CHAPTER 3
THEORIES AND CALCULATIONS
3.1 INTRODUCTION This chapter presents the theories and standards that were used to design a sewage and drainage system in general. In Section 3.2, the wastewater flow sewer and drainage being designed is described. The Colebrook-White equation for the velocity of flow in a sewer is presented in Section 3.3. The design limitations of the sewerage system such as depth of flow, pipe gradients, pipe depths, pipe sizes and manholes are given in Section 3.4. Finally, Section 3.5 sets out the detailed sewerage design process, from the decision to adopt a sewerage system to the development of the overall sewerage layout whiles ample of calculations for the detailed design for sewers is represented in Section 3.6.
3.2 WASTEWATER FLOW This project involves two systems, a sewage system and drainage systems. The sewer system is designed to convey the wastewater from workshops, commercial establishments and industries, while the drainage system discharges the excess surface water from streets and roofs of buildings.
3.2.1 Sewage Wastewater Flow The flow rate of the wastewater flow used for the design of the main trunk sewer was based on the water consumption and the population according to the Abu-Dhabi Design Manual, 2000. This can be estimated as follows:
Q A.P.F Population Water Consumption (3.1)
Where: Q = wastewater flow (L/day) A.P.F = Abu-Dhabi Peaking Factor.
In this project, a water consumption figure of 280 (Lpcd) was used for the year 2020 based on Abu-Dhabi Design Manual, 2000.
The peaking factor was applied to all sewage flows to identify required pipe and pump station sizes. The Abu-Dhabi peaking factor (APF) is a variation of the Babbit formula. The formulation for Abu-Dhabi is:
population APF(Abu Dhabi Peaking Factor) 4.25 1000
16
(3.2)
The APF is used to project maximum sewage flows from a tributary area. The tributary area should include a contributing population equal to or greater than 500 persons. For tributary populations with fewer than 500 persons, an alternative method of estimating peak flows should be used.
3.2.2 Population Survey
A population survey is essential for sewer design, in order to come up with a sufficient peaking factor for acceptable design in real life; also to achieve the purpose of sewerage system, the design should use reasonable data relating to existing or expected population in the future. The survey is a collection of building types because the population intensity differs from one type to another. The number of floors also increases the population intensity.
The Population survey was determined through several site visits to observe the population at a certain factory or block. Then a suitable factor was obtained according to the population per square meter. Each area was multiplied by that factor to obtain the population for different blocks.
3.2.3 Drainage Wastewater Flow The actual amount of runoff flow can be determined by using the Rational method (Steel and McGhee, 1979). This can be estimated as follows:
Q 240 C I A (3.3)
Where: Q = peak runoff rate (m3/day) C = runoff coefficient (dimensionless) I = average rainfall intensity (mm/hr) A = drainage area (ha)
The rainfall intensities for different durations and return period storms for Abu-Dhabi are presented in Table 3.1 (Abu-Dhabi Design Manual, 2000). In this project, the return period is 5 years will be adapted and the storm duration is 2 hr, giving 16.35 mm/hr of rainfall intensity, whereas in Table 3.2, typical runoff coefficients for areas of various characteristics are given (Abu-Dhabi Design Manual, 2000).
Runoff coefficients to be used with design storms to estimate storm water runoff volumes. These coefficients are established on a sit-specific basis to reflect actual catchment characteristics. In this project, the runoff coefficient used in designing the storm water is 0.6. Table 3.1 Rainfall Intensity Duration Frequency Return Period 1000 Year 200 Year 100 Year 75 Year 40 Year 20 Year 10 Year 5 Year 2 Year
Intensity (mm/hr) by Duration (hr) 0.5 103.44 83.78 75.30 71.77 64.03 55.41 46.63 37.48 23.65
1.0 70.99 57.81 52.12 49.75 44.56 38.78 32.89 26.75 17.48
1.5 52.40 42.73 38.56 36.82 33.01 28.78 24.46 19.96 13.16
2.0 43.63 35.50 31.99 30.53 27.33 23.77 20.14 16.35 10.64
2.5 34.90 28.40 25.59 24.43 21.87 19.02 16.11 13.08 8.51
6 20.51 16.43 14.66 13.93 12.32 10.53 8.71 6.81 3.94
24 7.62 6.12 5.48 5.21 4.62 3.97 3.30 2.61 1.56
Table 3.2 Typical Runoff Coefficients Area Description Coefficient Categories by surface Brick Concrete and Asphalt Sandy Soil Categories by use Cemeteries, Parks and Playgrounds
0.70 – 0.85 0.70 – 0.95 0.05 – 0.20 0.10 – 0.25
Business districts 0.70 – 0.95 Residential Apartments 0.50 – 0.70 Industrial Light 0.50 – 0.80 Heavy 0.60 – 0.90 Note that for preliminary calculation of runoff, these coefficients are consistent with those used with the Rational method for estimating runoff.
3.3 VELOCITY OF FLOW 3.3.1 Colebrook-White Equation Throughout this project, the Colebrook-White equation will be used to determine the velocity of the calculated flows presented previously in section 3.2, either for sewer flows or drainage flow. This can be estimated as follows:
2.51 ν Κs V 2gDS log 2gDS D 3.7D (3. 4)
Where:
V = velocity of flow at d/D (m/s) g = gravitational acceleration (m/s2) D = pipe diameter (mm) S = hydraulic gradient, (mm/mm) (Invert slope for full pipes, water surface slopes for open channels, 1m/1000m)
ks = linear measure of effective roughness (mm) ν = kinematics viscosity of fluid (m2/s)
The roughness coefficient is a measure of the variation and magnitude of protuberances on the interior surface of the pipe. The roughness, therefore, is a function of the pipe material, age and condition. Typical coefficients for the various pipe materials are given in Table 3.3 (Abu-Dhabi Design Manual, 2000). Note that poor sewer pipe conditions are to be assumed for Abu-Dhabi system designs (Ks=1.5) where drainage design should be based on (Ks=0.6) assuming asbestoscement pipes.
Table 3.3 Typical Roughness Coefficients For Pipes
Pipe Material UPVC GRP Coated Cast Iron Uncoated Cast Iron Ductile Iron Asbestos cement Vitrified Clay Concrete
Colebrook-White, Ks (mm) Good Normal Poor 0.3 0.6 1.5 0.3 0.6 1.5 0.09 0.15 0.3 0.15 0.3 0.6 0.15 0.3 0.6 0.15 0.3 0.6 0.3 0.6 1.5 0.15 0.3 0.6
3.3.2 Minimum and Maximum Flow Velocities Design flow velocities should be within the limits presented in Tables 3.4 and 3.5 (Abu-Dhabi Design Manual, 2000). Minimum velocities are based on providing selfcleansing velocities and preventing solids sedimentation in the sewer and drainage pipes.
Maximum velocities are set to prevent manhole corrosion and minimize sewer gases in the sewer system and minimize the negative effects of abrasion on the drainage pipes and manholes.
Table 3.4 Maximum and Minimum Velocities in Sewers. Pipe Description Gravity line Pressure Line
Minimum (m/s) 0.6 1.0
Maximum (m/s) 2.5 3.0
Design (m/s) 0.75 1.5
Table 3.5 Maximum and Minimum Velocities in Drainage. Pipe Description Gravity line Pressure Line
Minimum (m/s) 0.75 1.0
Maximum (m/s) 2.5 3.0
Design (m/s) 0.75 1.0
3.4 DESIGN LIMITATIONS OF THE SEWERAGE SYSTEM 3.4.1 Depth of Flow The design criteria for depth of flow in sewer lines are presented in Table 3.6 (AbuDhabi Design Manual, 2000). Sanitary sewers should be checked for percentage full at all times.
Table 3.6 Maximum Pipe Percentages Full in Sewer Pipes. Pipe Description Maximum d/D Minimum d/D Trunk sewer lines 0.75 0.50 Main and lateral sewer lines 0.85 0.50 d/D is ratio of flow depth to (d) nominal pipe diameter (D).
3.4.2 Pipes Depths
The minimum depth for sewer and drainage pipes in Abu-Dhabi is 1.2 m to the crown of the sewer pipe. This is to provide pipe protection from external loads. If circumstances require installation of a pipe with a depth of less than 1.2 m above the crown, then concrete protection is required. The maximum depth to invert is based on maintaining a cost-effective and safe design.
The recommended maximum cover for Abu-Dhabi sewer and drainage pipes is approximately 10 m. Depth with cover greater than this should be investigated with pipe manufacturers to identify any special requirements that may be necessary. In this case, the engineer should determine whether or not any additional provisions are required to protect the pipe from soil loads.
3.4.3 Pipes Gradients Pipe gradients, often the same as the hydraulic gradient, directly influence sewer pipe capacity. In order to achieve the required minimum velocity in sewer lines, pipes should be designed by observing the minimum gradients in Table 3.7.
Table 3.7 Minimum Sewer Line Gradients. Minimum Gradient (mm/mm) Sewer Diameter (mm) 200 250 315 400 500 600 700 800 900 1000 1200 and larger
Velocity 0.75 (m/s) 5.00 3.70 2.70 2.00 1.50 1.20 1.00 0.85 0.70 0.60 0.50
Velocity 0.6 (m/s) 3.20 2.40 1.75 1.30 1.00 0.80 0.65 0.55 0.45 0.40 0.35
Minimum gradients based on the Colebrook-White formula
3.4.4 Pipes Sizes The current standard for the minimum size of sewer mains is 200 mm. The minimum pipe size recommended for house connections is 150 mm or 160 mm outside diameter. The minimum pipe size permissible on drainage projects is 250 mm.
One exception is pipe used for land drains. The land drain minimum is 160 mm. However, slotted carrier pipes, serving as both land and carrier drain, must meet the 250 mm minimum.
3.4.5 Manholes Manholes should be of sufficient size to permit access for maintenance activities. In addition, their design and material should be such to guarantee maximum performance for an extended service life.
Note that this project was not deal with designing manholes or studying the manholes criteria. It was just indication of their locations in the system.
3.5 DETAILED DESIGN PROCESS The theories introduced previously allow a sewer system to be analyzed in order that sewer and drainage flows and velocities can be determined. This is only one part of the overall design process. Detailed design requires a combination of hydraulic calculations and the application of standard designs, procedures and details.
A sanitary sewer has two main functions: to convey the designed peak discharge and to transport solids so that deposits are kept to a minimum. It is essential; therefore, that the sanitary sewers have sufficient capacity for the peak flow and that it function at minimum flows without excessive maintenance and generation of odors as well as sufficient velocity of that flow to transport the solids.
Based on the criteria and the design limitation stated previously throughout this chapter, the detailed design procedure is as follows:
1. Label each manhole based on the flow direction. SMH1 and DMH1 are an example of manholes labels where SMH1 refers to sewer manhole No.1 as well as DMH1 refers to drainage manhole No.1 and so on.
2. Determine the cover level (C.L) in m for each manhole from the contours levels shown in Figure 2.1 in Appendix A.
3. Additional depth = 0.2 m is added to the C.L of future pavements or construction in the unpaved areas. Therefore, C.L can be estimated as follows:
C.L G.L 0.2 (4.1)
4. Determine the first manhole invert level (I.L1) in m from the survey study of the location which will be designed, where the second I.L2 will be calculated as follows:
S I.L2 L I.L1 1 1000
(4.2)
Where:
S = pipe gradient (%) L = pipe Length (m) 5. Calculate the depth to invert for each manhole (D.I) as follows:
D.I C.L I.L (4.3)
6. Determine the pipes diameters (proposed), lengths and gradients according to the design limitation based on the Abu-Dhabi Design Manual, 2000.
7. Determine the junction population, the number of persons served for each manhole and the increment population. Note that increment population is an accumulative summation between the junction population and the number of person served for each manhole.
8. Calculate the pecking factor (P.F) using the Babbit formula, Equation (3.2).
9. Calculate the total flow in L/s using Equation (3.1).
10. Calculate the full flow velocity in m/s using Colebrook-White formula, Equation (3.4).
11. Calculate the flow full in L/s based on the velocity calculated in the previous step and the area of the pipe as follows:
Q VA
(4.4)
12. Calculate the ratio between the partial flow (total flow of the pipe) and the full flow of the pipe as follows:
Ratio
QPartial QFull
(4.5)
13. Determine the ratio between the actual velocity and the full velocity of the pipe (V/Vf) and the actual ratio between the flow depth and the pipe diameter (d/D) based on the partial flow to full flow ratio calculated in the previous step. The values of V/Vf and d/D are represented in Table 3.8 in Appendix B (Abu-Dhabi Design Manual, 2000).
14. Find the value of the actual velocity based on the V/Vf. Then compare the actual velocity and the actual d/D with design limits represented in Table 3.4 and Table 3.6 to be sure that the design is acceptable.
All the previous steps are followed in designing sewer pipes, whereas the following steps are required for designing drainage pipes. Steps from 1 to 6 are same as sewer design where the remaining steps are as follows:
7. Determine the catchments area, the junction area for each pipe, the total area and the cumulative catchment areas. Note that total area is the total of the catchments areas and the junction area for each pipe.
8. Determine the rainfall intensity using Table 3.2.
9. Determine the runoff coefficient using Table 3.3.
10. Calculate the runoff flow in m3/s using Rational method, Equation (3.3). Then calculate the accumulative runoff flow.
The remaining steps from 11 to 14 are the same as for sewer design. Note that in step 13 you must use Table 3.9 in Appendix B instead of Table 3.8 for determining the values of V/Vf and actual d/D for drainage pipes.
3.6 SAMPLES OF CALCULATIONS
The following assumptions will be used in both sewer and drainage systems:
D = 400 mm
S=1%
A = 37.5 mm2 (the width of street = 5 m and the length = 7.5 m)
Sample 1: Sewer design calculation from SMH12/8/3 to SMH12/8/3A as shown in Table 5.4.
C.L G.L 0.2
SMH12/8/3 103.9 0.2 104.10m
SMH12/8/3A 103.9 0.2 104.10m
S I.L2 L I.L1 1 1000
1 SMH12/8/3A 100 102.97 1 101.97 m 1000
D.I C.L I.L
SMH12/8/3 104.10 102.07 2.03 m
SMH12/8/38 104.10 101.97 2.13 m
population APF(Abu Dhabi Peaking Factor) 4.25 1000
16
Assuming population intensity is 1000 persons:
16
1000 APF(Abu Dhabi Peaking Factor) 4.25 1000
4.25
Q A.P.F Population Water Consumption
Q 4.25 1
280 13.77 L/s 3600 24 1000
2.51 ν Κs V 2gDS log 2gDS D 3.7D
V 2 9.807 (
400 1 )( ) 1000 1000
1.5 2.51 1.141 105 log 2 9.807 0.4 0.001 3.7 0.4 0.4 0.425 m/s (Downward)
QFULL V A
π QFULL 0.425 1000 (0.4)2 53.41 L/s 4
Ratio
QPartial 13.77 0.26 53 . 41 QFull
From Table 3.8 in Appendix B:
V
0.843
Vf V 0.843 0.425 0.36 m/s d 0.35 D
Comparing the actual velocity and the actual d/D with the design limits presented in Table 3.4 and Table 3.6, we found the following:
V = 0.36 m/s < Vmin = 0.6 m/s.
d/D = 0.35 < d/D min = 0.5
This means that the design is not acceptable. So, the pipe dimensions must be changed, either the pipe diameters or the pipe gradients.
Sample 2: Drainage design calculation from DMH6/18/7/4 to DMH6/18/7/3 as shown in Table 5.5.
C.L G.L 0.2
SMH6/18/7/4 103.5 0.2 103.70 m
SMH6/18/7/3 103.5 0.2 103.70 m
S I.L2 L I.L1 1 1000
1 SMH2 100 102 .5 1 102 .4 m 1000
D.I C.L I.L
DMH6/18/7/4 103.70 102.5 1.2 m
DMH6/18/7/3 103.70 102.4 1.3 m
Q 240 C I A
Q 240 0.6
16.35 x 37.5 24.5 L/s 3600
2.51 ν Κs V 2gDS log 2gDS D 3.7D
V 2 9.807 (
400 1 )( ) 1000 1000
0.6 2.51 1.141 105 log 2 9.807 0.4 0.001 3.7 0.4 0.4 0.425 m/s (Downward)
QFULL V A
π QFULL 0.425 1000 (0.4)2 53.41 L/s 4
Ratio
QPartial 24.5 0.46 53.41 QFull
From Table 3.9 in Appendix B: V
0.9825
Vf V 0.9825 0.425 0.42 m/s d 0.48 D
Comparing the actual velocity and the actual d/D with the design limits presented in Table 3.5 and Table 3.6, we found the following:
V = 0.42 m/s < Vmin = 0.75 m/s.
d/D = 0.48 < d/D min = 0.5
This means that the design is not acceptable. So, the pipe dimensions must be changed, either the pipe diameters or the pipe gradients.
