System components and Design

Lecture Note: Part 2

Solomon Seyoum

1 Design philosophy A general approach to sewer design is illustrated in Figure 1-1 and Figure 1-2 (Butler and JW, 2011). A sewer system is a network of pipes used to convey storm runoff and/or sanitary sewer in a city.

• The design of storm sewer system involves the determination of o diameters, o slopes, and o crown or invert elevations for each pipe in the system.

• Free surface flow exits for the design discharges; o that is, the sewer system is designed for “gravity flow”; o pumping stations and pressurized sewers should be avoided as much as possible.

• The sewers are of commercially available sizes. • The design diameter is the smallest commercially available pipe having flow capacity equal

to or greater than the design discharge and satisfying all the appropriate constraints. • Sewers must be placed at a depth such that they

o will not be susceptible to frost, o will be able to drain basements, and o will have sufficient cushioning to prevent breakage due to ground surface loading. o To these ends, minimum cover depths must be specified.

• The sewers are joined at junctions such that the crown elevation of the upstream sewer is no lower that of the downstream sewer.

• To prevent or reduce excessive deposition of solid material in the sewers, a minimum permissible flow velocity at design discharge or at barely full-pipe gravity flow is specified.

• To prevent scour and other undesirable effects of high-velocity flow, a maximum permissible flow velocity is also specified.

• At any junction or manhole, the downstream sewer cannot be smaller than any of the upstream sewers at that junction.

• The sewer system is a dendritic, or branching, network converging in the downstream direction without closed loops.

Figure 1-1 Urban drainage design procedure

Topographical map Obtain or develop a map of the contributing area. Add location and level of existing or proposed details such as:

• contours • physical features (e.g. rivers) • road layout • buildings • sewers and other services • outfall point (e.g. near lowest point, next to receiving water body).

Preliminary horizontal layout Sketch preliminary system layout (horizontal alignment):

• locate pipes so all potential users can readily connect into the system • try to locate pipes perpendicular to contours • try to follow natural drainage patterns • locate manholes in readily-accessible positions.

• Preliminary sewer sizing • Establish preliminary pipe sizes and gradients.

Preliminary vertical layout • Draw preliminary longitudinal profiles (vertical alignment): • ensure pipes are deep enough so all users can connect into the system • try to locate pipes parallel to the ground surface • ensure pipes arrive above outfall level • avoid pumping if possible.

Revise layout Revise the horizontal and/or vertical alignment to minimise system cost by reducing pipe:

• lengths • sizes • depths.

Figure 1-2 Sewer system design

Design period Select suitable design period:

• population and industrial growth rate

• water consumption growth rate.

Sanitary sewers

Design Storm Select suitable design storm:

• return period • intensity • duration.

Storm sewers

Contributing area Quantify:

• domestic population • unit water consumption • commercial/industrial output • infiltration.

Dry weather flows Select design method. Calculate:

• dry weather flows • peak flow-rates.

Contributing area Quantify:

• catchment area • surface types • imperviousness.

Runoff flows Select design method. Calculate:

• peak flow-rates and/or • hydrographs.

Hydraulic design Establish hydraulic constraints:

• pipe roughness • velocities • depths.

Calculate pipe: • sizes • gradients • depth.

1.1 Design procedure When analyzing the functioning of existing sewer systems or designing sewerage systems for a large urban area, the runoff factor and the wastewater production are related to the unit area and classified into a number of classes (e.g. maximum 5 classes). Accordingly the total urban area is divided into zones in relation to classes of wastewater production and run-off coefficient.

A sewer is divided into a number of sewer sections for the purpose of calculations. The sections are identified by selecting points of calculation. Suitable points are at locations with a big inflow or at a regular distance. A suitable section length is, for example, 300 m for sanitary sewer or 50 m for storm water calculations. The determination of the time of concentration requires short upstream sections due to a rapid increase of the sewer size.

Establishment of design criteria

The following criteria need to be formulated for design of sewer systems:

- peak rates of dry weather flow (wastewater + groundwater infiltration) - heavy producers of wastewater - allowance for illicit rain water connections to sanitary sewers - design storm - runoff factor - drain profiles (and materials) - hydraulic friction constants - minimum slopes of sewers. - outlet levels (maximum water level, invert for storm water)

Dry weather flow - Determine wastewater production rates in l/s/ha

The wastewater production rate can be determined using Table 1. The water consumption relates to the metered consumption that is measured at the house connections thus excluding losses in the water distribution system. The water loss in the table considers piped water used for washing floors and for gardening. The use of private wells may contribute to wastewater production.

Table 1: Wastewater production

District/ Area

Population density

Water consumption

Water loses

Wastewater production

Average Peak factor Maximum p/ha l/p/d l/p/d l/p/d l/s/ha l/s/ha 1 2 3 Total

Heavy producers of wastewater - Determine design flow rate of heavy sewage producers

Wastewater from a laundry, beverage factories, etc. cannot be included on an area basis, because of the large quantities of wastewater produced. These are introduced as single producers (without an area) and indicated as heavy producers.

A laundry operates a number of hours per day. The average flow in l/s being the daily flow divided by the number of working hours is considered when data are not available.

Infiltration to sewer pipes

Sewers laid in groundwater are subject to groundwater infiltration. Sewer pipes with caulked joints primarily transport groundwater, because the (cemented) joints crack. Sewers with rubber ring joints may be completely watertight.

Assume specific rate of groundwater infiltration (in l/s/ ha) for sewers with their invert located below the groundwater table.

Allowance for illicit inflow

Storm water may enter the sanitary sewer system and an allowance should be given for unintended storm water and any other illicit inflow to sanitary sewers. Literature indicates an allowance of 50 to 60% of the pipe capacity. This means that only less than half of the pipe capacity is available for the transport of the peak dry weather flow

Compile available sewer sizes

Indicate what sewer diameters will be used. Give minimum and regular or available pipe sizes.

Storm water quantities

The amount of storm water to be transported is determined with the rational method.

- Indicate what design frequency (return period) is used for the design of storm sewers. - Determine the rainfall intensity - duration curve for the required frequency. - Indicate runoff coefficients

Hydraulic criteria (for storm water and wastewater)

Steady and uniform flow conditions are assumed for the hydraulic design of sewers. Specify flow formulae and friction constants used for the hydraulic design.

Usually the flow formula of Colebrook-White based on a physical mathematical formulation of flow conditions is used for the design of circular conduits:

2.512log 23.712k Dv gDS

D gDSυ

= − +

where: v = velocity of flow (m/s) D = diameter of pipe (m) S = hydraulic gradient (m/m) kinematic viscosity (m2/s) = טk = wall roughness (m)

The kinematic viscosity affects the velocity of flow, only when a laminar boundary layer is present. The kinematic viscosity is determined by temperature:

( )

61.5

497 1042.5T

υ −=+

where: T = temperature in 0C for 10 0C → υ = 1.31 10-6 m2/s; 20 0C → υ = 1.01 10-6

The factor k is a measure of the irregularities of the pipe wall. The value of k is:

Table 2 Wall roughness for different pipe materials Pipe material K (mm) Plastic pipes, PE, PVC 0.02 – 0.05 Concrete, centrifugal manufactured 0.025 Concrete, smooth surface 0.2 – 0.4 Glazed stone ware pipes 0.02 – 0.05 Steel, corroded 1 – 2 Stone masonry 2 – 5 Dry stone masonry 5 – 20 Earth channels, grit transport 1 – 10 Earth channels, bad condition with vegetation 10 – 40

A limited amount of sediment will be deposited on the bottom of sewers. Therefore, the following values are used for sewerage:

- street sewers k = 1.5 mm - pumping mains k = 0.4 mm (no house connections and branch sewers)

Non-circular profiles (open channels, box profiles) are designed with the Manning formula or any other experimental formula.

Manning: 2 3 1 21v R Sn

=

where: n is roughness factor

The recommended roughness values for some conduit materials are given below.

Table 3 Recommended values of wall roughness Type of conduit White-Colebrook (mm) Manning (m1/3/s) Street sewers, storm water culverts, properly constructed 1.5 0.013 Old sewers and concrete culverts 0.017 main sewers 1.0 0.0125 pumping lines 0.4 0.011

Hydraulic performance of pipes - Determine the hydraulic performance of selected profiles

Circular conduits are preferably calculated with the formula of Colebrook-White with a wall roughness of k = 1.5 mm by using tables for the hydraulic calculation of pipes.

Establish partial flow diagrams if necessary

Partially filled sewers are calculated by using partial flow diagrams and tables indicating the relation between water depth, velocity of flow and rate of flow.

Partially filled pipes act as open channels; the hydraulic characteristics are similar, but the velocity of flow is reduced by increased air friction in the pipe with increased water level, particularly near the top of the pipe. Partial floe diagram for circular pipes is shown in Figure 1-3.

Figure 1-3 Partial flow diagram of circular pipes

Partial flow diagrams can be developed using the following relationships.

Figure 1-4 Partially full circular pipe

For the partial full pipe cross section shown in Figure 1-4 the top width, wetted are, wetted perimeter and hydraulic radius can be expresses in terms of θ as follow;

sinT D θ=

( )1 cos2Dy θ= −

P Dθ=

( )2

2 sin 28

DA θ θ= −

sin 214 2hDR θ

θ = −

From these relationships you can develop a partial flow diagram.

Pariah flow diagrams or tables can also be developed using the formula of Colebrook-White. Hydraulic characteristics of circular sewers flowing partly full are given in Table 4 based on Colebrook-White formula for pipe roughness k=1.5mm and water temperature T 25oC.

Minimum slopes of sewers

Sanitary sewers must be designed so that sediment does not accumulate during periods of low flow without providing some period with enough flow to clean out the pipes. To assure that sewers will carry suspended sediment, two approaches have been used:

- the minimum (or self-cleansing) velocity and - the minimum boundary shear stress method, also called the “tractive force”

The traditional approach to self-cleansing is to require a full-pipe velocity of at least 0.6 m/s. This approach has proven adequate to avoid serious sediment buildup in most sewer lines, but it does not address self-cleansing as accurately as does the tractive force method.

Tractive Tension

The component of the gravitational force parallel to the axis of the pipe per unit boundary area is known as the tractive tension, tractive force, or boundary shear stress

Figure 1-5 Tractive tension in a circular sewer

Tractive Tension

sin sin sinhW gaL gR

pL pL

Where W is weight of water, ρ is density of water, g is gravitational acceleration, L is length of conduit, p is wetted perimeter and Rh is hydraulic radius.

When θ is small, it is approximately equal to the slope, S,

hgR s

The equations for tractive tension can be rearranged to give the minimum slope for any tractive tension and flow rate.

h

sgR

If a minimum velocity is considered for the determination of minimum grades of sewers Manning’s formula could be used.

2min

min 4 3

*S =

n vR

To determine the minimum tractive force, usually a sieve analysis is performed mechanically. From the amounts retained on each sieve, the cumulative amounts retained on each sieve are calculated for the compilation of a cumulative frequency distribution curve.

Figure 1-6 Sediment distribution curve

It is assumed that 90% or 95% of the material should be transported to limit maintenance cost of sewers. When the available gradient is not sufficient to create self-cleansing, open drains and canals should be considered to facilitate maintenance work.

The filling rate of a sewer is an important consideration for the determination of minimum sewer slopes, because sewers are seldom running full. The capacity of storm drains and combined sewers for residential areas are designed on a rainfall occurrence of once per year and sanitary sewers on 40% or 50% running full. The filling rate to be considered for the determination of minimum slopes is as follows:

Storm drains:

Erosion will be neglect able at times of small rainfalls. The amount of erosion is determined by the intensity of rainfalls. A filling rate of 10 to 20 % related to the pipe capacity should be acceptable for the design of storm water drains: Q : Qf = 0.20

Sanitary sewers:

The minimum flow at night, which is about two-third of the average flow, will carry a neglect able amount of grit. Average flow conditions should, therefore, be considered for the determination of minimum sewer gradients. Only 40% to 50% of the pipe capacity should be utilized to carry the peak flow as mentioned before.

The required minimum tractive force of the flow should be larger than the resistance of the sediments (τmin) or the critical tractive force which is given by the following formula;

min ( )g wfgdτ ρ ρ= −

where d = selected specific diameter of sediment (grit) (from the sieve analysis) f = a constant called Shields parameter, for sewers f=0.056

Usually minimum tractive forces are specified based on experience and it varies from place to place. For example in the Netherlands, a minimum tractive force of 1.25N/m2 is considered which is equal to 0.6N/m2 at filling rate of 10%. Example: Determine the minimum slope of a 250mm diameter pipe to transport sediments specific grit diameter of 1mm at filling rate of 10%. Solution:

The critical tractive force is min ( )g wfgdτ ρ ρ= −

2min 0.06*9.81*0.001*(2650 1000) 0.97 N mτ = − =

0.97 is less than 1.25 (the minimum tractive force) so we use the minimum tractive force.

The minimum slope is given by h

sgR

For a diameter of 250mm and filling rate of 10%, we can get the hydraulic radius of the partial flow (R) form the partial flow diagram or table. R = 0.1265*D = 0.1265*0.25 =0.0316m

1.25 0.004

1000*9.81*0.0316h

sgR

Require minim slope is 4‰.

Criteria for the discharge of storm water

Give other relevant criteria, for example maximum discharge levels. The water level of the receiving water body (sea, river, lake) varies. The maximum discharge level for drainage outlet has to be given. Free outfall may not be always possible. In this case an outlet sewer may be submerged. If the sewer is submerged, the capacity is determined based on outlet water level of the receiving water.

Figure 1-7 Submerged sewer outfall (outlet)

1.2 Design Procedure for storm sewers The design of storm drains can be accomplished by using the following steps and the computation table provided in Table 4.

Step 1. Prepare a working plan layout and profile of the drainage system establishing the

following design information: a. Location of drain pipes. b. Direction of Flow. c. Location of manholes and other structures. d. Number or label assigned to each structure. e. Location of all existing utilities (water, sewer, gas, underground cables,

etc.).

Step 2. Determine the following hydrologic parameters for the drainage areas to each inlet to the storm drainage system:

a. Drainage areas. b. Runoff coefficients c. Travel time

Step 3. Using the information generated in Steps 1 and 2, complete the following

information on the design form for each run of pipe starting with the upstream most storm drain run:

a. "From" and "To" stations, Columns 1 and 2 b. "Length" of run, Column 3 c. "Inc." drainage area, Column 4

The incremental drainage area tributary to the inlet at the upstream end of the storm drain run under consideration.

d. "C," Column 5

The runoff coefficient for the drainage area tributary to the inlet at the upstream end of the storm drain run under consideration. In some cases a composite runoff coefficient will need to be computed.

e. "INC." area x "C," Column 6

Multiply the drainage area in Column 4 by the runoff coefficient in Column 5. Put the product, CA, in Column 6.

f. "TOTAL" area, Column 7

Add the reduced incremental area in Column 6 to the previous sections total area and place this value in Column 7.

g. "System" time of concentration, Column 10

The time for water to travel from the most remote point in the storm drainage system to the upstream end of the storm drain run under consideration. For the upstream most storm drain run this value will be the same as the "Inlet" time of concentration. For all other pipe runs this value is computed by adding the "System" time of concentration (Column 8) and the "Section" time of concentration (Column 26) from the previous run together to get the system time of concentration at the upstream end of the section under consideration.

Step 4. Using the information from Step 3, compute the following: a. "i," Column 9

Using the times of concentration in Columns 8, and an Intensity-Duration-Frequency (IDF) curve, determine the rainfall intensity, i, and place this value in Column 9.

b. "TOTAL Q," Column 10

Calculate the discharge as the product of Columns 7 and 9. Place this value in Column 10.

c. Ground surface elevation, Column 11 and 12

Indicate the ground surface elevation for the upper and lower end of the pipe run under consideration.

d. Invert level, Column 13 and 14

Indicate the invert level for the upper and lower end of the pipe run under consideration.

e. "SLOPE," Column 15

Place the pipe slope value in Column 15. Minimum slopes requirement based on tractive force or self-cleansing velocity will be considered except for pipes with a steeper ground slope.

f. "PIPE DIA.," Column 16

Size the pipe using minimum required slope. In preparing design criteria at the first step, table of minimum required slopes for each pipe size should be compiled.

g. "CAPACITY FULL," Column 17

Compute the full Flow capacity of the selected pipe using Manning equation or other appropriate formula and place this value in Column 17.

h. "VELOCITY," Columns 18

Compute the full Flow velocity in the conduit and place the value in Columns 18. The velocity and flow rate when flowing full are computed using the appropriate formula if the slope is greater than the minimum required or from a table compiled for minimum slopes for sewers at minimum gradients for the minimum possible gradient.

i. "Partial FLOW," Columns 19

Compute the ratio between storm flow in column 10 and the sewer capacity in column 17 and place this value in Column 19. This ratio determines the partial flow velocity in column 20 by using partial flow diagrams.

j. "Partial FLOW Velocity" Columns 20

From partial flow diagram determine the partial flow velocity for the partial flow to full flow ratio computed in column 19 and place this value in Column 20.

k. Backwater flow check, column 21-24

Backflow conditions must be checked, if applicable. A backflow arises when the calculated water level at the downstream end is below the required discharge level (below the water level of the receiving water body). The available hydraulic gradient is accordingly determined. The calculation procedure is accordingly as follows:

First design the sewer system and carry out the calculations of the storm flow with the rational method. The hydraulic calculations of the respective sewer sections were performed in the direction of the flows.

When a backflow arises, proceed with determination of hydraulic gradient and water levels against the direction of the flow, because the water levels are determined by the downstream water levels.

If necessary, a larger size of conduit is selected to accommodate the flow at the available hydraulic gradient.

Piezometric flow conditions will occur in underground drains. The hydraulic gradient is determined by the flow and size of conduit. The (piezometric) water levels are accordingly calculated which again are determined by the downstream water levels.

l. "Flow TIME," Column 25

Calculate the travel time in the pipe section by dividing the pipe length (Column 3) by the design Flow velocity (Column 20). Place this value in Column 25.

m. "Section time of concentration," Column 26

Calculate the section time of concentration by adding inlet time to flow travel time in column 25. Place this value in Column 26. Correct calculations, if necessary. If the time concentration in column 26 is different from the assumed time of concentration in column 8,repeat calculations starting from updating column 8 with new time of concentration.

1.3 Design Procedure for sanitary sewers The design of sanitary sewers can be accomplished by using the following steps and the computation table provided in Table 5.

Step 1. Prepare a working plan layout and profile of the drainage system establishing the following design information:

a. Location of drain pipes. b. Direction of Flow. c. Location of manholes and other structures. d. Number or label assigned to each structure. e. Location of all existing utilities (water, sewer, gas, underground cables,

etc.).

Step 2. Determine the following the following parameters for the drainage areas to each inlet to the sanitary sewer system:

a. domestic population b. unit water consumption c. commercial/industrial output (heavy producers) d. peaking factors e. infiltration

Step 3. Using the information generated in Steps 1 and 2, complete the following information on the design form for each run of pipe starting with the upstream most sanitary sewer run:

a. "From" and "To" stations, Columns 1 and 2 b. "Length" of run, Column 3 c. "Inc." drainage area, Column 4

The incremental drainage area to the inlet at the upstream end of the sewer run under consideration.

d. "Cumulative area," Column 5

The cumulative drainage area to the inlet at the upstream end of the sewer run under consideration.

e. Rate of peak wastewater flow per area, Column 6 f. Incremental wastewater flow, Column 7

Multiply incremental area in column 4 by flow rate in column 6. Place this value in Column 7.

g. Cumulative wastewater, Column 8

Calculate cumulative wastewater flow rate.

h. Cumulative wastewater, Column 9 and 10

Determine incremental and cumulative infiltration. Infiltration rate can be specified as a design criteria.

i. Total peak dry weather flow, Column 11

This is the sum of column 8 and 10.

Step 4. Using the information from Step 3, compute the following: a. Ground surface elevation, Column 12 and 13

Indicate the ground surface elevation for the upper and lower end of the pipe run under consideration.

b. Invert level, Column 14 and 15

Indicate the invert level for the upper and lower end of the pipe run under consideration.

c. "SLOPE," Column 16

Place the pipe slope value in Column 16. Minimum slopes requirement based on tractive force or self-cleansing velocity will be considered except for pipes with a steeper ground slope.

d. "PIPE DIA.," Column 17

Size the pipe using minimum required slope. In preparing design criteria at the first step, table of minimum required slopes for each pipe size should be compiled.

e. "CAPACITY FULL," Column 18

Compute the full Flow capacity of the selected pipe using Manning equation or other appropriate formula and place this value in Column 17.

f. "VELOCITY," Columns 19

Compute the full Flow velocity in the conduit and place the value in Columns 18. The velocity and flow rate when flowing full are computed using the appropriate formula or from a table compiled for minimum slopes for sewers at minimum gradients.

g. "Partial FLOW," Columns 20

Compute the ratio between storm flow in column 10 and the sewer capacity in column 17 and place this value in Column 19. This ratio determines the partial flow velocity in column 20 by using partial flow diagrams.

h. "Partial FLOW Velocity" Columns 21

From partial flow diagram determine the partial flow velocity for the partial flow to full flow ratio computed in column 19 and place this value in Column 20.

Table 4: Hydraulic characteristics for circular sewers, flowing partly full based on the flow formula of Colebrook-White and considering air friction for wall roughness k=1.5mm and water temperature T=25oC.

Q/Qfull h/D V/Vfull R/D B/D Q/Qfull h/D V/Vfull R/D B/D 0.001 0.023 0.17 0.0152 0.2998 0.41 0.445 0.95 0.2313 0.9939 0.002 0.032 0.21 0.021 0.352 0.42 0.451 0.96 0.2334 0.9952 0.005 0.049 0.28 0.0319 0.4317 0.43 0.458 0.96 0.2359 0.9965

0.01 0.068 0.34 0.0439 0.5035 0.44 0.464 0.97 0.238 0.9974 0.015 0.083 0.38 0.0532 0.5518 0.45 0.47 0.97 0.2401 0.9982

0.02 0.095 0.41 0.0605 0.5864 0.46 0.476 0.98 0.242 0.9988 0.03 0.116 0.46 0.0731 0.6404 0.47 0.462 0.99 0.2441 0.9994 0.04 0.134 0.5 0.0837 0.6813 0.48 0.488 0.99 0.2461 0.9997 0.05 0.149 0.54 0.0923 0.7122 0.49 0.494 1 0.2481 0.9999 0.06 0.163 0.57 0.1002 0.7387 0.5 0.5 1 0.25 1 0.07 0.176 0.59 0.1075 0.7616 0.51 0.506 1 0.2519 0.9999 0.08 0.188 0.61 0.1141 0.7814 0.52 0.512 1.01 0.2538 0.9997 0.09 0.2 0.63 0.1206 0.8 0.53 0.519 1.01 0.2559 0.9993

0.1 0.211 0.65 0.1265 0.816 0.54 0.525 1.02 0.2577 0.9987 0.11 0.221 0.67 0.1317 0.8289 0.55 0.531 1.02 0.2595 0.9981 0.12 0.231 0.69 0.1369 0.8429 0.56 0.537 1.02 0.2612 0.9973 0.13 0.241 0.7 0.1421 0.8554 0.57 0.543 1.03 0.2629 0.9963 0.14 0.25 0.72 0.1466 0.866 0.58 0.55 1.03 0.2649 0.995 0.15 0.259 0.73 0.1511 0.8762 0.59 0.556 1.03 0.2665 0.9937 0.16 0.268 0.74 0.1556 0.8858 0.6 0.562 1.04 0.2681 0.9923 0.17 0.276 0.76 0.1595 0.894 0.62 0.575 1.04 0.2715 0.9987 0.18 0.285 0.77 0.1638 0.9028 0.64 0.587 1.05 0.2745 0.9847 0.19 293 0.78 0.1676 0.9103 0.65 0.594 1.05 0.2762 0.9822

0.2 0.301 0.79 0.1714 0.9174 0.66 0.6 1.05 0.2776 0.9798 0.21 0.309 0.8 0.1751 0.9242 0.68 0.613 1.06 0.2806 0.9741 0.22 0.316 0.81 0.1784 0.9298 0.7 0.626 1.06 0.2834 0.9677 0.23 0.324 0.82 0.182 0.936 0.72 0.64 1.07 0.2862 0.96 0.24 0.331 0.83 0.1851 0.9411 0.74 0.653 1.07 0.2887 0.952 0.25 0.339 0.84 0.1887 0.9465 0.75 0.66 1.07 0.29 0.9474 0.26 0.346 0.85 0.1918 0.9514 0.76 0.667 1.07 0.2912 0.9426 0.27 0.353 0.86 0.1948 0.9558 0.78 0.682 1.07 0.2936 0.9314 0.28 0.36 0.86 0.1978 0.96 0.8 0.697 1.07 0.2958 0.9191 0.29 0.367 0.87 0.2007 0.964 0.82 0.713 1.08 0.2979 0.9047

0.3 0.374 0.88 0.2037 0.9677 0.84 0.729 1.07 0.2997 0.889 0.31 0.381 0.89 0.2066 0.9713 0.85 0.738 1.07 0.3006 0.8794 0.32 0.387 0.89 0.209 0.9741 0.86 0.747 1.07 0.3014 0.8695 0.33 0.394 0.9 0.2118 0.9773 0.88 0.766 1.07 0.3028 0.8467 0.34 0.401 0.91 0.2146 0.9802 0.9 0.786 1.07 0.3038 0.8203 0.35 0.407 0.92 0.217 0.9802 0.92 0.808 1.06 0.3043 0.7877 0.36 0.414 0.92 0.2197 0.9851 0.94 0.834 1.05 0.304 0.7442 0.37 0.42 0.93 0.222 0.9871 0.95 0.849 1.05 0.3033 0.7161 0.38 0.426 0.93 0.2243 0.989 0.96 0.865 1.04 0.3022 0.6834 0.39 0.433 0.94 0.2269 0.991 0.98 0.905 1.03 0.2972 0.5864

0.4 0.439 0.95 0.2291 0.9925 1 1 1 0.25 0

Table 5: Design computation table for design of storm sewers

Section Rainfall - Runoff Pipe Characteristics Flow Conditions (Storm flow)

Remarks

from to

Leng

th

Drainage Area

Sys

tem tim

e of c

once

ntrati

on t c

Ave

rage

rainf

all in

tensit

y

Flow Elevation

Slop

e of s

ewer

Pro

file &

size

Drain full Partially

filled Piezometric Flow time

In

creme

nt ar

ea A

Run

-off c

oeffic

ient C

Red

uced

Incre

ment

Area

Ar =

C*A

Cum

ulativ

e Red

uced

Ar

ea Σ

Ar

Q r =

CiA

Ground surface Invert

Cap

acity

Qo

Velo

city V

o

Q st /

Q o

Velo

city

Hyd

rauli

c gra

dient

Water level

Velo

city v

Tra

vel ti

me t =

L/v

Sys

tem tim

e of

conc

entra

tion

Uppe

r end

Lowe

r end

Uppe

r end

Lowe

r end

Uppe

r end

Lowe

r end

No No m ha ha ha min mm/hr m3/s m m m m o/oo m m3/s m/s % o/oo m m m/s min min

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Table 6: Design computation table for design of sanitary sewers

Section Dry Weather Flow Pipe Characteristics Remarks

from to Le

ngth

Drainage Area Peak domestic wastewater Infiltration Peak flow Elevation

Slop

e of s

ewer

Pro

file &

size

Drain full Partially filled

Incre

ment

area

A

cumu

lative

area

Σ A

Rate

, qs

Incre

menta

l qs*A

Cumu

lative

Σ q s

A

Incre

menta

l

total

Ground surface Invert

Cap

acity

Qo

Velo

city V

o

Q st /

Q o

Velo

city

Uppe

r end

Lowe

r end

Uppe

r end

Lowe

r end

No No m ha ha m3/s ha m3/s m3/s m m m m o/oo m m3/s m/s % 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Figure 1-8 Sewer scheme with details of hydraulic calculation

Design Example:

Design the sewerage network shown in Figure 1-8 for a rain fall intensity of 1 year return period given by the following equation. Use inlet time of 5 min and minimum concentration time of 10 min. The design criteria are given in Table 7.

0.708

195it

= where I is in mm/hr and t is in minutes.

The runoff coefficient classes are as follows;

Class Runoff coefficient C A 0.10 B 0.35 C 0.65 D 0.85

Table 7 Design criteria

Diameter Minimum slope ‰

Full capacity

Flow (m3/s)

Velocity (m/s)

0.25 4.0 0.038 0 78 0.30 3.3 0.056 0.79 0.40 2.5 0.105 0.83 0.50 2.0 0.169 0.86 0.60 1.7 0.252 0.89 0.70 1.4 0.343 0.89 0.80 1.25 0.461 0.92 0.90 1.11 0.595 0.93 1.00 1.00 0.741 0.94

The Design of the sewer network is completed using the calculation sheet and the results is provided in the two table below.

Design example calculation sheet: Column 1to 14

from to

Leng

th

Drainage Area

Syste

m tim

e of

conc

entra

tion t

c

Aver

age r

ainfal

l inten

sity Flow Elevation

Incre

ment

area

A

Run-

off co

effici

ent C

Redu

ced I

ncre

ment

Area

Ar =

C*A

Cumu

lative

Re

duce

d A

rea Σ

Ar

Q r =

CiA

/360

Ground surface Invert

Uppe

r end

Lowe

r end

Uppe

r end

Lowe

r end

No No m ha ha ha min mm/hr m3/s m m m m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1 2 100 1.500 0.650 0.975 0.975 <10 38.200 0.103 10.000 9.800 8.600 8.350 2 3 100 1.000 0.650 0.650 1.625 <10 38.200 0.172 9.800 9.000 8.350 7.500 3 4 100 0.880 0.650 0.572 2.197 10.000 38.200 0.233 9.000 9.000 7.400 7.230 7 8 100 1.500 0.350 0.525 0.525 <10 38.200 0.056 9.300 9.100 7.900 7.650 8 4 100 0.750 0.650 0.488 1.013 <10 38.200 0.107 9.100 9.000 7.650 7.330 4 5 100 0.620 0.850 0.527 3.737 12.000 33.600 0.349 9.000 9.200 7.030 6.900 9 10 100 1.500 0.350 0.525 0.525 <10 38.200 0.056 9.200 8.800 7.900 7.570

10 5 100 0.880 0.850 0.748 1.273 <10 38.200 0.135 8.800 9.200 7.370 7.170 5 6 100 0.750 0.850 0.638 5.647 12.000 33.600 0.527 9.200 9.000 6.800 6.690

11 12 100 1.500 0.100 0.150 0.150 <10 38.200 0.016 9.800 8.700 7.550 7.150 12 6 100 0.750 0.350 0.263 0.413 <10 38.200 0.044 8.700 9.000 7.100 6.770 6 13 50 0.380 0.350 0.133 6.193 13.000 31.700 0.545 9.000 9.000 6.170 6.100

Design example calculation sheet: Column 15to 26 S

lope o

f sew

er

Pro

file &

size

Drain full Partially filled Piezometric Flow time

Cap

acity

Qo

Velo

city V

o

Qst /

Qo

Velo

city

Hyd

rauli

c gra

dient Water level

Velo

city v

Tra

vel ti

me t =

L/v

Sys

tem tim

e of

conc

entra

tion

Upp

er en

d

Lowe

r end

o/oo m m3/s m/s o/oo m m m/s min min

15 16 17 18 19 20 21 22 23 24 25 26 2.500 0.400 0.105 0.834 0.985 0.859 116.440 416.440 6.941 8.500 0.400 0.194 1.542 0.890 1.650 60.613 477.053 7.951 1.700 0.600 0.252 0.892 0.924 0.980 102.057 579.110 9.652

2.500 0.400 0.105 0.834 0.532 0.842 118.746 418.746 6.979 3.200 0.400 0.119 0.944 0.906 1.010 99.000 517.746 8.629 1.300 0.800 0.471 0.936 0.741 1.002 99.804 617.550 10.293

3.300 0.300 0.056 0.795 0.992 0.795 125.823 425.823 7.097 2.000 0.500 0.169 0.861 0.799 0.921 108.553 534.376 8.906 1.100 0.900 0.590 0.928 0.893 0.993 100.735 635.111 10.585

4.000 0.250 0.038 0.777 0.418 0.769 130.065 430.065 7.168 3.300 0.300 0.056 0.795 0.779 0.850 117.592 547.657 9.128

1.400 0.900 0.666 1.047 0.818 1.131 44.205 591.861 9.864

Reference

Butler, D., and JW, D. (2011), Urban Drainage, Taylor & Francis.