Urban Drainage Notes-CHAPTER 2

7/28/2019 Urban Drainage Notes-CHAPTER 2

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URBAN DRAINAGE AND SEWERAGE E.O. AKINYEMI

STORMWATER AND WASTEWATER DEMAND FLOW 1

CHAPTER TWO

UNDERSTANDING URBAN STORMWATER AND

WASTEWATER LOADING CHARACTERISTICS

This chapter describes the basic concepts and techniques used in the quantification of thestormwater and wastewater loads in an urban area. It is expected that, at the end of the

lectures, you will be able to estimate the current or likely future value of the most

critical quantity of stormwater and wastewater that will flow at different locations

on an existing or proposed drainage system in an urban area.

Thus, in this chapter, the three main aspects presented are:

Definition of Points of Interest for Quantification of Flow and

Conceptualization of Drainage Basins and Sub-Basins

Definition of Critical Storm Characteristics at Each Point of Interest (for

stormwater drainage) Techniques for Estimation of Peak Discharge at Each Point of Interest

2.1 Points of Interest for Quantification of Flow, Drainage

Basins and Sub-Basins

Analysis and re-design of a drainage system in an urban area requires, first and foremost,

the identification and preparation of the plan/layout of the existing network. Theplan/layout of the network should indicate among other things, the locations of the inlets,

pipes, channels, structures, outlets appurtenances etc. as well as the dimensions

/characteristics of each of the components such as:pipe sizes and lengths, manholeelevations and locations, and pump sizes.


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Figure 2.1- Examples of existing or proposed drainage systems

Figure 2.1B Drainage Basin and Layout for StormwaterDepending on the purpose of a study, basins can vary in size; this is a small,approximately 10 acre hypothetical urban drainage basin

Another important requirement is the identification of nodes and segments on the

network. In an existing network, nodes are the inlets or open ditches. In a proposed


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network, node points can be assigned to the principal road intersections where cross flow

cannot be allowed, to sag points, to points where the direction of flow changes

significantly and locations where flow will enter from major sub-divisions or from

commercial/ industrial estates. The nodes are linked by flow paths using existing or

planned conduits (pipes or open channels), down-slope roadways, swales, and overlandflow paths. All of these flow paths are collectively termed 'links'. Thus the network

structure consists ofnodes and links. A segment or run consists of a node and a link

that may be a pipe length, a roadside or median ditch or an engineered waterway.Following the identification of the flow paths and the drainage network nodes and links

and runs, the drainage basin(s) and each basin should be discretised into sub-basins.

There are two main types of drainage basins: stormwater and wastewater drainagebasins.

A stormwater drainage basin is an area draining to a discharge point. It is an area of land

from which all water drains, running downhill, to a shared destination - a river, pond,stream, lake, or estuary. An urban drainage basin can range in size from under a square

kilometer to hundreds of square kilometers. Any rain that falls within the area willeventually drain to the discharge point.

A drainage basin is the area drained by a stream and all of its tributaries. Any rainthat falls within the watershed will pass through the main stream channel.

A divide separates each basin

from the surrounding drainagebasins. Divides follow ridgesand hill tops. If a raindrop fallson one side of a divide, it willflow down one side of the hill,and into one drainage basin. Ifthe raindrop falls on the otherside of a divide, it will flow intoa different drainage.

Watersheds are composed of many smallerdrainage basins. In the diagram, a sub-basinhas been drawn for every tributary.

Figure 2.2

Stormwater drainage basin boundaries can be identified from contour maps assuming

that water will flow at right angles to the contours. In addition, location of discharge


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points (outfalls), can be located along with their capacity and downstream constraints

can be identified together with the natural drainage paths through the area. The

influences of ditches and roads must be taken into account as well as other features that

could divert runoff from the natural runoff channels shown by the contours. The

drainage basin area is usually expressed in units of hectares (ha) or square kilometers(km2). Since water flows downhill, delineating a drainage area is a matter of identifyingan outfall and locating the drainage area boundary such that any rain that falls within the

boundary will be directed toward that point of discharge. By using a planimeter and/or

other methods, the area and slope etc. can be measured. An example is shown in Figure

2.3.

.

Runoff Travel Path and Features of a Natural Drainage Area

Figure 2.3

Similarly, a sewage drainage area is the territory being considered within which it is

possible to find a continuously downhill surface route from any point to the establishedoutlet/treatment plant. Sewage drainage areas should also include areas that are tributary

by gravity that will be served by future sewer construction and areas that are not

tributary by gravity that could be served by pumping or adverse grade construction. It

should be noted that natural drainage boundaries do not necessarily coincide withpolitical boundaries.


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After identifying drainage basin boundaries, drainage sub-basins can be defined. Adrainage sub-basin is a defined area within which all the stormwater or wastewater flows

to the node. An example for stormwater is illustrated in Figure 2.4. It is usually desirable

for sub-catchments to be chosen so that they have homogeneous physical characteristics

and/or land-use characteristics.

Figure 2.4 Example Link and Sub-Area (Node) Numbering System for Hydrologic Model


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Figure 2.4

After preparing a base plan of the existing or proposed drain system, each node or

structure can be given a number in the form U.V where U, the integral part of the


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number, denotes the branch to which the length belongs and V, the fractional part of

the number, denotes the position of the structure within the branch. The integral part of

the number is called the branch number.

The main line is identified alphabetically, for example as line A and the structurefurthest downstream is assigned structure A1. It is useful for ease of reference if the

designation of the main line has a physical significance, such as the abbreviation of a

suburb, administrative area, watercourse name, or road name. Thus the main channel in

administrative area XY could be numbered XY-A, and so on.

Working upstream, number the remaining structures on the main line A2, A3, A4, etc.Branch lines are identified as B, C etc. and their nodes are numbered as line B (B1, B2,

B3, . . . ), line C (C1, C2, C3, . ..) etc. This system allows for future upstreamextensions or additions. If new structures are inserted, for example between nodes B.9

and B.10, they are numbered B.9A, B.9B etc. See Figure 2.5.

Figure 2.5 Example Detailed Numbering System for Open Drains and Pipes

In addition to defining the sub-basins, information such as (a) the land-use characteristics (in terms of gross area, population, household size, zoning designation, the total per cent that

is impervious (TIA), per cent directly connected impervious area (DCIA), etc. (b) soil

characteristics and (d) shape and orientation characteristics are needed for each sub-area.


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2.2 Design Storm

2.2.1 Background

A rainfall or storm event is defined in terms of the following

-depth (mm) or volume (mm3) of rainfall in a specified time

-duration of the storm (min or hr.)- intensity (rate of rainfall) (mm/hr) [i.e. depth divided by the duration of the storm over a

time interval] and

-frequency of the storm event. Frequency is expressed in terms of the return period, T, orthe recurrence interval (years) of the event. The recurrence interval is the average length of

time expected to elapse between the occurrences of events of equal or greater magnitude. It

is also related to the storm events exceedance probability, P, which is the probability thatthe storm will be equaled or exceeded in any given year. That is:

T=1/P(2.1)

Furthermore, every rainfall event is unique. Temporal and spatial distribution of rainfall

varies seasonally as well as within a storm event due to the prevailing climatic

conditions at the time of the storm. Just as every rainfall event is unique, the resultingrunoff from a storm event is also unique. Surface conditions such as the amount of

vegetation, land use, type of soil, soil condition, topography, and other factors affect

runoff volume and distribution. Finally, the condition of conveyance elements such asblockage by sediment or obstruction by trees and vegetation also has an effect on runoff

spatial and temporal distribution. While the effects of the temporal and spatial

distribution of runoff are in general relatively small, however, these effects must be

considered in designing large components such as detention basins or delineatingfloodplains. Furthermore, the variables relating to time and space, rainfall variation,

abstractions, surface conditions, and numerous others that affect runoff are considered

continuous-that is, quantitatively they can assume any real value. Because the

combinations of values of all such variables are infinite, an exact repeat occurrence of an

event, although not impossible, is very unlikely.

The infinite number of possible rainfall and runoff events presents an improbable task of

ever obtaining all of the unique data potentially available in the hope of predicting

hydrologic events precisely and accurately. Thus, rainfall events are predicted by statingthe "Annual Exceedance Probability"AEP or the ARI, Average recurrence interval

also referred to as the return period. The AEP is the probability that an event ofspecified magnitude, or volume and duration, will be exceeded in a time period. It is theaverage length of time between events that have the same magnitude, or volume and

duration. Specifically, the ARI is given by:

PARI

100= ..(2.2 )

wherePis the AEP in percent. Hence, a 1% AEP has an ARI of 100 years.The concept of AEP and ARI is frequently misinterpreted in two ways. First, the ARI of

100 years does not imply that 50 m3/s will occur only once in 100 years. Thinking that if

a particular event occurs today then it will not occur for the next Tryears is not the


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proper interpretation of the ARI. This misconception is a deterministic perspective, and

if hydrology were so predictable, many of the world's water resource problems could be

easily solved. The ARI represents the statistical average number of years between

similar events given a very long period of record. The second common misuse is the

failure to recognise the AEP concept. This 50 m3/s discharge has a 1 in 100 chance ofbeing exceeded in any given year. Not that the exact value of 50 m

3/s has a 1%

probability of occurrence. Technically, the probability of exactly 50 m3/s occurring is

zero.Occasionally it is necessary to determine the probability of a specific event being

exceeded within a specific time. The probabilityPof an event having a given ARI, x

occurring at least once inNsuccessive years is given as;

N

xP }

11{1 = (2.3)

A distinction exists between the probability of an event occurring at least once and

exactly once in a given time period. Another form of the risk equation determines the

probability of an event occurring a precise number of times in a given period. In this

equation;

)!(

}1

1{}1

{! 1

INI

xxN

P

NN

=

(2.4)

Here,Iis the exact number of times the event with the ARI of x occurs inNsuccessive

years. These concepts are also used in the definition ofmajor and minor design storms,the frequency of which is expressed in terms of ARI.

2.2.2 Design Storm Event Characteristics at Each Point of Interest

Design storm is the rainfall pattern that is considered the most critical for the drainage

system in the area. Specification of the design storm involves definition of the designreturn period, total depth, duration of the storm and the temporal distribution or storm

hyetograph at the location. A hyetograph shows how the total depth (or intensity) of

rainfall in a storm is distributed among time increments within the storm while thetemporal distribution of rainfall over the duration of the storm is also described in terms

of a mass rainfall (or cumulative distribution) curve.


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Rainfall for various storm frequencies vs. rainfall duration.

Similar to this is a hydrograph- a graphical plot of flow versus time for a specific

location. Two types of design storm are recognised: synthetic and actual (historic)

storms. Synthesis and generalisation of a large number of actual storms is used to derivethe former. The latter are events which have occurred in the past, and which may have

well documented impacts on the drainage system. However, it is the usual practice in

urban stormwater drainage to use synthetic design storms. A synthetic rainfall

distribution is obtained by distributing a selected/known total rainfall depth/volume overa selected duration of the storm based on a defined mathematical distribution.

The most popular way to obtain the design storm characteristics is to obtain and use

what is known as the Intensity-Duration-Frequency (IDF) curves or equations. A typicalIDF relationship is illustrated in Figure 2.6 below.

Figure 2.6

Alternatively, IDF relationships are given as:

n

m

p

Db

RaI

)(

)(

+= ..2.5

where I = intensity of rainfall (mm/hr)

Rp = frequency or return period of the rainfall (year)


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D = duration of the rainfall (min or hr)

a, b, m and n are coefficients.

Examples are:

796.0

185.0

)189.0(

)45.0(6.40

+

=D

RI p ..(2.6)

Where

D = duration in hr

and

4.36t

T5693i

178.0

+= .(2.7)

where i = rainfall intensity (mm/hr)

T = return period (year)

t = rainfall duration (min)

Equations 2.6 and 2.7 imply that the estimation of the design value of intensity at alocation requires the knowledge of design frequency or return period and the designstorm duration. Very often, a design storm event frequency is specified in terms of its

"Annual Exceedance Probability" (AEP), e.g. the 5% storm event i.e. there is a 5%

chance of such a storm occurring in any year or on average five such storms would be

expected to occur in a period of 100 years, i.e. the average recurrence interval of a storm

of this severity is 20 years.. Typical recommendations are shown in Table 2.1 below.

Table 2.1 a -Design Average Recurrence Intervals

Effect of surcharge (Overflow) and overland flow ARI (years)

Small impact, in low density area 1

Normal impacts 2

Ponding in flat topography; or flooding of parkinglots to depths greater than 150 mm

10

Impeded access to commercial and industrial building 10

Ponding against adjoining buildings; or impededaccess to institutional or important buildings (e,g,

hospitals, city halls, school entrances)

20

Table 2.1b- Design Storm Return Periods

Land Use or Zoning Design Storm Return Period

Initial Storm Major Storm

Residential 2-year 100-year

Business 5-year 100-year

Public Building Areas 5-year 100-year

Parks, Greenbelts, etc. 2-year 100-year

Open Channels andDrainageways

- 100-year

Detention Facilities - 100-year


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In general, the design average recurrence interval (ARI) can be obtained by using the

following equation:

)]1ln([ AEP

DLARI

= .(2.8)

Where DL = expected or selected design life of the system (yr)

AEP = acceptable probability of exceedance (fraction)

2.2.2A Design Storm Duration

Design storm duration is an important parameter that defines the rainfall depth or

intensity for a given frequency, and therefore affects the resulting runoff peak andvolume. It is assumed that peak stormwater flow at a given location will usually result

when the entire drainage area is contributing flow from rainfall on the area. The current

practice is to select the design storm duration as equal to the time of concentration forthe catchment [or some minimum value (usually 5 min) when the time of concentration

is short].

The time of concentration is the flow travel time from the most hydraulically remote

point in the contributing area to the point of interest.

Depending on the particular location, the calculation of Tc will include one or a numberof components as shown in Table 2.2.

Table 2.2 Flow Time Components

Flow Type Components

Overland or 'sheet'

flow

natural surfaces

landscaped surfaces

impervious surfaces

Roof to main pipe

system

residential roofs

commercial/industrial

roofs

Open channel open drains

kerbs and gutters

roadside table drains

engineered waterways

natural channels

Underground pipe downpipe to street gutter

pipe flow within lots

including roof drainage,

car parks, etc

street drainage pipe flow

Thus, pchgodirect

c ttttiT +++=)( (2.9)

Where


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Tcdirect= flow travel time from the hydraulically most remote point on a sub-catchment to

point of interest i on the same sub-catchment.

to, tg, and tch , tp are the tc components attributed to overland flow, kerb gutter flow, open

channel flow and pipe flow respectively.

Overland Flow Time

Overland flow can occur on either grassed or paved surfaces. The major factorsaffecting time of concentration for overland flow are the maximum flow distance,

surface slope, surface roughness, rainfall intensity, and infiltration rate. Overland flow

over unpaved surfaces initially occurs as sheet flow for a short time and distance afterwhich it begins to form a runnel or rill and travels thereafter in a natural channel form. In

urban areas, the length of overland flow will typically be less than 50 metres after which

the flow will become concentrated against fences, paths or structures or intercepted by

open drains. The formula shown below, known as Friends formula, should be used to

estimate overland sheet flow times. The formula was derived from previous work in theform of a nomograph (Figure 1.7) for shallow sheet flow over a plane surface.

..(2.10)

where,

to = overland sheet flow travel time (minutes)

L = overland sheet flow path length (m)

n = Horton's roughness value for the surface

S = slope of surface (%)

Note : Values for Horton's 'n ' are similar to those for Manning's 'n ' for similar surfaces.

Values are given in Table 2.3. Some texts recommend an alternative equation, theKinematic Wave Equation. However this theoretical equation is only valid for uniform

planar homogeneous flow. It is not recommended for practical application.

Table 2.3 Values of Mannings 'n' for Overland Flow

Surface Type Mannings

n

Range

Concrete/Asphalt** 0.011 0.01-0.013

Bare Sand** 0.01 0.01-0.06

Bare Clay-Loam(eroded)**

0.02 0.012-0.033

Gravelled Surface** 0.02 0.012-0.03

Packed Clay** 0.03

Short Grass** 0.15 0.10-0.20


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Light Turf* 0.20

Lawns* 0.25 0.20-0.30

Dense Turf* 0.35

Pasture* 0.35 0.30-0.40

Dense Shrubbery and

Forest Litter*

0.40

Figure 2.7. Nomograph for Estimating Overland Sheet Flow Times

Where the characteristics of segments of a sub-catchment are different in terms of landcover or surface slope, the sub-catchment should be divided into these segments, and the

calculated travel times for each combined. However, it is incorrect to simply add thevalues oft0for each segment as Equation 2.10 is based on the assumption that segments

are independent of each other, i.e. flow does not enter a segment from upstream.

The following method for estimating the total overland flow travel time for segments in

series is recommended. For two segments, termed a and b (Figure 2.8):

aba LbLLbLaatotaltttT ,)(,, += + (2.11)

where,La = length of flow for Segment a

Lb = length of flow for Segment b

ta,(La) = time of flow calculated for Segment a over length L atb ,(...) =time for Segment b over the lengths indicated


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Figure 2.8. Overland Flow over Multiple Segments

For each additional segment, the following value should be added:

)(,, atotaltotal LLaLatt

..(2.12)

where,

a = segment name

L total = total length of flow, including the current segment a

La = length of flow for current segment a

ta(...) = time for the current segment aover the lengths indicated

Kerb Gutter Flow Time

The velocity of water flowing in kerb gutters is affected by:

the roughness of the kerb gutter and road surface

the cross-fall of the road pavement

the longitudinal grade of the kerb gutter

the flow carried in the kerb gutterThe flow normally varies along the length of a kerb gutter due to lateral surface inflows.

Therefore, the flow velocity will also vary along the length of a kerb gutter. As the

amount of kerb gutter flow is not known for the initial analysis of a sub-catchment, theflow velocity and hence the kerb gutter flow time cannot be calculated directly. An

initial assessment of the kerb gutter flow time must be made.

An approximate kerb gutter flow time can be estimated from Figure 2.9 or by the

following empirical equation:

(2.13)

where,tg = kerb gutter flow time (minutes)

L = length of kerb gutter flow (m)

S =longitudinal grade of the kerb gutter (%)


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Kerb gutter flow time is generally only a small portion of the time of concentration for a

catchment. The errors introduced by these approximate methods of calculation of the

kerb gutter flow time result in only small errors in the time of concentration for a

catchment, and hence only small errors in the calculated peak flow.

Figure 2.9 Kerb Gutter Flow Time

Channel Flow Time

The time stormwater takes to flow along an open channel may be determined by dividingthe length of the channel by the average velocity of the flow. The average velocity of

the flow is calculated using the hydraulic characteristics of the open channel.

The Manning's Equation is suitable for this purpose:

( 2.14)

From which,

( 2 .15)

Where,V = average velocity (m/s)n = Manning's roughness coefficient

R =hydraulic radius (m)

S = friction slope (m/m)L =length of reach (m)

t = travel time (minutes)

Where an open channel has varying roughness or depth across its width it may be

necessary to sectorise the flow and determine the average velocity of the flow, to

determine the flow time.


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Pipe Flow Time

The velocity Vin a pipe running just full can be estimated from pipe flow charts derivedfrom Mannings equation where the flow, pipe diameter and pipe slope are known. The

time of flow, tp , is then given by:

.(2.16)where,

L = pipe length (m)

Where the pipe diameter is not known, the diameter can be first estimated given the flowat the upstream end of the pipe reach and the average grade of the land surface between

its ends.

As is the case with kerb gutter flow time, pipe flow time is generally only a small portionof the time of concentration for a sub-catchment. The error in the estimated pipe flow

time introduced by the adoption of the wrong diameter or slope, or by the assumption

that the pipe is flowing full when in fact it is only flowing part full, will not introduce

major errors into the calculated peak flow.

Although travel time from individual elements of a system may be very short, the totalnominal flow travel time to be adopted for all individual elements within any catchment

to its point of entry into the stormwater drainage network shall not be less than 5

minutes. For small catchments up to 0.4 hectare in area, it is acceptable to use the

standard minimum times of concentration given in Table 2.4 instead of detailed

calculation.

Table 2.4 Standard Minimum Times of Concentration

Location Standard Tc (minutes)

Roof and property

drainage

5

Road inlet pits 5

Small areas < 0.4 hectare 10

Furthermore, the time of concentration to a point of interest due to flow from many sub-catchments can be estimated by first defining the hydraulic flow path from each sub-

catchment to the point of interest.

After defining the hydraulic flow path, the next task is to estimate the time of concentrationto the point of interest i as:

))](),..(),((),([)(,2,1,

iTiTiTiTMAXiTchmentlastsubcatindirect

c

ntsubcatchmeindirect

c


c

direct

c

net

c =

(2.17)Where:

Tcnet

(i) = governing time of concentration at location i on the network (min or hr)

Tcdirect

(i) = time of concentration along the direct flow path (i.e. along the sub-catchment of

the point of interest i) to i (min or hr)


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Tcindirect,subcatchment(i) = time of concentration from another sub-catchment (i.e. along the

hydraulic flow path) to location i (min or hr)

Furthermore:

),1()1()(,,

iiTiTiTntsubcatchme

conduit

ntsubcatchmenet

c


c

+= (2.18)

whereTconduit

subcatchment(i-1,i)= travel time on the conduit (pipe or open channel) that links i-1 and i.

in a sub-catchment (min)

),1(

),1(*60),1(

iivelocity

iiLiiT

conduit

conduitntsubcatchme

conduit

= (2.19)

Lconduit(i-1,i)= length of conduit between i-1 and i (meters)

velocityconduit(i-1,i)= velocity of flow in the conduit between i-1 and i (m/sec)The velocity can be estimated by using the chart below or by using the relationship given

as:

n

SR

velocityconduitconduit

conduit

5.0667.0

= ..(2.20)

Rconduit= hydraulic radius of the conduit

Sconduit= slope of the conduit.

Exercise:

On the following page you are given a topographic map of the post-developed conditionfor a proposed development.

1) Sketch the principle flow path for basin 4 and determine the map scale.

2) Estimate the time of concentration for basin 4


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Note that you may use a mixed method to find the time of concentration. For example,

you may use the kinematic wave for sheet flow and combine with the Manning equationto handle any concentrated flow.

High Point


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2.2.2.BRainfall Intensity

For a given duration Tc and recurrence interval ARI, the intensity i at a point of interest

is determined from the appropriate rainfall intensity-duration-frequency (IDF) curve for

the area concerned.

2.3 Peak Flow/Discharge

2.3.1 Stormwater Runoff

Peak Runoff flow or discharge is the maximum rate of runoff passing a particular

location during a storm event. Peak runoff discharge has units of volume/time (e.g.m

3/sec). The peak flow/discharge is a primary design variable for the design of

stormwater runoff facilities such as pipe systems, storm inlets and culverts, and smallopen channels. It is also used for some hydrologic planning such as small detentionfacilities in urban areas. Peak discharge can be estimated with or without calculating a

hydrograph. In general, a hydrograph is used to establish the peak discharge when an

analysis of the effect of water storage [ponds, reservoirs etc] on the drainage area underconsideration needs to be considered.

There have been many different approaches for determining the peak runoff from an

area. As a result many different models (equations) for peak discharge estimation have

been developed. There are two general classes of peak discharge hydrologic models.They are CalibratedModelsand UncalibratedModels.

2.3.1.A Calibrated Models

Calibrated models are generally multi-parameter regression models that were

derived from a frequency analysis from long-term gaged data from watersheds inthe region.

Some examples of calibrated models include:

USGS Urban Peak Discharge FormulasIndex-Flood Estimation

Moment Estimation

Calibrated models are based on the analysis of stream gage data. For small watersheds,

especially those undergoing urban/suburban development, regional equations that are

appropriate for assessing the impact of development of peak discharges are not available,with the possible exception of the USGS regression equations. However, these are not

widely used because they do not include variables that are typically used to reflect

changes in watershed conditions. Thus, there is a demand for methods that provide peakdischarge estimates that use readily available input data such as watershed and design-

storm rainfall characteristics.


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2.3.1.B Uncalibrated Models

Rational Method

The most widely used uncalibrated equation is the Rational Method. The rational methoduses a formula that expresses a supposedly rational relation between rainfall intensity

and catchment area as independent variables and the peak flood discharge resulting from

the rainfall as the dependent variable. It has been in use for about 150 years and iswidely used in the design of stormwater drainage systems, farm dam spillways, and

small culverts in road and railway embankments. The rational method is based on the

following major assumptions.

Rainfall intensity and duration is uniform over the area of study

Storm duration must be equal to or greater than the time of concentration of thewatershed.

Mathematically, the rational method relates the peak discharge (Q, m3/sec) to the

drainage area (A, ha), the rainfall intensity (i, mm/hr), and the runoff coefficient (C).

The formula is:

360

. totalyty

AICQ c= ..( 2.21 ) or

DCIAytAIQ c= ..(2.22)

where,

Qy =y year ARI peak flow (m3/s)

C = dimensionless runoff coefficient

Iyt =y year ARI average rainfall intensity over time of concentration, tc , (mm/hr)Atotal = total drainage area (ha)

ADCIA = directly connected impervious area

To estimate peak flow using the rational formula, the A, I and C must be determined.

The runoff coefficient can be estimated as by using one of the available charts or tables

which is illustrated in Figure 2.10


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Figure 2.10 Runoff Coefficients for Urban Catchments


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For a heterogeneous sub-basin (i.e. in areas where the runoff coefficient is not constant

over the entire area), a weighted runoff coefficient should be determined. The runoff

coefficient for each sub-area is determined and a single weighted runoff coefficient is

obtained as:

(2.23)

Alternatively, for a heterogeneous watershed that can be subdivided into homogeneoussub areas Aj with associated curve number Cj, Q becomes:

j

J

j

j ACiQ .0028.01

=

= ..(2.24)

Limitations

A principal limitation of the Rational Method is that only a peak discharge is produced.Therefore, the simple form of the Rational Method cannot be used to calculate thevolume or shape of the runoff hydrograph, which is required for the design of facilities

that use storage such as detention and retention basins.


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Figure 2.11 General Procedure for Estimating Peak Flow for a Single Sub-catchment Using the Rational

Method


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Worked Examples

Example 2-1

A culvert on a road is to be designed to pass a flood of ARI = 10 years; the catchment areais 5 km

2. The statistical runoff coefficient C10 is found to be 0.3. A fragment of the rainfall

intensity-duration relation for ARI = 10 years at the site is given below. Calculate the

design discharge by the rational method.

100

80

60

40

20

1 2

Duration, hours

Intensity,mm/h

1012631.4

-1

Intensity-duration relation for

Average Recurrence Interval = 10 years

Solution

Using equation 2.21 .

Q = 0.28 CIA

C = 0.3

A = 5 km2

To determine I, first calculate tc = 1.4 hours

For a storm duration of 1.4 h, from the above intensity-duration diagram,I = 65 mmh

-1

Q = 0.28 x 0.3 x 65 x 5= 27.3 m

3s

-1

The design discharge is 27 m3s

-1


28/52



Example 2-2

50

50

100

50

Drain

Outflow

Dimensions in m.

A paved parking area is defined in the above diagram. Runoff occurs as sheet flow and is

collected in a drain as shown. Time of concentration to the drain is 12 minutes, time of flow

in the drain can be assumed negligible. What is the peak discharge at the outflow?

Q = 0.28 CIA

CI = mean rate of rainfall-excess in mm/h= (4 + 8 + 3 + 1) x 60/12

= 80 mm/h

A = catchment area in km2

= (100 x 100 - 50 x 50) x 10

-6

= 0.0075 km2

Q = 0.28 x 80 x 0.0075 m3s

-1

= 0.28 x 80 x 7.5 Ls-1

= 168 Ls-1

Repeat the above Worked Example for a parallelogram shaped area 100 m x 100 m, i.e. like

the one used in the Worked Example but without the 50 m x 50 m corner cut out.


29/52



The following information is given about your development area:

o The information given below defines the IDF curve for this area.

5min 10min 15min 30min 1hr 2hr 3hr 6hr 12hr 24hr

1 year 0.13 0.18 0.23 0.31 0.39 0.45 0.50 0.64 0.77 0.90

2 year 0.15 0.22 0.28 0.38 0.47 0.55 0.63 0.82 1.00 1.18

5 year 0.19 0.24 0.30 0.43 0.55 0.67 0.78 1.06 1.31 1.56

10 year 0.13 0.23 0.31 0.46 0.59 0.73 0.86 1.19 1.49 1.80

25 year 0.15 0.27 0.36 0.53 0.69 0.86 1.03 1.44 1.81 2.19

50 year 0.16 0.30 0.40 0.59 0.77 .96 1.16 1.63 2.05 2.48

100 year 0.12 0.27 0.39 0.60 0.80 1.02 1.24 1.76 2.23 2.71

o The area is considered to be pasture/range land before development

o All analysis/design should be for a 50-year return period.o Model units are in meters.

o Assume a longitudinal roadway slope of .01 and a transverse slope of .03.

o Use 450 mm wide P-1-7/8 grates that are 1 m long for all storm draininlets.

o The highpoint of the development is the north east corner and the low

point is the southwest corner. In other words flow will travel from east towest and north to south (the crown in the road can be assumed sufficient

to contain flows for basin delineation purposes).o The minimum storm drain pipe size that can be used is 450 mm.

1. Using the data provided compute the 50-year peak runoff for the development

site with the rational method.2. Determine the peak flow for each sub-basin after development. Sub-basin

boundaries should be determined from the storm drain inlets (shown in red).

Since you do not have elevation data you will need to delineate the basins- makeapproximations.

3. Determine the amount flow captured at each storm drain and the amount that

bypasses. Is a 450 mm storm drain pipe adequate (you can use Manning's

equation with the assumption that the pipe is flowing full to determine thecapacity of the 450 mm storm drain pipe)?


30/52



SCS Triangular Hydrograph Method

In this method, peak runoff is determined using the curve number approach. The

assumption of uniform rainfall still applies. The hydrograph takes on a triangular shape

with equal peak and flow volume as in the rational method. This can be seen below.

Peak runoff rate is calculated by

q = 0.0021QA/Tp .(2.25)

where Q = runoff volume in mm depth (from the curve number)q = runoff rate in m3/s

A = watershed area in ha.

Tp = time of peak in hours

In this method, the time to peak does not equal the time of concentration as in the

rational method, in this method time to peak Tp equals

Tp = D/2 + TL = D/2 + 0.6Tc..(2.26)Where Tp = time to peak (hours)

D = duration of excess rainfall

TL = time of lag

Tc = time of concentrationIt is assumed that the total time of flow is 2.67 Tp and the recession time of the

hydrograph is 1.67 Tp.

Time of concentration is calculated using the SCS Lag formula discussed earlierTc = 0.002 L

0.8(1000/CN 9)0.7 S-0.5..(2.27)

where L = watershed length (m)

S = watershed slope (m/m)

CN = curve number


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Table 2.5-Runoff Curve Numbers*

Hydrologic Soil Group

Land Use, Crop, and Management A B C D

CULTIVATED, with crop rotations

Row Crops, poor management 72 81 88 91

Row Crops, conservation mgmt 65 75 82 86

Small Grains, poor management 65 76 84 88

Small Grains, conservation mgmt 61 73 81 84

Meadow 55 69 78 83

PASTURE, permanent w/moderate grazing 39 61 74 80

WOODS, permanent, mature, no grazing 25 55 70 77ROADS, hard surfaces and roof areas 74 84 90 92

Hydrologic Soil Group Descriptions:

A -- Well-drained sand and gravel; high permeability.

B -- Moderate to well-drained; moderately fine to moderately coarse texture; moderate

permeability.

C -- Poor to moderately well-drained; moderately fine to fine texture; slow permeability.

D -- Poorly drained, clay soils with high swelling potential, permanent high water table,

claypan, or shallow soils over nearly impervious layer(s).

*Foraverage antecedent mositure conditions in a watershed.


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Graphical Peak Discharge Method

The graphical peak discharge method of calculating runoff was developed by the

USDA-Soil Conservation Service and is contained in SCS Technical Release No. 55

entitled Urban Hydrology for Small Watersheds. This method of runoff calculationyields a total runoff volume as well as a peak discharge. It takes into consideration

infiltration rates of soils, as well as land cover and other losses to obtain the net runoff.

As with the rational formula, it is an empirical model and its accuracy is dependent uponthe judgment of the user. Following is the procedure to use the peak discharge method of

runoff determination:

Task 1 - Measure the drainage area. Use surveyed topography, aerial photographs,soils maps, etc.

Task 2 - Calculate a curve number (CN) for the drainage area.

The curve number (CN) is similar to the runoff coefficient of the rational formula. It is

an empirical value which establishes a relationship between rainfall and runoff based

upon characteristics of the drainage area. The soil type also influences the curvenumber. Each soil belongs to a different hydrologic soil group. If the soil name is

unknown, a judgment must be made based upon knowledge of the soils and the soil

group description. Soil names can be obtained from county soil surveys, the local Soil

Conservation Service office, or analysis of actual soil borings.

Table 2.6-Hydrologic Soil Groups

Soil Group

ARepresents soils having a low runoff potential due to high infiltrationrates. These soils consist primarily of deep, well-drained sands and

gravel.

Soil Group B

Represents soils having a moderately low runoff potential due to moderate

infiltration rates. These soils consist primarily of moderately deep to deep,

moderately well-drained to well-drained soils with moderately fine to

moderately coarse textures.

Soil Group C

Represents soils having a moderately high runoff potential due to slow

infiltration rates. These soils consist primarily 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.

Soil Group D

Represents soils having a high runoff potential due to very slow infiltrationrates. These soils consist primarily of clays with high water tables, soils

with a claypan or clay layer at or near the surface, and shallow soils over

nearly impervious parent material.

If the watershed has uniform land use and soils, the curve number value can be easilydetermined directly. Curve numbers for nonhomogenous watersheds may be determined

by dividing the watershed into homogeneous sub-areas and performing a weighted

average.


33/52



=

i

i

i

ii

A

xACN

CN ..(2.28)

Table 2.7-Runoff Curve Numbersfor Graphical Peak Discharge Method

Cover DescriptionHydrologic Soil

Group

A B C D

Fully Developed Urban Areas

(Vegetation Established)

Open Space (lawns,parks,etc.)

Poor Condition; GrassFair Condition; Grass 50 - 75% cover

Good Condition; Grass > 75% cover

684939

7969

61

8679

74

8984

80

Impervious Areas Paved parking lots, roofs, driveways 98 98 98 98

Streets and RoadsPaved; curbs and storm sewersPaved; open ditches (w/ right-of-way)

Gravel (with right-of-way)

Dirt (with right-of-way)

98

83

76

72

98

89

85

82

98

92

89

87

98

93

91

89

Urban Districts

Average % Impervious

Commercial and Business 85

Industrial 7289

81

92

8894

91

95

93

Residential Districts

(by average lot size)

Average % Impervious

1/8 acre (town house) 65

1/4 acre 38

1/3 acre 30

1/2 acre 25

1 acre 202 acres 12

77

61

5754

51

46

85

75

7270

68

65

90

83

8180

79

77

92

87

8685

84

82

Urban Areas - Development UnderwayNo Vegetation Established

Newly graded area 81 89 93 95

Pavement and Roofs, Commercial & Business Areas 98 98 98 98

Row Houses, Town Houses and Residential w/ lot sizes:

1/8 acre or less1/4 acre

1/2 acre

1 acre

2 acres

9388858281

9693919089

9795949392

9897969594

Cultivated Agricultural Lands

Fallow:Bare SoilCrop Residue (CR) poor

Crop Residue (CR) good

777674

868583

919088

949390

Row Crops:Straight row (SR) poor

Strai ht row SR ood

7267

8178

8885

9189


34/52



Contoured (C) poor

Contoured (C) goodContoured and Terraced (C&T) poor

Contoured and Terraced (C&T) good

70656662

79757471

84828078

88868281

Other Agricultural Lands

Pasture, grassland or range

poor

fair

good

684939

796961

867974

89

8480

Meadow 30 58 71 78

Brush - brush, weed, grass mixpoor

fair

good

483530

675648

777065

837773

Woods - grass combinationpoor

fair

good

574332

736558

827672

868279

Woodspoorfair

good

453630

666055

777370

837977

Porous Pavement**

Gravel SubbaseThickness

(inches)

Porous Pavement (Properly Maintained)

10

1824

36

57535247

66615852

69646155

75696658

Porous Pavement (Not Properly Maintained) 10 - 36 98 98 98 98

**This information is not intended for design purposes.

Task 3 - Determine runoff depth and volume for the design storm.

The rainfall depth (in inches) can be determined from theRainfall Depths forSelectedDesign Storms. (For the examples in this lesson, the design storms are based upon the

SCS Type II 24-hour rainfall distribution.

The runoff depth (in inches) can be determined from the graph contained on theRainfall

Depths for Selected Design Storms. Enter the graph with the rainfall depth (inches) at

the bottom, move vertically to intersect the appropriate curve, then move horizontally

and read inches of runoff. The volume of runoff from the site can be calculated by

simply multiplying the drainage area of the site by the runoff depth.

Task 4 - Determine time of concentration.

Task 5 - Determine initial abstraction (Ia).


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Initial abstraction (Ia) refers to all losses that occur before runoff begins. It

includes water retained in surface depressions, water intercepted by vegetation,

and evaporation and infiltration. Ia is highly variable but generally is correlated

with soil and cover parameters. The relationship of Ia to curve number is

presented below.

Table 2.8- Ia Values for Runoff Curve Numbers

CurveNumber

Ia(inches)

CurveNumber

Ia(inches)

CurveNumber

Ia(inches)

40 3.000 60 1.333 80 0.500

41 2.878 61 1.279 81 0.469

42 2.762 62 1.226 82 0.439

43 2.651 63 1.175 83 0.410

44 2.545 64 1.125 84 0.381

45 2.444 65 1.077 85 0.353

46 2.348 66 1.030 86 0.326

47 2.255 67 0.985 87 0.299

48 2.167 68 0.941 88 0.273

49 2.082 69 0.899 89 0.247

50 2.000 70 0.857 90 0.222

51 1.922 71 0.817 91 0.198

52 1.846 72 0.778 92 0.174

53 1.774 73 0.740 93 0.151

54 1.704 74 0.703 94 0.12855 1.636 75 0.667 95 0.105

56 1.571 76 0.632 96 0.083

57 1.509 77 0.597 97 0.062

58 1.448 78 0.564 98 0.041

59 1.390 79 0.532

Task 6 - Determine the unit peak discharge.

Divide the initial abstraction by the rainfall to obtain the Ia/P ratio. Enter Figure 2. with

the calculated Tc in hours, move up the Ia/P ratio (this can be a linear interpolation) andread the unit peak discharge (qu) on the left in cubic-feet per second per square mile of

drainage area per inch of runoff (csm/in). Convert to cubic meter per sec per square km

of drainage area per mm of runoff (m3/s/km

2/mm)

Unit Peak Discharge (qu) for SCS Type II Rainfall Distribution


36/52



Figure 2.12

To determine the peak discharge (q), multiply the value of (qu) by the drainage area in

square km and by the runoff in mm.

q = Qu Am Q ..(2.29)where: q = peak discharge in cubic meter per sec

Qu = unit peak discharge in (m3/s/km

2/mm)

Am = drainage area in square km

Q = runoff in mm

Task 7 - Determine whether ponding and swampy conditions in the watershed area will

affect the peak discharge. This adjustment is not always needed. Ponds or swamps on

the main stream or that are in the path used for calculating time of concentration (Tc) arenot considered here. Only ponds and swamps scattered throughout the watershed that

are not in the Tc path are considered.

Table below contains the adjustment factors for ponds and swamps spread throughout

the watershed. Measure or estimate the area covered by ponds and/or swamps, convert

to percentage of the watershed drainage area, enter the Table and read (or interpolate)

the multiplying factor (Fp).


37/52



Table 2.9-Adjustment Factor (Fp) for Pond and Swamp Areas

Spread Throughout the Watershed

Percentage of pond and swamp

areas

Fp

0 1.00

0.2 0.97

1.0 0.87

3.0 0.75

5.0 0.72

If the Fp adjustment is needed, then the discharge from step 5 is multiplied by the Table

value to obtain the final peak discharge (qp).

qp = (q) (Fp) .(2.30)


38/52



TR55/SCS MethodPeak discharge, runoff depth, initial abstraction, unit peak discharge, and pond/swamp

factor are computed as follows:

)4.25)(101000

(

2.0

)( 2

=

=

+

=

=

CS

SI

SIP

IPQ

AQFQQ

a

a

a

pUP

(2.31)

where: A = total watershed area (km2). CN = overall curve number for the watershed.

Fp = pond and swamp adjustment factor. Ia = initial abstraction (mm); losses before

runoff begins (surface depressions, interception by leaves, evaporation, infiltration) -SCS determined the above equation for Ia after numerous studies. P = precipitation(mm) for 24-hr duration storm of return period for which you are interested. Q = depth

of runoff over entire watershed (mm). Qp = peak discharge (m3/sec ). Qu = unit peak

discharge (m3/sec /km

2-mm); outside the USA, use the rainfall distribution type that best

represents your typical storm.

SCS 24-hour rainfall distributions (SCS, 1986):(y-axis reads "Fraction of 24-hour rainfall" and x-axis reads "Time, hours")


39/52



h o u r s

Figure 2.13

S = potential maximum watershed water retention after runoff begins (mm). Tc = time

of concentration for the watershed (hr); time for runoff to travel from the furthest

distance (by time) in the watershed to the location where you wish to determine Qp.

A user can divide a watershed into a maximum of five sub-regions represented by

different curve numbers. Then, the overall curve number and total area are computed.

Alternatively, if there are more than five sub-regions, you may compute the overallcurve number by hand and enter that value into our calculation. Overall curve number

is computed from:

.(2.32)

Example 2-3

A 1.2-ha development site is comprised of 0.4 ha of impervious surface and 0.8 ha of

lawn and woods with a NRCS Curve Number (CN) of 65. The entire impervious surfaceis directly connected to the sites drainage system. Compute the sites total runoff

volume for the 31.75-mm design Storm using the Weighted Average CN technique.

Compare the results with the Weighted Average Volume technique.Stormwater Quality Design Storm = P = 31.75 mm

Total drainage area = 1.2 ha


40/52



Impervious area = 0.4 ha (1/3 of total area)

Pervious area = 0.8 ha (2/3 of total area)

Pervious cover = mixture of lawn and woods Pervious CN = 65

Impervious cover = asphalt Impervious CN = 98

Note: All impervious cover is connected to the drainage system

1. Using Weighted Average Curve Number Technique

Weighted CN = (65)(2/3) + (98)(1/3) = 76Average S = [(1000/76)-10]x25.4 = 80 mm

Average initial abstraction = Ia = 0.2S = (0.2)(80) = 16 mm

0.8S = (0.8)(16) = 12.8 mm

Runoff volume = Q = SIP

SP

a +

2)2.0(

= (31.75 - 16)2/(31.75+0.8*80) = 2.54 mm

Runoff volume = (2.54 mm/1000 mm per m)(1.2 ha)(10000 sq m per ha)Total site runoff volume = 30.4 cubic meters

2. Using Weighted Average Volume Technique

Impervious Area

Impervious area S = [(1000/98)-10] x 25.4 = 50 mm

Impervious area initial abstraction = 0.2S = (0.2)(50) = 10 mm

0.8S = (0.8)(10) = 8 mm

Impervious area runoff volume = Q = =SIP

SP

a +

2)2.0(

= (31.75 -10)2/(31.75+0.8*50) =

25.4 mm

Runoff volume = (25.4mm/1000 mm per m)(0.4 ha)(10000 sm per ha)

Impervious area runoff volume = 102 cubic meter

Pervious Area

Pervious area S = [(1000/65) 10](25.4) = 136.6 mm

Pervious area initial abstraction = 0.2S = (0.2)(136.6) = 27.3 mm

0.8S = (0.8)(136.6) = 109.2 mm

Pervious area runoff volume = Q = =SIP

SP

a +

2)2.0(

= 0.13 mm

Runoff volume = (0.13 mm/1000 mm per m)(0.8 ha)(10000 sm per ha)

Pervious area runoff volume = 0.97 cubic meters


41/52



Total site runoff volume = 102 + 0.97 = 103 cubic meters(vs. 30.4 cubic meters using weighted average CN)As can be seen in this Example, the weighted average CN technique produced an

estimated Stormwater Quality Design Storm runoff volume that was less than 30 percent

of the volume produced by the weighted average volume technique. Perhaps moresignificantly, the example also demonstrates how virtually the entire site runoff for the

Stormwater Quality Design Storm comes from the impervious portion and that very little

comes from the pervious portion (i.e., 102 cubic meters vs. 0.97 cubic meters). Thesignificant but erroneous initial loss that the NRCS cautions about in TR-55 can also be

seen in the 16 mm initial abstraction for the entire site (including one acre of impervious

surface) produced by the weighted average CN technique. It is important to note that, incomputing a weighted average runoff volume from the development site, the example

does not address the resultant peak discharge or hydrograph from the site. If both the

pervious and directly connected impervious site areas will have the same Time ofConcentration, the weighted runoff volume can then be used directly to compute the

peak site discharge or hydrograph. However, if these areas will respond to rainfall withdifferent TCs, separate hydrographs should be computed for each and then combined to

produce the peak site discharge or hydrograph.


42/52



Example 2-4

Design Flow Estimate

In some instances, more than one design flow calculation method should

be used. The designer should evaluate all the results and finally estimatea design flow based on the reliability of input data, past events, historic

high flow records and experience.

Background

Thames Creek is

located onthe east side of

Vancouver

Island nearDenman Island.

Problem

Since thehighway crosses

Thames Creek, abridge or

culvert will be

required.

Estimate the 200year (Q200)

flow.


43/52



Solution

Step 1 - Determine Basin Size and Creek Length.

From the 1:50,000 scale mapping, the following dimensions weremeasured:

A = 6.6 km2 = 660 ha

L = 8.2 km

Step 2 - Determine Basin Slope

A profile of the main channel was plotted. Since the upper portion of

basin is steep, the basin slope was estimated using the Equivalent Slope

Method.

S = 0.051 m/m = 5.1%

Step 3 - Determine Land Characteristics

Design flows are estimated assuming worst case conditions.

Considerations include basin slope, type of vegetation, recurrence

intervals, snowmelt, antecedent moisture condition (AMC), etc. Since

the Thames Creek basin is relatively low with light forest cover, thefollowing land characteristic values were selected:

r = 0.60, deciduous timber land

CN = 85, forest land with good cover, Hydrologic Soil Group C,AMC III

C = 0.40, flat, forested.

Step 4 - Determine Time of Concentration

There are numerous ways of estimating the time of concentration (tc). A

few different methods will be used and an average value will be

selected.Method 1 - BC Rational Formula Method

A = 6.6 km2 = 2.6 km

tc = 3.6hr (interpolated)

tc = (rL)0.467 = ((0.60)(8.2km))0.467 = 2.6hr

1.65s0.234 1.65(0.051m/m)0.234


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Design Flow Estimate continued

Method 2 - SCS Curve Number Method

SCN = 254 (100 - 1) = 254 (100 - 1) = 44.8

CN 85

TL = L0.8 (0.039CN + 1)0.7 = (8200m)0.8 (0.039(44.8) +1)0.7 = 1.7hr

735s0.5 735(5.1%)0.5

tc = 1.7TL = 1.7(1.7hr) = 2.8hr

Method 3 - Bransby Williams Formula

tc = 0.605L = 0.605(8.2km) = 3.0hrs0.2 A0.1 (5.1%)0.2 (6.6km2)0.1

Taking an average, it is assumed that tc = 3 hours.

Step 5 - Determine Rainfall Intensity

The nearest rainfall gauging station is located at Comox Airport

(El.24m). Since the basin elevation varies from El.20 m to El.760 m, aprecipitation gradient is expected. The 10-year rainfall intensity

corresponding to the time of concentration will be used due to the

increased reliability of rainfall data over more frequent return periods

(e.g. 2-year). A previous hydrological study estimated the averageintensity over the basin will increase at a rate of 5% per 100 m rise in

elevation.

i = (9mm/hr)((740m)(0.5)(0.05)+1) = 10.7 mm/hr100m


45/52



Step 6- Determine Design Flow

There are numerous ways of estimating the design flow. A few different

methods will be used.

Method 1 - Rational Formula

Since the basin is small and there is limited data, the Rational Formula

will be used to determine the 10-year flow. The 10-year flow will thenbe converted to a 200-year flow. Studies have shown that the Q200/Q100

ratio is approximately 1.7 for this region.

Q10 = CiA = (0.40)(10.7mm/hr)(660ha) = 7.9 m3/s

360 360

Q200 = 1.7Q10 = 1.7(7.9m3/s) = 13.4m3/s

Design Flow Estimate continued

Method 2 - SCS Method

For this creek, a 24-hour, Type 1A rainfall distribution is used in the

analysis. The 10-year 24-hour total rainfall volume is obtained from theComox Airport IDF curve. The estimated 10-year flow will be converted

to a 200-year flow.Total Rainfall = (3.2mm/hr)(24hr) = 76.8mm.

Q10 = 7.4m3/s

Q200 = 1.7Q10 = 1.7(7.4m3/s) = 12.6m3/s

Method 3 - Regional Frequency Analysis

Hydrological studies have resulted in regional frequency curves for the

area.Q200 = (A)(unit runoff)(peaking factor)

= (6.6km2)(1.8m3/skm2)(1.5)= 17.8m3/s

Since the results do not vary significantly, an average will be taken.

The 200 year flow is estimated to be 15 m3/s.


46/52



2.3.2 Peak Wastewater Flow

2.3.2.A Characteristics

There are two main categories of sanitary sewer loads. The major oneconsists of sanitary loads or dry weather loads that result from human activity

and are not weather dependent. The main sources of these loads are the

activities from many land-use types- residential, commercial, industrial etc.

The second category consists of wet weather loads that are to rainfall activitysuch as groundwater infiltration- water leaking into a pipe through cracks,

joints, and defects) and structure inflow (surface water entering a structure

through openings around the cover, or due to a missing cover). In addition,they sometimes include flow of stormwater through illegal connection of

roof, yard and foundation drains to sanitary sewers as well as to poorly

constructed manholes and or connections and improperly laid house laterals,high water table etc. It is known that leakage through manhole covers may

be up to 180 liters per km with a depth of 5.54 mm. of water over the cover.

Sanitary sewer loads vary with time. The variation depends on the land use

characteristics. Thus, the loads are presented as hydrographs (flow vs time

data) or as pattern loads that is as a combination of base load and anassociated loading pattern which is a series of multipliers relating loading to

time.

Sewer analysis and design generally consider a variety of loading conditions

such as minimum, average and peak conditions. Base or average loads are

transformed into peak loads using a variable peaking factor. Total load in a sewer segment is a combination of load that is generated

within the segment (node and link) and accumulated load from upstream

segments(see Figure below).

When calculating flows for a sewer, you have to start from the upstream end

of an individual line and works downstream to accumulate flows to the givenpipe. The total flow to a pipe is computed by adding accumulated flows to the

flow contributed by the gravity line. The flow contributed by an individual

pipe is calculated by adding up the flow from different land uses (residential,commercial and miscellaneous) and the infiltration flows. The flow in a

forcemain (pressurized sewer pipe) is found by selecting the appropriate

system operating point computed for the corresponding pump station.

2.3.2.B Estimation


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Based on the characteristics of the loads described earlier, peak sewage load generated

within a segment can be estimated as:

86400

][ iuiuik

i

i

i

gen

FNQQQQ

+== .(2.33)

where:

Qi= peak load generated by each land use type i in liters per sec

Qk= fixed load for the land use type in the segment in lpd. [Qinf+ Qin ]

Qinf= infiltration flow on the link. (liters/day)

1000inf

line

u

LfQ = (2.34)

where Qinf= infiltration on a line of length Lline in km.fu = unit infiltration in liters/day/kmQui=flow rate per unit of land-use type i in lpd.

Nui= Number of units of land-use type i in lpd.

Fi=Peak(ing) factor.

Also, uiui aWQ = .(2.35)

where

Wui = unit water consumption in lpd and a is the return factor i.e. wastewater flow/water

consumption. Typical values are: W=500 lpd and 4000 lpd per household for developing

and developed countries respectively and a=0.85

Peak(ing) factor is defined in several ways-depending on the locality. One commonexpression is:

5.0

5.0

DPC

BPAFi

+

+= ..(2.36)

where Fi=Peak(ing) factor for a land-use type i

A,B,C,D are user defined constants { typical values are A=18, B=1,C=4 and D=1)P= population equivalent/1000.

In general, peak factors range between 1.3 and 2. A value of 1.8 has been used in some

developing countries.

Total flow at the end of a segment l:

gencuminputl QQQtot += , ..(2.37)

where:

Qtotl =total load at the end of a segment or line l in liters per sec

Qinput,cum = cumulative load (summation of average input flows for all lines upstream of

line l whose flows pass through line l) (lps)

Qgen = loads generated within the line.


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Typical values of land-use map and peak factors in developed countries are as follows.


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.


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1. The coefficients of discharge used in the example are as follows:


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(cfs per acre)

Low Density LD .0031

Medium Density MD .0116

High Density HD .0217

Commercial Comm .006

2. Peak(ing) Factors (PF) are shown in the Peak Factor Table

3. Qav flows are accumulated as they become tributary to the line. See Sample Land Use

Map and Sample of Flow Estimating Calculations . Dr. Area 1 average flow is totaledand converted to Qpk in Manhole (MH) A, Dr. Area 2 is added at MH B, Dr. Area 3 is

added at MH C, Dr. Area 4 is added at MH D. Dr. Area 5 is served by a number of house

connection sewers directly tributary to the study sewer all along the Drainage Area. To

simplify calculations the flow from this area has been lumped together and added at onepoint. The point arbitrary selected was MH D so Dr. Areas 4 and 5 are both added at that

point. As each Qav is added to the sum of upstream Qav's the subtotal is converted to

Qpk with the Pf. The Qpk or Qd downstream from MH D in this example is 4.5 cfs.

4. If a larger sewer was being studied, this entire area could be considered one DrainageArea with the same procedures followed to accumulate Qav and then convert to Qpk

using the Peak Factors.

5. If a relief sewer was proposed that would intercept a portion of this Study Area the

average flow from Drainage Areas or parts of Drainage Areas tributary to the new line

would be added to the relief line and subtracted from the existing line. The average flowswould be totaled and converted to Peak using Peak Factors.

6. The estimated Qav and Qpk's are shown on the Sample Land Use Map. The Qav's areshown because they can be easily added and subtracted and are useful when studying

alternate routes, etc. The Qpk's are the quantities to be used to determine the adequacy of

an existing sewer or to design a new one. These Qpk's can also be called Qd.

Example: 2-5 Peak Sanitary Load

A shopping center and a residential area consisting of average and luxury homes load a

gravity sanitary sewer. The shopping center has 100 parking spaces. 80 people live ineach average home, whereas 30 people live in each luxury home. What is the averagebase load contributing to the sanitary sewer at this point? What would be an approximate

peak flow applied to this system? The local ordinance dictates that for all population

based sanitary loads, the peaking factor should be estimated as:

5.0)1000

(0.4

0.140.1

PPF

+

+= .

In addition, a constant peaking factor of 2 should be applied to all non-population-based

loads.


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Solution

First, to get the average base load, find the amount of load per unit for the three loading

categories. In this problem, assume the following [ based on the location of the housing]:

Land-use Type Unit Load

Shopping center 4 l/d-spaceAverage housing 280 l/d-resident

Luxury housing 380 l/d-resident

We then multiply this unit flow by the number of units as follows:

Shopping Center 100x4 = 400 l/dAverage housing 80x280 = 22400 l/d

Luxury housing 30x380 = 11400 l/d

Total = 34200 l/d

PF = 1.0+14/{4+[(80+30)/1000]0.5 }=4.23

By applying this peaking factor to the base loads from the population and then a peaking

factor of 2 to the load from the shopping center, the total peak load can be computed as:

4.23(22400+11400)+2x400 = 144000 l/d

Urban Drainage Notes-CHAPTER 2

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