequisite to identifying flood hazard areas and determining
those locations where construction and maintenance will be unusually expensive or
hazardous. Since many levels of government plan, design, and construct highway and
water resource projects that might affect each other, interagency coordination is desirable
and often necessary. In addition, agencies can share data and experiences within project
areas to assist in the completion of accurate hydrologic analysis.

Chapter 5

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Experience indicates that the design of highway drainage structures should be
documented adequately. Frequently, it is necessary to refer to plans and specifications
long after the actual construction has been completed. Thus it is necessary to fully
document the results of all hydrologic analysis.
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For all hydrologic analyses, the following factors shall be evaluated and included when
they will have a significant effect on the final results:
• Drainage basin characteristics including: size, shape, slope, land use, geology, soil
type, surface infiltration, and storage;
• Stream channel characteristics including geometry and configuration, natural and
artificial controls, channel modification, aggradation - degradation, and debris;
• Flood plain characteristics; and
• Meteorological characteristics such as precipitation amounts and type (rain, hail, or
combinations), storm cell size and distribution characteristics, storm direction, and
time rate of precipitation (hyetograph).
)/22'+,6725
All hydrologic analysis shall consider the flood history of the area and the effect of these
historical floods on existing and proposed structures. The flood history includes the
historical floods and the flood history of any existing structures.
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Many hydrologic methods are available. The methods to be used and the circumstances
for their use are listed below. If possible the method shall be calibrated to local
conditions and tested for accuracy and reliability. The hydrologic methods approved by
ERA and limitations on their use follows:
• Rational method shall be used only for catchment areas less than 50 hectares (0.5
km
2
);
• SCS and other unit hydrograph methods for catchment areas greater than 50 hectares;
• Catchment area regression equations shall be used for all routine designs at sites
where applicable;
• Gumbel or Log Pearson III analyses shall preferably be used for all routine designs
provided there is at least 10 years of continuous or synthesized record for 10-year
discharge estimates and 25 years for 100-year discharge estimates;
• Suitable computer programs such as HYDRAIN’s HYDRO, HEC 1, and TR-20 may
be used to facilitate tedious hydrologic calculations.
Of these possible hydrologic methods, it should be noted that, at the present time, only
the Rational and SCS methods are applicable to the whole country. Regression equations
and derivations from stream gauging (Gumbel, Log Pearson) are often preferred but rely
on data not available. For this reason, only the rational method and the scs method are
given in this chapter. regression equations and derivations from stream gaging are
however given in appendix A.

Chapter 5

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All proposed structures are sized using the specified design frequency as provided in
Table 2-1 of KDSWHU6WDQGDUGVDQG'HSDUWXUHVIURP6WDQGDUGV. The following text
further develops the choices presented in that table.
A design frequency shall be selected to match the facility’s cost, amount of traffic,
potential flood hazard to property, expected level of service, political considerations, and
budgetary constraints, considering the magnitude and risk associated with damages from
larger flood events. With long highway routes having no practical detour, where many
sites are subject to independent flood events, it may be necessary to increase the design
frequency at each site to avoid frequent route interruptions from floods. In selecting a
design frequency, potential upstream land use that could reasonably occur over the
anticipated life of the drainage facility shall be considered.
Hydrologic analysis should include the determination of several design flood frequencies
for use in the hydraulic design. These frequencies are used to size different drainage
structures to allow for an optimum design, that considers both risk of damage and
construction cost. Consideration shall be given to what frequency flood was used to
design other structures along a highway corridor.
Since it is not economically feasible to design a structure for the maximum runoff a
catchment area is capable of producing, a design frequency must be established. The
frequency with which a given flood can be expected to occur is the reciprocal of the
probability or chance that the flood will be equaled or exceeded in a given year. If a
flood has a 20 percent chance of being equaled or exceeded each year, over a long period
of time, the flood will be equaled or exceeded on an average of once every five years.
This is called the UHWXUQ SHULRG RU UHFXUUHQFH LQWHUYDO (RI). Thus the exceedence
probability equals 100/RI.
The designer should note that the 5-year flood is not one that will necessarily be equaled
or exceeded every five years. There is a 20 percent chance that the flood will be equaled
or exceeded in any year; therefore, the 5-year flood could conceivably occur in several
consecutive years. The same reasoning applies to floods with other return periods.
Cross Drainage: A drainage facility shall be designed to accommodate a discharge with a
given return period(s) for the following circumstances. The design shall be such that the
backwater (the headwater) caused by the structure for the design storm does not:
• increase the flood hazard significantly for property;
• overtop the highway; or
• exceed a certain depth on the highway embankment.
Based on these design criteria, a design involving roadway overtopping of short duration
for floods larger than the design event is acceptable practice. Usually, if overtopping is
allowed, the structure may be designed to accommodate a flood of some lower frequency
without overtopping.
Storm Drains: A storm drain shall be designed to accommodate a discharge with a given
return period(s) for the following circumstances. The design shall be such that the storm
runoff does not:

Chapter 5

• increase the flood hazard significantly for property;
• encroach on to the street or highway so as to cause a significant traffic hazard; or
• limit traffic, emerging vehicle, or pedestrian movement to an unreasonable extent.
Based on these design criteria, a design involving a street or road inundation of short
duration for floods larger than the design event is an acceptable practice.
5(9,(:)5(48(1
After sizing a drainage facility using a flood (and the hydrograph) corresponding to the
design frequency, it is necessary to review this proposed facility with a base discharge.
This is done to insure that there are no unexpected flood hazards inherent in the proposed
facility(ies). The review (check) flood shall be at least the 100-year event, or as provided
in KDSWHU, Table 2-1. In some cases, a flood event larger than the specified review
flood might be used for analysis to ensure the safety of the drainage structure and
downstream development.
Certain hydrologic procedures use rainfall and rainfall frequency as the basic input rather
than flood frequency. It is commonly assumed that the 10-year rainfall will produce the
10-year flood. Depending on antecedent soil moisture conditions, and other hydrologic
parameters, there may not be a direct relationship between rainfall and flood frequency.
5.3 HYDROLOGY
,1752'87,21
The analysis of the peak rate of runoff, volume of runoff, and time distribution of flow is
fundamental to the design of drainage structures. Errors in the estimates will result in a
structure that is either undersized and causes more drainage problems or oversized and
costs more than necessary. On the other hand, it must be realized that any hydrologic
analysis is only an approximation. The relationship between the amount of precipitation
on a drainage basin and the amount of runoff from the basin is complex, and too little
data are available on the factors influencing the rural and urban rainfall-runoff
relationship to expect exact solutions.
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In the hydrologic analysis for a drainage structure, it must be recognized that there are
many variable factors that affect floods. Some of the factors that need to be recognized
and considered on an individual site by site basis are:
• rainfall amount and storm distribution;
• catchment area size, shape and orientation;
• ground cover;
• type of soil;
• slopes of terrain and stream(s);
• antecedent moisture condition;
• storage potential (overbank, ponds, wetlands, reservoirs, channel, etc.); and
• catchment area development potential.
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The type and source of information available for hydrologic analysis will vary from site
to site and it is the responsibility of the designer to determine what information is

Chapter 5

available and applicable to a particular analysis. A comprehensive list of data sources is
included in KDSWHU+GURJUDSKLF6XUYHof this manual.
5.4 HYDROLOGIC ANALYSIS PROCEDURE FLOWCHART
The hydrologic analysis procedure flowchart Figure 5-1 shows the steps needed for the
hydrologic analysis and the designs that will use the hydrologic estimates.
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Chapter 5

5.5 RAINFALL CURVES
Rainfall data have been collected from many Ministry of Water Resources meteorology
stations in the country (see Table 5-2). They have been subjected to statistical techniques
to develop the information needed from hydrologic analyses. The results indicate that the
country can be divided into several hydrological regions which display similar rainfall
patterns, as indicated on the map in Figure 5-8 at the end of this chapter. Using the
statistical analyses, rainfall intensity-duration curves have been developed for commonly
used design frequencies. Figures 5-9 through 5-12 at the end of this chapter show the
curves presently available.
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Meteorological
Region
Station Years
of
Record
Meteorological
Region
Station Years
of
Record
A1 Axum 18 B Bedele 19
Mekele 35 Gore 45
Maychew 24 Nekempte 27
A2 Gondar 40 Jima 45
Debre Tabor 22 Arba Minch 11
Bahir Dar 35 Sodo 28
Debre Markos 44 Awasa 26
Fitche 25 C Kombolcha 46
Addis Ababa 33 Woldiya 23
A3 Nazareth 40 Sirinka 17
Kulumsa 31 D1 Gode 29*
Robe/Bale 19 Kebri Dihar 38
A4 Metehara 28 D2 Kibre Mengist 24
Dire Dawa 46 Negele 45
Mieso 35 Moyale 18
* max 24 hour rainfall not given Yabelo 34
Years of record through 1997
127(6215$,1)$//$1$/6,6
The rainfall data available is too sparse to develop highly accurate intensity-duration-
frequency curves. The 24-hour rainfall depth records were generally adequate to project
the frequency of 24-hour rainfall depths. Based on the monthly rainfall depths and
patterns, the country was divided into regions and sub-regions.
The 24-hour depth frequency data for each sub-region was analyzed for each station in
the sub-region. Regression analysis was used to develop depth-frequency curves for each
sub-region. The curves were selected so that approximately 75% of the data lay BELOW
the selected design curve. This means that the total 24-hour rainfall estimated for a
particular region will be greater on average than the rainfall depth that might actually
occur, and that these rainfall curves are reasonably conservative estimates of rainfall
depths. It is recommended that hydraulic engineers using these curves do not also take

Chapter 5

conservative estimates of the other independent variables used in runoff estimation as
this will likely lead to excessively conservative and uneconomical designs.
The amount of data available for shorter duration storms was too sparse for the
development of intensity-duration-frequency curves, and was insufficient to do a
frequency distribution plot for each rainfall period. In order to develop intensity-duration-
frequency curves for each rainfall region, the ratios of the short duration data available
were compared to the 24-hour data. Based on this comparison and making similar
comparisons for published rainfall data from other regions, principally the United States,
it seemed that reasonable estimations of rainfall depths occurring in shorter periods could
be expressed as a fraction of the 24-hour rainfall depth.
Many recommendations for depth-duration-frequency curves in the technical literature
suggest a broken-leg approach such that the depth duration frequency equation for
shorter duration rainfalls, less than one hour, is different from that derived for longer
duration rainfalls. Because of the scarcity of data this approach was not taken and one
curve was developed. The amount of rainfall data obtained for peak rainfall intensities of
periods shorter than one-half hour was too limited to be useful. The curves presented are
satisfactory for rainfall durations of one-half hour or more. Intensities for periods shorter
than 15 minutes appear to be overestimated by the curves presented.
It is recommended in this manual for the design of most drainage structures that the
minimum time of concentration be taken as fifteen minutes. The design of gutters and
inlets may be based on shorter rainfall durations, but this isn’t serious conservatism. The
overall drainage system - drainage conduit - will usually be designed for a storm duration
of nearly 15 minutes or more, thus the most expensive part of the drainage system will
not be unnecessarily over-designed.
Relevant background information collected during the course of the preparation of this
manual is presented in $SSHQGL[%
5.6 HYDROLOGIC PROCEDURE
29(59,(:
Streamflow measurements for determining a flood frequency relationship at a site are
usually unavailable. In such cases, it is an accepted practice to estimate peak runoff rates
and hydrographs using statistical or empirical methods. In general, results from using
several methods shall be compared, not averaged. Standard practice is to use the
discharge that best reflects local project conditions with the reasons documented. Use is
outlined with each hydrologic procedure given below.
+'52/2*,352('85(6
The methods presented in this manual were selected to be consistent with the methods
available in the computer program HYDRAIN Integrated Drainage Design Computer
System and HEC 1. The hydrologic model within the HYDRAIN system is called
HYDRO and this model allows the user to select among several hydrologic procedures.
The possibilities generally applicable to available data for Ethiopia include:

Chapter 5

Rational Method - Provides peak runoff rates for small urban and rural catchment areas,
less than 50 hectares, but is best suited to urban storm drain systems and rural ditches. It
shall be used with caution if the time of concentration exceeds 30 minutes. Rainfall is a
necessary input.
SCS Synthetic Unit Hydrograph – The U.S. Soil Conservation Service has developed a
synthetic unit hydrograph procedure that has been used widely for developing rural and
urban hydrographs. The unit hydrograph used by the SCS method is based upon an
analysis of a large number of natural unit hydrographs from a broad cross section of
geographic locations and hydrologic regions. The rainfall depth to be used as input is
presented in Figure 5-13 at the end of this chapter.
5.7 RATIONAL METHOD
,1752'87,21
The Rational Method is most accurate for estimating the design storm peak runoff for
areas up to 50 hectares (0.5 km
2
). This method, while first introduced in 1889, is still
widely used. Even though it has come under frequent criticism for its simplistic
approach, no other drainage design method has achieved such widespread use.
$33/,$7,21
Some precautions shall be considered when applying the Rational Method:
• The first step in applying the Rational Method is to obtain a good topographic map
and define the boundaries of the catchment area in question. A field inspection of the
area should also be made to determine if the natural drainage divides have been
altered.
• In determining the runoff coefficient C value for the catchment area, thought shall be
given to future changes in land use that might occur during the service life of the
proposed facility that could result in an inadequate drainage system. Also, the effects
of upstream detention structures must be taken into account.
• Restrictions to the natural flow such as highway crossings and dams that exist in the
catchment area shall be investigated to see how they affect the design flows.
• The charts, graphs, and tables included in this section are not intended to replace
reasonable and prudent engineering judgment that should permeate each step in the
design process.
+$5$7(5,67,6
Characteristics of the Rational Method that generally limit its use to 50 hectares include:
(1) The rate of runoff resulting from any rainfall intensity is a maximum when the
rainfall intensity lasts as long or longer than the time of concentration. That is, the
entire catchment area does not contribute to the peak discharge until the time of
concentration has elapsed.
This assumption limits the size of the drainage basin that can be evaluated by the
Rational Method. For large catchment areas, the time of concentration can be so large
that constant rainfall intensities for such long periods do not occur and shorter more
intense rainfalls can produce larger peak flows. Further, in semi-arid and arid regions,

Chapter 5

storm cells are relatively small with extreme intensity variations thus making the
Rational Method inappropriate for catchment areas greater than 50 hectares.
(2) The frequency of peak discharges is the same as that of the rainfall intensity for the
given time of concentration.
Frequencies of peak discharges depend on rainfall frequencies, antecedent moisture
conditions in the catchment area, and the response characteristics of the drainage system.
For small and largely impervious areas, rainfall frequency is the dominant factor. For
larger drainage basins, the response characteristics control. For catchment areas with few
impervious surfaces (little urban development), antecedent moisture conditions usually
govern, especially for rainfall events with a return period of 10 years or less.
(3) The fraction of rainfall that becomes runoff (C) is independent of rainfall intensity
or volume.
This assumption is only reasonable for impervious areas, such as streets, rooftops, and
parking lots. For pervious areas, the fraction of runoff does vary with rainfall intensity
and the accumulated volume of rainfall. Thus, the application of the Rational Method
requires the selection of a coefficient that is appropriate for the storm, soil, and land use
conditions. Many guidelines and tables have been established, but seldom, if ever, have
they been supported with empirical evidence.
(4) The peak rate of runoff is sufficient information for the design.
Modern drainage practice includes detention of urban storm runoff to reduce the peak
rate of runoff downstream. Using only the peak rate of runoff, the Rational Method
severely limits the evaluation of design alternatives available in urban and in some
instances, rural drainage design.
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The rational formula estimates the peak rate of runoff at any location in a catchment area
as a function of the catchment area, runoff coefficient, and mean rainfall intensity for a
duration equal to the time of concentration (the time required for water to flow from the
most remote point of the basin to the location being analyzed). The rational formula is
expressed as:
Q = 0.00278 CIA (5.1)
where:
Q = maximum rate of runoff, m
3
/s
C = runoff coefficient representing a ratio of runoff to rainfall (see
Tables 5-3 through 5-5)
I = average rainfall intensity for a duration equal to the time of
concentration, for a selected return period, mm/hr
A = catchment area tributary to the design location, ha
,1)5(48(1767250
The coefficients given in Tables 5-3 through 5-5 are applicable for storms of 5-yr to 10-
yr frequencies. Less frequent, higher intensity storms will require modification of the

Chapter 5

coefficient because infiltration and other losses have a proportionally smaller effect on
runoff (11). The adjustment of the Rational Method for use with major storms can be
made by multiplying the right side of the rational formula by a frequency factor C
f. The
rational formula now becomes:
Q = 0.00278 CC
f IA (5.2)
C
f values are listed below. The product of C
f times C shall not exceed 1.0.
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+GURORJLF6RLO*URXSLQJVDQG6ORSH5DQJHV VHHDOVR7DEOH
Soil Type

Terrain Type
A B C D
Flat, 2% 0.04-0.09 0.07-0.12 0.11-0.16 0.15-0.20
Rolling, 2-6% 0.09-0.14 0.12-0.17 0.16-0.21 0.20-0.25
Mountain, 6-15% 0.13-0.18 0.18-0.24 0.23-0.31 0.28-0.38
Escarpment, 15% 0.18-0.22 0.24-0.30 0.30-0.40 0.38-0.48
7DEOH5HFRPPHQGHG5XQRIIRHIILFLHQWIRU9DULRXV6HOHFWHG/DQG8VHV
Description of Area Runoff Coefficients
Business: Downtown areas 0.70-0.95
Neighborhood areas 0.50-0.70
Residential: Single-family areas 0.30-0.50
Multi units, detached 0.40-0.60
Multi units, attached 0.60-0.75
Suburban 0.25-0.40
Residential (0.5 hectare lots or more) 0.30-0.45
Apartment dwelling areas 0.50-0.70
Industrial: Light areas 0.50-0.80
Heavy areas 0.60-0.90
Parks, cemeteries 0.10-0.25
Playgrounds 0.20-0.40
Railroad yard areas 0.20-0.40
Unimproved areas 0.10-0.30
Source: Hydrology, Federal Highway Administration, HEC No. 19, 1984
7DEOHRHIILFLHQWVIRURPSRVLWH5XQRII$QDOVLV
Surface Runoff Coefficients
Street : Asphalt 0.70-0.95
Concrete 0.80-0.95
Drives and walks 0.75-0.85
Roofs 0.75-0.95
Source: Hydrology, Federal Highway Administration, HEC No. 19, 1984

Chapter 5

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Recurrence Interval (years) C
f
5 1.0
10 1.0
25 1.1
50 1.2
100 1.25
352('85(6
The results of using the Rational Formula to estimate peak discharges is very sensitive to
the parameters that are used. The designer must use good engineering judgment in
estimating values that are used in the method.
Time of Concentration
The time of concentration is the time required for water to flow from the hydraulically
most remote point of the catchment area to the point under investigation. Use of the
Rational Method requires the time of concentration (t
c) for each design point within the
catchment area. The duration of rainfall is then set equal to the time of concentration and
is used to estimate the design average rainfall intensity (I). For a specific drainage basin,
the time of concentration consists of an inlet time plus the time of flow in a closed
conduit or open channel to the design point. Inlet time is the time required for runoff to
flow over the surface to the nearest inlet and is primarily a function of the length of
overland flow, the slope of the drainage basin, and surface cover. Pipe or open channel
flow time can be estimated from the hydraulic properties of the conduit or channel. An
alternative way to estimate the overland flow time is to use Figure 5-2 to estimate
overland flow velocity and divide the velocity into the overland travel distance.
For design conditions that do not involve complex drainage conditions, Figure 5-3 can be
used to estimate inlet time. For each catchment area, the distance is determined from the
inlet to the most remote point in the tributary area. From a topographic map, the average
slope is determined for the same distance. The runoff coefficient (C) is determined by the
procedure described in a subsequent section of this chapter.
To obtain the total time of concentration, the pipe or open channel flow time must be
calculated and added to the inlet time. After first determining the average flow velocity in
the pipe or channel, the travel time is obtained by dividing velocity into the pipe or
channel length. Manning’s Equation can be used to determine velocity (see KDSWHU
KDQQHOV).
Common Errors
Three common errors should be avoided when calculating t
c. First, application of
simplified general equations such as Kirpich for determining t
c can result in too short of a
time of concentration particularly when the average basin slope varies significantly from
the mean channel slope as in steep mountainous areas. Neglecting the overland flow time
can also dramatically shorten the time of concentration thus increasing the design peak

Chapter 5

runoff. Computing t
c for two reaches of main channel, from the low point to the 0.7
point, then from there to the end of the channel, has been found to give better results.
Second, in some cases runoff from a portion of the catchment area that is highly
impervious may result in a greater peak discharge than would occur if the entire area
were considered. In these cases, adjustments can be made to the catchment area by
disregarding those areas where flow time is too slow to add to the peak discharge.
Sometimes it is necessary to estimate several different times of concentration to
determine the design flow that is critical for a particular application.

Chapter 5


Chapter 5

Third, when designing a drainage system, the overland flow path is not necessarily
perpendicular to the contours shown on available mapping. Especially in urban areas, the
land will be graded and swales will intercept the natural contour and conduct the water to
the streets, which reduces the time of concentration. Care shall be exercised in selecting
overland flow paths in excess of 100 meters in urban areas and 200 meters in rural areas.
Rainfall Intensity
The rainfall intensity (I) is the average rainfall rate in mm/hr for a duration equal to the
time of concentration for a selected return period. Once a particular return period has
been selected for design and a time of concentration calculated for the catchment area,
the rainfall intensity can be determined from Rainfall-Intensity-Duration curves. Rainfall-
Intensity-Duration curves for use in Ethiopia are given in Figures 5-9 through 5-12 at the
end of this chapter.
Runoff Coefficient
The runoff coefficient (C) is the variable of the Rational Method least susceptible to
precise determination and requires judgment and understanding on the part of the
designer. A typical coefficient represents the integrated effects of many drainage basin
parameters. The following discussion considers the effects of soil groups, land use, and
average land slope.
Three methods for determining the runoff coefficient are presented based on soil groups
and land slope (Table 5-3), land use (Table 5-4), and a composite coefficient for complex
catchment areas (Table 5-5).
Table 5-3 gives the recommended runoff coefficient (C) for pervious surfaces by selected
hydrologic soil groupings and slope ranges. From this table the C values for non-urban
areas such as forest land, agricultural land, and open space can be determined.
Hydrological Soil Groups for Ethiopia
Soil properties influence the relationship between runoff and rainfall since soils have
differing rates of infiltration. Permeability and infiltration are the principal data required
to classify soils into Hydrologic Soils Groups (HSG). Based on infiltration rates, the Soil
Conservation Service (SCS) has divided soils into four hydrologic soil groups as follows:
Group A: Sand, loamy sand or sandy loam. Soils having a low runoff potential due to
high infiltration rates. These soils primarily consist of deep, well-drained sands and
gravels.
Group B: Silt loam, or loam. Soils having a moderately low runoff potential due to
moderate infiltration rates. These soils primarily consist of moderately deep to deep,
moderately well to well drained soils with moderately fine to moderately coarse textures.
Group C: Sandy clay loam. Soils having a moderately high runoff potential due to slow
infiltration rates. These soils primarily consist of soils in which a layer exists near the
surface that impedes the downward movement of water or soils with moderately fine to
fine texture.
Group D: Clay loam, silty clay loam, sandy clay, silty clay or clay. Soils having a high
runoff potential due to very slow infiltration rates. These soils primarily consist of clays
with high swelling potential, soils with permanently-high water tables, soils with a

Chapter 5

claypan or clay layer at or near the surface, and shallow soils over nearly impervious
parent material.
Data from direct field measurements on soil permeability and infiltration rates for
Ethiopian soils are very limited. Data is generally available only for soil types located
near major irrigation projects and agricultural research stations. The hydrological soils
groups presented in Table 5-7 are based on limited field measurements and from profile
morphology and physical characteristics, and are subject to further review and
refinement.
7DEOH7SLFDO+GURORJLF6RLOV*URXSVIRU(WKLRSLD
Soil Types Hydrologic Soil Group
Ao Orthic Acrisols B
Bc Chromic Cambisols B
Bd Dystric Cambisols B
Be Eutric Cambisols B
Bh Humic Cambisols C
Bk Calcic Cambisols B
Bv Vertic Cambisols B
Ck Calcic Chernozems B
E Rendzinas D
Hh Haplic Phaeozems C
Hl Luvic Phaeozems C
I Lithosols D
Jc Calcaric Fluvisols B
Je Eutric Fluvisols B
Lc Chromic Luvisols B
Lo Orthic Luvisols B
Lv Vertic Luvisols C
Nd Dystric Nitosols B
Ne Eutric Nitosols B
Od Dystric Histosols D
Oe Eutric Histosols D
Qc Cambric Arenosols A
Rc Calcaric Regosols A
Re Eutric Regosols A
Th Humic Andosols B
Tm Mollic Andosols B
Tv Vitric Andosols B
Vc Chromic Vertisols D
Vp Pellic Vertisols D
Xh Haplic Xerosols B
Xk Caloic Xerosols B
Xl Luvic Xerosols C
Yy Gypsic Yermosols B
Zg Gleyic Solonchaks D
Zo Orthic Solonchaks B
Source: Ministry of Agriculture

Chapter 5

As the slope of the drainage basin increases, the selected runoff coefficient C should also
increase. This is caused by the fact that as the slope of the catchment area increases, the
velocity of overland and channel flow will increase allowing less opportunity for water to
infiltrate the ground surface. Thus, more of the rainfall will become runoff from the
catchment area.
It is often desirable to develop a composite runoff coefficient based on the percentage of
different types of surface in the catchment area. Composites can be made with Tables 5-3
and 5-4. At a more detailed level composites can be made with Table 5-3 and the
coefficients with respect to surface type given in Table 5-5. The composite procedure can
be applied to an entire catchment area or to typical sample” blocks as a guide to
selection of reasonable values of the coefficient for an entire area.
5.8 EXAMPLE PROBLEM - RATIONAL METHOD
The following is an example problem which illustrates the application of the Rational
Method to estimate peak discharges.
Estimate the maximum rate of runoff at the inlet to a culvert on a road near Debre
Markos.
Site Data
From a topographic map and field survey, the area of the drainage basin upstream from
the point in question is found to be 35 hectares. The Rational Method is selected as per
subsection 5.2 as the area in question is less than 50 hectares.
The initial estimate is that the structure required is a small culvert. The road has a
functional classification of a Link Road, with a design standard of DS3 (VHH (5$
*HRPHWULF'HVLJQ0DQXDO±7DEOH), indicating, as per Table 2-1, a design
storm frequency of 10 years. Determine the maximum rate of runoff for a 10-year and
check a 25-year return period. The following data were measured:
Length of overland flow = 45 m Average overland slope = 2.0%
Length of main basin channel = 700 m
Slope of channel = 0.018 m/m = 1.8 %
Estimated Manning’s n Roughness coefficient (n) of channel:
See KDSWHUKDQQHOV7DEOH: Channels not maintained, dense brush, n = 0.090
Hydraulic radius = A/P, or, as per Glossary, can be approximated by average depth, =
0.6m
Land Use and Soil Data
From existing land use maps, land use for the drainage basin was estimated to be:
Residential (multi-units, attached) 40%
Undeveloped (2.0% slope),with good vegetative cover 60%
For the undeveloped area the soil group was determined from field analysis to be:
Ao Orthic Acrisols Hydrologic Soils Group B 100%
The land use for the overland flow area at the head of the basin was estimated to be:
Undeveloped, (Soil Group B, 2.5% slope) 100%

Chapter 5

Overland Flow
The runoff coefficient (C) for the overland flow area from Table 5-3 is 0.12-0.17, use
0.14.
From Figure 5-3 with an overland flow length of 45 m, slope of 2.0 % and a C of 0.14,
the inlet time is 17 min. Channel flow velocity is determined from Manning’s formula
(see KDSWHUKDQQHOV, Formula 6.6):
V = (1/n)R
2/3
S
1/2

Using n = 0.090, R = 0.6 m and S = 0.018m/m, V = 1/1 m/s. Therefore,
Flow Time = (700 m)/(1.1 m/s)(60 s/min) = 10.61 min
and t
c = 17 + 10.61 = 28.61 min - say 29 min
Rainfall Intensity
From Figure 5-8 Debre Markos is in Region A2. From Figure 5-10 for Region A2 with a
duration equal to 29 minutes,
I
10 (10-yr return period) = 67 mm/hr
I
25 (25-yr return period) = 80 mm/hr
Runoff Coefficient
A weighted runoff coefficient (C) for the total catchment area is determined in the
following table by using the values from Tables 5-3 and 5-4.
(1) (2) (3)
Percent Weighted Runoff
Total Runoff Coefficient
Land Use Land Area Coefficient (1) x (2)
Residential (multi-units, attached) .40 .68 .27
Undeveloped (Soil Group B) .60 .14 .08
Total Weighted Runoff Coefficient .35
Peak Runoff
From the rational equation (5-1):
Q
10 = 0.00278CIA = 0.00278 x 0.35 x 67 mm/h x 35 ha = 2.28 m
3
/s
Q
25 = C
fCIA = 1.1 x 0.00278 x 0.35 x 100 mm/h x 35 ha = 3.75 m
3
/s
These are the estimates of peak runoff for a 10-year and 100-year design storm for the
given basin. The culvert, channel, and erosion protection design would proceed with
these values.

Chapter 5

5.9 SCS UNIT HYDROGRAPH
,1752'87,21
Techniques developed by the U. S. Soil Conservation Service (12) for calculating rates of
runoff require the same basic data as the Rational Method: catchment area, a runoff
factor, time of concentration, and rainfall. The SCS approach, however, is more
sophisticated in that it considers also the time distribution of the rainfall, the initial
rainfall losses to interception and depression storage, and an infiltration rate that
decreases during the course of a storm. With the SCS method, the direct runoff can be
calculated for any storm, either real or fabricated, by subtracting infiltration and other
losses from the rainfall to obtain the precipitation excess (14).
$7+0(17$5($
A catchment area is determined from topographic maps and field surveys. For large
catchment areas it might be necessary to divide the area into sub-catchment areas to
account for major land use changes, obtain analysis results at different points within the
catchment area, or locate stormwater drainage structures and assess their effects on the
flood flows. A field inspection of existing or proposed drainage systems shall be made to
determine if the natural drainage divides have been altered. These alterations could make
significant changes in the size and slope of the subcatchment areas.
5$,1)$//
The SCS method is based on a 24-hour storm event which has a Type II time distribution.
The Type II storm distribution is a ’typical time distribution which the SCS has prepared
from rainfall records. It is applicable for interior rather than the coastal regions and
should be appropriate for Ethiopia. The Type II rainfall distribution will usually give a
higher runoff than a Type I distribution. Figure 5-4 shows this distribution. To use this
distribution it is necessary for the user to obtain 1) the 24-hour rainfall value (from
Figure 5-13) for the frequency of the design storm desired, and then 2) multiply this
value by 24 to obtain the total 24-hour storm volume in millimeters.
5$,1)$//5812))(48$7,21
A relationship between accumulated rainfall and accumulated runoff was derived by SCS
from experimental plots for numerous hydrologic and vegetative cover conditions. Data
for land-treatment measures, such as contouring and terracing, from experimental
catchment areas were included. The equation was developed mainly for small catchment
areas for which daily rainfall and catchment area data are ordinarily available. It was
developed from recorded storm data that included total amount of rainfall in a calendar
day but not its distribution with respect to time. The SCS runoff equation is therefore a
method of estimating direct runoff from 24-hour or 1-day storm rainfall. The equation is:
Q = (P- I
a)
2
/ (P - I
a) + S (5.3)
Where: Q = accumulated direct runoff, mm
P = accumulated rainfall (potential maximum runoff), mm
I
a = initial abstraction including surface storage, interception, and
infiltration prior to runoff, mm (see Table 5-15)
S = potential maximum retention, mm

Chapter 5

)LJXUH7SH,,'HVLJQ6WRUPXUYH

Chapter 5

The relationship between I
a and S was developed from experimental catchment area data.
It removes the necessity for estimating I
a for common usage. The empirical relationship
used in the SCS runoff equation is:
I
a = 0.2S (5.4)
Substituting 0.2S for I
a in equation 5.3, the SCS rainfall-runoff equation becomes:
Q = (P - 0.2S)
2
/ (P + 0.8S) (5.5)
S is related to the soil and cover conditions of the catchment area through the CN. CN
has a range of 0 to 100, and S is related to CN by:
S = 1000/CN –10 (5.6)
Figure 5-5 shows a graphical solution of this equation which enables the precipitation
excess from a storm to be obtained if the total rainfall and catchment area curve number
are known. For example, 180 mm of rainfall with a Curve Number of 85 would result in
direct runoff of would result in 135 mm of runoff.
5812)))$7256
Runoff is rainfall excess or effective rainfall - the amount by which rainfall exceeds the
capability of the land to infiltrate or otherwise retain the rainwater. The principal physical
catchment area characteristics affecting the relationship between rainfall and runoff are
land use, land treatment, soil types, and land slope.
/DQG XVH is the catchment area cover, and it includes both agricultural and
nonagricultural uses. Items such as type of vegetation, water surfaces, roads, roofs, etc.
are all part of the land use. /DQGWUHDWPHQW applies mainly to agricultural land use, and
it includes mechanical practices such as contouring or terracing and management
practices such as rotation of crops.
The SCS uses a combination of soil conditions and land-use (ground cover) to assign a
runoff factor to an area. These runoff factors, called runoff curve numbers (CN), indicate
the runoff potential of an area. The higher the CN, the higher is the runoff potential.
+'52/2*,62,/*52836
6RLOSURSHUWLHV influence the relationship between rainfall and runoff by affecting the
rate of infiltration. The SCS has divided soils into four hydrologic soil groups based on
infiltration rates (Groups A, B, C, and D). These groups were previously described for
the Rational Formula (see Section 5.7, Table 5-7).
Consideration shall be given to the effects of urbanization on the natural hydrologic soil
group. If heavy equipment can be expected to compact the soil during construction or if
grading will mix the surface and subsurface soils, appropriate changes shall be made in
the soil group selected. Also runoff curve numbers vary with the antecedent soil moisture
conditions, defined as the amount of rainfall occurring in a selected period preceding a
given storm. In general, the greater the antecedent rainfall, the more direct runoff there is
from a given storm. A five-day period is used as the minimum for estimating antecedent
moisture conditions.

Chapter 5

)LJXUH665HODWLRQEHWZHHQ'LUHFW5XQRIIXUYH1XPEHUDQG3UHFLSLWDWLRQ

Chapter 5

Antecedent soil moisture conditions also vary during a storm; heavy rain falling on a dry
soil can change the soil moisture condition from dry to average to wet during the storm
period.
5812))859(180%(56
The following pages give a series of tables related to runoff factors. The first tables
(Tables 5-8 through 5-11) give curve numbers for various land uses. These tables are
based on an average antecedent moisture condition, i.e., soils that are neither very wet
nor very dry when the design storm begins. Curve numbers shall be selected only after a
field inspection of the catchment area and a review of cover type and soil maps. Table 5-
12 gives conversion factors to convert average curve numbers to wet and dry curve
numbers. Table 5-13 gives the antecedent conditions for the three classifications.
Care shall be taken in the selection of curve numbers (CN’s). Use a representative
average curve number, CN, for the catchment area. Selection of overly conservative
CN’s will result in the estimation of excessively high runoff and consequently
excessively costly drainage structures. Selection of conservatively high values for all
runoff variables results in compounding the runoff estimation. It is better to use average
values and design for a longer storm frequency. Often the runoff computed using
conservative CN's for a ten year storm will greatly exceed the computed runoff for
average CN's for a 25 or even 50 year storm. The hydrologic designer could consider
doing both in making the most appropriate selection of design discharge.
For antecedent moisture conditions (AMC) in Ethiopia, use dry for Region D1, wet for
Region B1, and average AMC for all other regions. The portion of Region A2 in the
vicinity of Bahir Dar should also be treated as wet. When wet AMC is used, it is unlikely
that the vegetation density will also be poor to sparse.

Chapter 5


7DEOH5XQRIIXUYH1XPEHUV8UEDQ$UHDV

Cover description Curve numbers for hydrologic soil groups
Cover type and Hydrologic condition Average %
impervious
area
2

A B C D
Open space (lawns, parks, cemeteries, etc.)
3
Poor condition (grass cover 50%)
Fair condition (grass cover 50 % to 75%)
Good condition (grass cover 75%)
Impervious areas:
Paved parking lots, roofs, driveways, etc.
(excluding right-of-way)
Streets and roads:
Paved; curbs and storm drains (excluding
right-of-way)
Paved; open ditches (including right-of-way)
Gravel (including right-of-way)
Dirt (including right-of-way)
Desert urban areas:
Natural desert cover
Urban districts:
Commercial and business
Industrial
85
72
68
49
39
98
98
83
76
72
63
89
81
79
69
61
98
98
89
85
82
77
92
88
86
79
74
98
98
92
89
87
85
94
91
89
84
80
98
98
93
91
89
88
95
93
Residential districts by average plot size:
0.05 hectare or less
0.1 hectare
0.135 hectare
0.2 hectare
0.4 hectare
0.8 hectare
65
38
30
25
20
12
77
61
57
54
51
46
85
75
72
70
68
65
90
83
81
80
79
77
92
87
86
85
84
82
Developing urban areas
Newly graded areas (pervious areas only, no vegetation) 77 86 91 94

1
Average runoff condition, and I
a = 0.2S

2
The average percent impervious area shown was used to develop the composite CNs. Other assumptions
are as follows: impervious areas are directly connected to the drainage system, impervious areas have a CN
of 98, and pervious areas are considered equivalent to open space in good hydrologic condition. If the
impervious area is not connected, the SCS method has an adjustment to reduce the effect.

3
CNs shown are equivalent to those of pasture. Composite CNs may be computed for other combinations
of open space cover type.

Chapter 5

7DEOHXOWLYDWHG$JULFXOWXUDO/DQG

Cover description
Curve numbers for
Hydrologic soil group
Cover
Type
Treatment
2

Hydrologic
condtion
3

A B C D
Fallow Bare soil
Crop residue
cover (CR)
-
Poor
Good
77
76
74
86
85
83
91
90
88
94
93
90
Row
Crops
Straight row (SR) Poor
Good
72
67
81
78
88
85
91
89
SR + CR Poor
Good
71
64
80
75
87
82
90
85
Contoured (C) Poor
Good
70
65
79
75
84
82
88
86
C + CR Poor
Good
69
64
78
74
83
81
87
85
Contoured
terraced (C T)
Poor
Good
66
62
74
71
80
78
82
81
CT + CR Poor
Good
65
61
73
70
79
77
81
80
Small grain SR Poor
Good
65
63
76
75
84
83
88
87
SR + CR Poor
Good
64
60
75
72
83
80
86
84
C Poor
Good
63
61
74
73
82
81
85
84
C + CR Poor
Good
62
60
73
72
81
80
84
83
CT Poor
Good
61
59
72
70
79
78
82
81
CT + CR Poor
Good
60
58
71
69
78
77
81
80
Close-seeded SR
or broadcast
Poor
Good
66
58
77
72
85
81
89
85
Legumes or C
Rotation
Poor
Good
64
55
75
69
83
78
85
83
Meadow CT Poor
Good
63
51
73
67
80
76
83
80

1
a = 0.2S.

2
Crop residue cover applies only if residue is on at least 5% of the surface throughout the year.

3
Hydrologic condition is based on a combination of factors that affect infiltration and runoff, including (a)
density and canopy of vegetative areas, (b) amount of year-round cover, (c) amount of grass or closed-
seeded legumes in rotations, (d) percent of residue cover on the land surface (good 20%), and (e) degree
of roughness.
Poor : Factors impair infiltration and tend to increase runoff.
Good : Factors encourage average and better than average infiltration and tend to decrease
runoff.

Chapter 5


7DEOH2WKHU$JULFXOWXUDO/DQGV

Cover description Curve numbers for hydrologic soil group
Cover type
Hydrologic
condition
A B C D
Pasture, grassland, or range-
continuous forage for grazing
2

Meadow-continuous grass,
protected from grazing
Brush-weed-grass mixture
with brush the major element
3

Woods-grass combination
5

Woods
6

Farms—buildings, lanes,
driveways, and surrounding
lots
Poor
Fair
Good
--
Poor
Fair
Good
Poor
Fair
Good
Poor
Fair
Good
--
68
49
39
35
48
35
30
4

57
43
32
45
36
30
4

59
79
69
61
59
67
56
48
73
65
58
66
60
55
74
86
79
74
72
77
70
65
82
76
72
77
73
70
82
89
84
80
79
83
77
73
86
82
79
83
79
77
86

1
a = 0.2S

2
Poor: 50% ground cover or heavily grazed with no mulch
Fair: 50 to 75% ground cover and not heavily grazed
Good: 75% ground cover and lightly or only occasionally grazed

3
Poor: 50% ground cover
Fair: 50 to 75% ground cover
Good: 75% ground cover

4
Actual curve number is less than 30; use CN = 30 for runoff computations.

5
CNs shown were computed for areas with 50% grass (pasture) cover. Other combinations of conditions
may be computed from CNs for woods and pasture.

6
Poor: Forest litter, small trees, and brush are destroyed by heavy grazing or regular burning.
Fair : Woods grazed but not burned, and some forest litter covers the soil.
Good : Woods protected from grazing, litter and brush adequately cover soil.

Chapter 5

7DEOH$ULGDQG6HPLDULG5DQJHODQGV
Cover type
Hydrologic
condition
2

A
3
B C D
Mixture of grass, weeds, and low-
growing brush, with brush the minor
element
Mountain brush mixture of small trees
and brush
Small trees with grass understory
Brush with grass understory
Desert shrub brush
Poor
Fair
Good
Poor
Fair
Good
Poor
Fair
Good
Poor
Fair
Good
Poor
Fair
Good
63
55
49
80
71
62
66
48
30
75
58
41
67
51
35
77
72
68
87
81
74
74
57
41
85
73
61
80
63
47
85
81
79
93
89
85
79
63
48
89
80
71
85
70
55
88
86
84

1
a = 0.2S

2
Poor : 30 % ground cover (litter, grass, and brush overstory)
Fair : 30 to 70 % ground cover Good: 70 % ground cover

3
Curve numbers for Group A have been developed only for desert shrub

7DEOHRQYHUVLRQIURP$YHUDJH$QWHFHGHQW0RLVWXUHRQGLWLRQV
WR'UDQG:HWRQGLWLRQV
CN For Average
Conditions
Corresponding CN’s For
100
95
90
85
80
75
70
65
60
55
50
45
40
35
30
25
15
5
Dry
100
87
78
70
63
57
51
45
40
35
31
26
22
18
15
12
6
2
Wet
100
98
96
94
91
88
85
82
78
74
70
65
60
55
50
43
30
13
Ethiopian Rainfall Region D1 ( 100 mm) Source: Ref. 15
Ethiopian Rainfall Region A2 B1 (mean monthly Peak 300 mm)

Chapter 5

7DEOH5DLQIDOO*URXSVIRU$QWHFHGHQW6RLO0RLVWXUHRQGLWLRQV
'XULQJ*URZLQJDQG'RUPDQW6HDVRQV
Antecedent
Condition
Conditions
Description
Growing Season
Five-Day
Antecedent
Rainfall
Dormant Season
Five-Day
Antecedent
Rainfall
Dry
Average
Wet
An optimum Condition of
catchment area soils, where soils
are dry but not to the wilting point,
and when satisfactory plowing or
cultivation takes place
The average case for annual floods
When a heavy rainfall, or light
rainfall and low temperatures, have
occurred during the five days
previous to a given storm
Less than 36 mm
36 to 53 mm
Over 53 mm
Less than 13 mm
13 to 28 mm
Over 28 mm
Source: Soil Conservation Service
75$9(/7,0((67,0$7,21
The next step in the SCS Method is to determine the Time of Concentration.
Travel Time
Travel time (T
t) is the time it takes water to travel from one location to another in a
catchment area. T
t is a component of time of concentration (T
c), which is the time for
runoff to travel from the hydraulically most distant point of the catchment area to a point
of interest within the catchment area. T
c is computed by summing all the travel times for
consecutive components of the drainage conveyance system.
Following is a discussion of procedures and equations for calculating travel time and
time of concentration.
Travel Time
Water moves through a catchment area as sheet flow, shallow concentrated flow, open
channel flow, or some combination of these. The type that occurs is a function of the
conveyance system and is best determined by field inspection.
Travel time is the ratio of flow length to flow velocity:
T
t = L/(3600V) (5.7)
Where:
T
t = travel time, hr
L = flow length, m
V = average velocity, m/s
3600 = conversion factor from seconds to hours.

Chapter 5

The time of concentration is the sum of T
t values for the various consecutive flow
segments:
T
c = T
t1 + T
t2 + … T
tm (5.8)
Where:
T
c = time of concentration, hr
m = number of flow segments.
Sheet Flow
Sheet flow is flow over plane surfaces. It usually occurs in the headwater of streams.
With sheet flow, the friction value (Manning's n) is an effective roughness coefficient
that includes the effect of raindrop impact; drag over the plane surface; obstacles such as
litter, crop ridges, and rocks; and erosion and transportation of sediment. These n values
are for very shallow flow depths of about 0.03 m or so. Table 5-14 gives Manning's n
values for sheet flow for various surface conditions.
7DEOH5RXJKQHVVRHIILFLHQWV 0DQQLQJ¶VQ IRU6KHHW)ORZ
Surface Description
Smooth surfaces (concrete, asphalt, gravel, or bare soil
Fallow (no residue)
Cultivated soils:
Residue cover ≤ 20%
Residue cover 20%
Grasses:
Short grass
Dense Grasses
Range (natural)
Woods:
2

Light underbrush
Dense underbrush
n
1
0.011
0.05
0.06
0.17
0.15
0.24
0.13
0.40
0.80

1
The n values are a composite of information complied by Engman (1986).

2
When selecting n, consider cover to a height of about 0.03 m. This is the only part of the plant cover
that will obstruct sheet flow.
For sheet flow of less than 100 meters, use Manning's kinematic solution (Overton and
Meadows 1976) to compute T
t:
T
t = [0.091 (nL)
0.8
/ (P
2)
0.5
s
0.4
] (5.9)
Where:
T
t = travel time, hr
n = Manning's roughness coefficient (Table 5-14)
L = flow length, m
P
2 = 2-year, 24-hour rainfall, mm
s = slope of hydraulic grade line (land slope), m/m

Chapter 5

This simplified form of the Manning’s kinematic solution is based on the following:
1. shallow steady uniform flow,
2. constant intensity of rainfall excess (rain available for runoff),
3. rainfall duration of 24 hours, and
4. minor effect of infiltration on travel time.
Another approach is to use the kinematic wave equation. For details on using this
equation consult Ref. 16.
Shallow Concentrated Flow
After a maximum of 100 meters, sheet flow usually becomes shallow concentrated flow.
The average velocity for this flow can be determined from equations 5.10 and 5.11, in
which average velocity is a function of watercourse slope and type of channel.
Unpaved V = 4.9178 (s)
0.5
(5.10)
Paved V = 6.1961 (s)
0.5
(5.11)
Where:
V = average velocity, m/s
S = slope of hydraulic grade line (watercourse slope), m/m
These two equations are based on the solution of Manning’s equation with different
assumptions for n (Manning’s roughness coefficient) and r (hydraulic radius, meters).
For unpaved areas, n is 0.05 and r is 0.12; for paved areas, n is 0.025 and r is 0.06.
After determining average velocity, use equation 5.7 to estimate travel time for the
shallow concentrated flow segment.
Open Channels
Open channels are assumed to begin where surveyed cross section information has been
obtained, where channels are visible on aerial photographs, or where blue lines
(indicating streams) appear on Ethiopian Mapping Authority (EMA) topographic maps
(1:50,000). Average flow velocity is usually determined for bank-full elevation.
Manning’s equation or water surface profile information can be used to estimate average
flow velocity. When the channel section and roughness coefficient (Manning’s n) are
available, then the velocity can be computed using the Manning Equation
V = (r
2/3
s
1/2
)/n (5.12)
Where: V = average velocity, m/s
r = hydraulic radius, m (equal to a/p
w)
a = cross sectional flow area, m
2
P
w = wetted perimeter, m
s = slope of the hydraulic grade line, m/m
n = Manning’s roughness coefficient

Chapter 5

After average velocity is computed using equation 5.12, T
t for the channel segment can
be estimated using equation 5.7.
Reservoir or Lake
Sometimes it is necessary to compute a T
c for a catchment area having a relatively large
body of water in the flow path. In such cases, T
c is computed to the upstream end of the
lake or reservoir, and for the body of water the travel time is computed using the
equation:
V
w = (gD
m)
0.5
(5.13)
Where:
V
w = the wave velocity across the water, m/s
g = 9.81 m/s
2

D
m = mean depth of lake or reservoir, m
Generally, V
w will be high (2.44 – 9.14 m/s)
One must not overlook the fact that equation 5.13 only provides for estimating travel
time across the lake and for the inflow hydrograph to the lake's outlet. It does not account
for the travel time involved with the passage of the inflow hydrograph through spillway
storage and the reservoir or lake outlet. This time is generally much longer and is added
to the travel time across the lake. The travel time through lake storage and its outlet can
be determined by the storage routing procedures in KDSWHU6WRUDJH)DFLOLWLHV.
Equation 5.13 can be used for swamps with much open water, but where the vegetation
or debris is relatively thick (less than about 25 percent open water), Manning's equation
is more appropriate.
Limitations
• Manning's kinematic solution should not be used for sheet flow longer than 100 m.
Equation 5.9 was developed for use with the four standard rainfall intensity-duration
relationships.
• In catchment areas with storm drains, carefully identify the appropriate hydraulic
flow path to estimate T
c. Storm drains generally handle only a small portion of a large
event. The rest of the peak flow travels by streets, grassed areas, and so on, to the
outlet. Consult a standard hydraulics textbook to determine average velocity in pipes
for either pressure or non-pressure flow.
• A culvert or bridge can act as a reservoir outlet if there is significant storage behind
it. Detailed storage routing procedures shall be used to determine the outflow through
the culvert.
5.10 EXAMPLE PROBLEM: SCS METHOD
The following is an example problem which illustrates the application of the SCS
Method to estimate peak discharges.
Estimate the maximum rate of runoff at the inlet to a proposed drainage structure located
near Nekempte.

Chapter 5

From a topographic map and field survey, the area of the drainage basin upstream from
the point in question is found to be 100 hectares. The SCS Method is selected as per
subsection 5.2 as the area in question is greater than 50 hectares.
The road has a functional classification of a Trunk Road, with a design standard of DS2
(see *HRPHWULF 'HVLJQ 0DQXDO, Table 2-1, KDSWHU ). The type of structure
required is not known, but Table 2-1 indicates a range of design storm frequencies
between 25 and 100 years. Thus, determine the maximum rate of runoff for a 25-, 50-
year, and 100-year return period. The following data were measured:
Site Data
From a topographic map and field survey, the following data were measured:
From the Soils Map of Ethiopia, and from the field survey, it appears that the soils are
Eutric and Humic Cambisols (BE and BH). From Table 5-7, BE is a silt loam of
Hydrologic Soil Group B, and BH is a sandy clay loam of Hydrologic Soil Group C.
Approximatly 30% (30 ha) is BE and 70% (70ha) is BH.
The cover type is pasture in poor hydrologic condition.
Curve Runoff Number
From Table 5-10:
Pasture, poor condition, Soil Group B CN = 79
Pasture, poor condition, Soil Group C CN = 86
CN = (0.30 x 79) + (0.70 x 86) = 84
From Figure 5-8, Nekempte is in Rainfall Region B1. As per page 5-25, this is a Wet
Antecedent Moisture Condition (AMC) Region. From Table 5-12, CN84
avg = CN93
wet.
However, use CN = 84, as we require the peak discharge for 25-year and greater storm
periods (see definition of Antecedent Moisture Conditions, page 5-1).
24- Hour Rainfall, P
For Region B1: 24-Hour rainfalls are:
P
25 = 118mm
P
50 = 132mm
P
100 = 147mm
Runoff, Q
From Figure 5-5 and CN = 84:
Q
25 = 81mm
Q
50 = 94mm
Q
100 = 108mm

Chapter 5

Travel Time

)LJXUHDWFKPHQW$UHD6HJPHQWV
For Segment A-B (see Figure 5-6): Sheet flow, natural range, slope = 0.10 m/m, length =
50m. From Table 5-14, Manning’s n = 0.13. The 2-year, 24-Hour rainfall is determined
from Figure 5-13 to be 65mm. From Equation 5.9,
T
t = [0.091 (nL)
0.8
/ (P
2)
0.5
s
0.4
] = 0.127 hr
For Segment B-C: Shallow concentrated flow, unpaved, s = 0.04 m/m, length = 500m.
From Equation 5.10:
V = 4.9178 (s)
0.5
= 0.984 m/s
From Equation 5.7:
T
t = L/(3600V) = 0.141 hr
For Segment C-D: channel flow, natural stream channel, winding with weeds and pools,
s = 0.01m/m, length = 2000m. From the survey, bottom width = 2m, sideslopes = 1V:1H,
25-year storm depth = 1m.
See Table 6-1 KDSWHUKDQQHOV: Manning’s n = 0.050.
A = Cross-sectional flow area = (2 x 1) + 2[1/2(1)] = 3m
2

P
w = wetted perimeter = 2m + 2¥ P
R = Hydraulic radius = A/P
w = 3/4.828 = 0.621m
From Equation 5.12
V = (r
2/3
s
1/2
)/n = 1.46 m/s. From Equation 5.7:
T
t = L/(3600V) = 0.381 hr
Total Time of Concentration = 0.127 + 0.141 + 0.381 = 0.649 hr
Peak Runoff
From the above data and calculations, catchment area = 100ha, Runoff Curve Number =
84, Time of Concentration = 0.649 hr, 25-year, 24-hour Storm, P = 118mm, Run-Off Q
25
= 81mm.
Determine Initial Abstraction from Table 5-15:

Chapter 5

7DEOH,
D9DOXHVIRU5XQRIIXUYH1XPEHUV

Curve Number I
a (mm) Curve Number I
a (mm) Curve Number I
a (mm)
40 76.2 60 33.9 80 12.7
41 73.1 61 32.5 81 11.9
42 70.2 62 31.1 82 11.2
43 67.3 63 29.8 83 10.4
44 64.6 64 28.6 84 9.7
45 62.1 65 27.4 85 9.0
46 59.6 66 26.2 86 8.3
47 57.3 67 25.0 87 7.6
48 55.0 68 23.9 88 6.9
49 52.9 69 22.8 89 6.3
50 50.8 70 21.8 90 5.6
51 48.8 71 20.6 91 5.0
52 46.9 72 19.8 92 4.4
53 45.1 73 18.8 93 3.8
54 43.3 74 17.9 94 3.3
55 41.6 75 16.9 95 2.7
56 39.9 76 16.1 96 2.1
57 38.3 77 15.2 97 1.6
58 36.8 78 14.3 98 1.0
59 35.3 79 13.5 99 0.4
For Curve Number = 84, I
a = 9.7mm
Compute I
a/P = 9.7/118 = 0.082
Determine Unit Peak Discharge Q
u from Figure 5-7 for T
c = 0.649 hr and I
a/P = 0.082,
Unit Peak Discharge, Q
u = 0.20 m
3
/s/100ha/mm
Peak Discharge, Q
p25 = Q
u x A x Q
25 = 0.20 x 1 x 81 = 16.2 m
3
/s
Use similar method to determine Q
p50 and Q
p100

Chapter 5

)LJXUH8QLW3HDN'LVFKDUJH7SH,,5DLQIDOO

Chapter 5

)LJXUH5DLQIDOO5HJLRQV

NOTE: RAINFALL DATA USED IN THE PREPARATION OF THIS FIGURE HAVE BEEN COLLECTED FROM MANY MINISTRY OF
WATER RESOURCES METEOROLOGY STATIONS (SEE TABLE 5-2). IN THE COURSE OF THE PREPARATION OF THIS MANUAL,
THEY HAVE BEEN SUBJECTED TO STATISTICAL TECHNIQUES. THE RESULTS INDICATE THAT THE COUNTRY CAN BE DIVIDED
INTO THE ABOVE HYDROLOGICAL REGIONS DISPLAYING SIMILAR RAINFALL PATTERNS. THE INFORMATION IS SUBJECT TO
REVIEW, AND FUTURE DATA MAY INDICATE THE NEED FOR A FURTHER REFINEMENT IN BOTH VALUES AND REGIONAL
BOUNDARIES.

Chapter
5
Hydrology
Drainage
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Chapter 5
duration 5 10 20 30 60 120 1440
Chicago 14 22 34 42 56 62 100
Conc Pipe
Manual 19 29 36 50 60 80 100
Curve 1: 13.75ln(x) Curve 2: 14.5*LN(x)-5.45 EHVWFXUYH OQ [
5 1440 5 1440 10 1440
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duration 5 10 20 30 60 120 240 360 720 1440
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Curve 2 18 28 38 44 54 64 74 80 90 100
EHVWFXUYH
spline depth 20 30 40 50 60 80 90 100 110 120
% 16 25 33 44 50 67 75 84 92 100
spline mm/hr 240 180 120 100 60 40
% 24 hour 200 150 100 0,83 50 33
HVWKU
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y = 15,135Ln(x) - 3,7868
y = 13.75Ln(x)
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20
40
60
80
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120
1 10 100 1000 10000
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Chicago from VT Chow Conc Pipe Dsgn Manual
Série3 SPLINE
BEST CURVE Logarithmique (Chicago from VT Chow)
Logarithmique (Conc Pipe Dsgn Manual) Design
Logarithmique (SPLINE) Logarithmique (BEST CURVE)
2 5 10 25 50 100
Bahir Dar 74 106 131 163 187 211
Region D 67 89 105 127 144 161
Reg. B C 65 84 98 118 132 147
A1, A4 60 79 93 113 127 142
A2, A3 52 67 79 95 107 118
duration 2 5 10 25 50 100 duration 2 5 10 25 50 100
5 134,9 193,2 237,3 295,6 339,6 383,7 5 117,3 152,3 178,7 213,7 240,1 266,6
10 113,8 162,9 200,1 249,2 286,4 323,6 10 98,9 128,4 150,7 180,2 202,5 224,8
20 80,1 114,6 140,8 175,4 201,5 227,7 20 69,6 90,3 106,0 126,8 142,5 158,2
30 62,4 89,4 109,7 136,7 157,1 177,5 30 54,3 70,4 82,7 98,8 111,1 123,3
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10 102,1 135,8 161,3 195,0 220,5 246,0 10 91,3 120,7 143,0 172,5 194,8 217,1
20 71,8 95,5 113,5 137,2 155,1 173,1 20 64,2 85,0 100,6 121,4 137,1 152,8
30 56,0 74,5 88,5 106,9 120,9 134,9 30 50,0 66,2 78,5 94,6 106,9 119,1
60 34,9 46,5 55,2 66,7 75,4 84,1 60 31,2 41,3 48,9 59,0 66,6 74,3
90 26,0 34,6 41,1 49,6 56,1 62,6 90 23,2 30,7 36,4 43,9 49,6 55,3
120 20,9 27,8 33,1 40,0 45,2 50,4 120 18,7 24,7 29,3 35,4 39,9 44,5
duration 2 5 10 25 50 100
5 94,1 122,4 143,8 172,1 193,5 214,9
10 79,3 103,2 121,3 145,1 163,2 181,3
20 55,8 72,6 85,3 102,1 114,8 127,5
30 43,5 56,6 66,5 79,6 89,5 99,4
60 27,1 35,3 41,5 49,6 55,8 62,0
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region
24 HOUR DEPTH
frequency
IDF-BAHIR DAR, mm/hr IDF-region B C, mm/hr
frequency
IDF-region A1 A4 mm/hr
frequency
IDF-Region A2 A3, mm/hr
frequency
frequency
IDF-Region D, mm/hr
frequency

Chapter 5

Chapter 5
5()(5(1(6
1. Highway Drainage Guidelines, Volume 11, Guidelines for Hydrology, Task Force
on Hydrology and Hydraulics, AASHTO Highway Subcommittee on Design.
2. Federal Highway Administration. 1990. HYDRAIN Documentation.
3. Gebeyehu, Admasu, 5HJLRQDO)ORRG)UHTXHQF$QDOVLV, Hydraulics Laboratory,
Royal Institute of Technology, Stockholm, Sweden, 1989.
4. Newton, D. W., and Herin, Janet C. 1982. Assessment of Commonly Used
Methods of Estimating Flood Frequency. Transportation Research Board.
National Academy of Sciences, Record Number 896.
5. Potter, W. D. Upper and Lower Frequency Curves for Peak Rates of Runoff.
Transactions, American Geophysical Union, Vol. 39, No. 1, February 1958, pp.
100-105.
6. Sauer, V. B., Thomas, W. O., Stricker, V. A., and Wilson, K. V. 1983. Flood
Characteristics of Urban Catchment areas in the United States -- Techniques for
Estimating Magnitude and Frequency of Urban Floods. U. S. Geological Survey
Water-Supply Paper 2204.
7. Wahl, Kenneth L. 1983. Determining Stream Flow Characteristics Based on
Channel Cross Section Properties. Transportation Research Board. National
Academy of Sciences, Record Number 922.
8. Overton, D. E. and M. E. Meadows. 1976. Storm Water Modeling. Academic
Press. New York, N.Y. pp. 58-88.
9. U. S. Department of Transportation, Federal Highway Administration. 1984.
Hydrology. Hydraulic Engineering Circular No. 19.
10. Water Resources Council Bulletin 17B. 1981. Guidelines for determining flood
flow frequency.
11. Wright-McLaughlin 1969.
12. Soil Conservation Service (SCS) Technical Release No. 55 (2
nd
Edition).
13. Applied Hydrology, V. T. Chow et al.
14. SCS National Engineering Handbook, Section 4.
15. USDA Soil Conservation Service TP-149 (SCS-TP-149), “A Method for
Estimating Volume and Rate of Runoff in Small Watersheds,” revised April
1973.
16. Regan, R. M., A Nomograph Based on Kinematic Wave Theory for Determining
Time of Concentration for Overland Flow,” Report No. 44, Civil Engineering
Department, University of Maryland at College Park, 1971.

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