- Email: [email protected]
A robust computer-aided design package for municipal stormwater drainage networks
Advances in Engineering Software 15 (1992) 43-53
~.~.i. v'~"
A robust computer-aided design package for municipal stormwater drainage networks K.W. Chau Department of Civil & Structural Engineering, Hong Kong Polytechnic, Kowloon, Hong Kong
In this paper a computer model for automation in the design of the municipal stormwater drainage system is developed and rigorously verified. Although the program is tailored for application and use in Hong Kong, it can be readily adapted to other situations. The numerical model, which is designed for use on IBM/PC/XT or PC/AT microcomputers, is written in PASCAL language and is compiled by PC software TURBO PASCAL version 5"0 due to the various advantages of the integrated programming environment supported. The computer-aided design package for flow prediction and drainage design applies the Colebrook Formula and the Rational Method to route pipe flows through tree-type drainage networks. By using the computer package, drainage pipe diameters are adjusted automatically to fulfill the flow criteria, namely, that the pipe capacities are large enough to convey the peak runoffs and that the backwater levels are not higher than the finished levels and hence ensure that flooding will not be resulted at all locations. The monotonous and iterative conventional method for designing municipal stormwater drainage networks can be taken over by this model. During the execution of the user-friendly and easily operated computer program, adequate user oriented information will be furnished. Its verification is effected by application of the program for municipal stormwater drainage design in a typical example.
Key words." computer-aided design, municipal stormwater drainage networks, backwater effect, flood prevention, pipe flow. NOTATION A D g H i K L N Q Qp R
Re
s t tc te
the catchment area in m 2 the diameter of the pipe the gravitational co0stant (= 9.81 m/s 2) the average fall f r o m summit of catchment to the point of design in m / 1 0 0 m the design mean rainfall intensity in m m / h r the runoff coefficient the longest distance on the line of flow to the design point in m number of pairs of values for the least square method peak runoff in litres/s at particular pipe section ( : KiA/3600) pipe capacity (= ~rDZv/4) the residuals in the least square method Reynold's number (= vD/u)
tf v ~ A u
the hydraulic gradient the duration of rainstorm in minutes time of concentration (-- te ÷ tf) the time of entry the time of flow the flow velocity the roughness value of the pipe the Darcy-Weisbach friction factor (= 2gDs/u 2) kinematic viscosity of water
INTRODUCTION The aims of modern municipal stormwater drainage networks are to prevent significant damage to life and property arising from surface runoffs as outcomes of any rainstorms and, at the same time, to be able to commission and operate against any worst foreseeable stormwater runoff of a designed return period, with a view to ensuring that a greater runoff event will not incur during the design life of the infrastructure.
Advances in Engineering Software 0965-9978/92/$05.00 © 1992 Elsevier Science Publishers Ltd. 43
44
K. W. Chau
The conventional design of stormwater drainage systems is effected by referring to design charts. ~ In the process, the pipe diameters are required to be adjusted by trial and error and hence enormously laborious work is usually entailed. Moreover, mistakes are easily incurred in the time consuming procedure. As such, there is a necessity to develop a user-friendly computer model coupled with automation of the design process in order to avoid the troublesome manual computations and to design the municipal drainage networks speedily as well as precisely. The program for municipal stormwater drainage design is written in T U R B O PASCAL language version 5.0, 2 for use on personal computers which are readily available in design offices. The mathematical model is developed to serve the purpose of systematic hydraulic design of the pipe sizes of a new drainage system, or of extensions and modifications to an existing drainage system, with prescribed design inflows. By using the computer package, drainage pipe diameters are adjusted automatically to fulfill the flow criteria, namely, that the pipe capacities are large enough to convey the peak runoffs and that the backwater levels are not higher than the finished levels and hence ensure that flooding will not be resulted at all times. Furthermore, the maximum actual flow velocities are limited to be not greater than 4m/s. The computer program will automatically adjust pipe diameters to appropriate magnitudes attaining the above criteria and hence any arbitrary pipe diameter can be initially assumed. During the execution of the user-friendly and easily operated computer program, adequate user oriented information will be furnished. The verification of the model is effected by subjecting it to application in a typical urban drainage system. The rainfall Intensity-Duration-Frequency curves in Hong Kong are approximated and represented by second order polynomial equations based on statistical records. The unknown coefficients of the simulated polynomial equations are computed by the least squares method. Although the computer program is tailored for application in Hong Kong, it can be readily adapted to other situations.
of units that provide many useful procedures and functions. Besides, it comprises a built-in full-screen editor and a debugger that allows any syntax error in the program to be detected easily. 3'4
COMPUTER PACKAGE FOR MUNICIPAL STORMWATER DRAINAGE NETWORK DESIGN
By simply executing the compiled file on the microcomputer, user-friendly and self-explanatory instructions will be displayed for the step-by-step data input procedure. The user may choose either one of the input modes, i.e. the interactive mode or the datafile mode, so that a fresh user can follow the guided instructions in the interactive mode to provide the input data whilst a more experienced user can save time by preparing datafiles directly in the fixed format before execution of the program. The main menu screen for the program and a sub-menu for input of flow line data are shown in Fig. 1 and Fig. 2 respectively. Figure 3 shows the screen during data input of the manhole. Only the commerically available pipe diameters are allowed, i.e. multiple increments of 75 mm from 150 mm to 1200mm and multiple increments of 150mm from 1200 mm to 2100 mm. Any other arbitrary input of pipe diameters not included in the above will prompt an error message 'This pipe size is not used'. The type of bedding required depends on the pipes under fields or under roads while the strength classes required depend on the depth of cover as well as the total design loads on pipes under fields, gardens, lightly trafficked access tracks and main traffic routes. Besides, some default designed values are applied if < E N T E R > is keyed in instead of other numerical values. These include kinematic viscosity of 1.141 x 10-6m2/s, runoff coefficient of 1.0,
COMPUTER-AIDED ~
MUNICIPAL
DESIGN
STORMWATER
PACKAGE
D R.~ AINAGE
FOR
NETWORKS
~
MAIN MENU CREATE A N E W FILE
RATIONALE FOR E M P L O Y I N G T U R B O PASCAL LANGUAGE
READ FROM EXIST FILE MODIFY A RECORD
The programming language PASCAL is used for the engineering program to automate the design of stormwater drainage networks while the compilation of the model is effected through PC software T U R B O PASCAL version 5.0 tailored for use on IBM/PC/XT or PC/AT microcomputers. There are a number of advantages in adopting T U R B O PASCAL as the programming tool. It is a fast, versatile and powerful version of the PASCAL language and possesses a library
PRINT
INPUT D A T A
PRINT O U T P U T D A T A QUIT
USE T ~ ~-- ~
TO SELECT THE OPTION AND PRESS
Fig. 1. Main menu screen of computer-aided design package for municipal stormwater drainage networks.
A robust computer-aided design package for municipal stormwater drainage networks COMPUTER-AIDED DESIGN PACKAGE FOR ~
COMPUTER-AIDED DESIGN PACKAGE FOR
MUNICIPAL STORMWATER DRAINAGE NETWORKS ~
FLOW NO.: _3_ F R O M
~
MUNICIPAL STORMWATER DRAINAGE NETWORKS ~
VALUE OF ROUGHNESS ( m m ) : _ _
MANHOLE OF NO.:3 _ _
TO MANHOLE OF NO.:4 _ _
45
VALUE OF KINEMATIC VISCOSITY(m^s):I.141*IOE-6
RUNOFF COEFFICIENT (I OR 0.8):I__
CATCHMENT AREA (m^2):250
OUTFALL INVERT LEVEL (mP.D.):
LENGTH OF FLOW (m):9~
BACKWATER LEVEL AT OUTFALL (mP.D.):2.5 _ _
DIAMETER OF PIPE (mm):30__0
D E S I G N E D
GRADIENT
NO.
P I P E
(1 IN):357 - -
CLASS: (N, M OR L ) : H
BEDDING: (A OR B):B _ _
RAINSTORM RETURN PERIOD (1-9):__ YEARS
NO.
YEARS
NO.
YEARS
1
2
2
5
3
i0
4
20
5
50
6
lO0
7
200
8
500
9
i 0 0 0
Fig. 2. Sub-menu screen for input of flow line data. existing backwater level at outfall of 2.5 mP.D., etc. The recommended design values of roughness in mm are 0.003, 0"006, 0.015, 0-03, 0.06, 0.15, 0.3, 0"6, 1-5, and 3 which cover a wide range of pipe surface. Figure 4 depicts the screen during data input integrating with some default values. When the program is being executed, the screen, as depicted in Fig. 5, will show the key parameters for that particular step in either one of the following forms: (i)
Flow number, pipe diameter, flow capacity, peak runoff; (ii) Flow number, pipe diameter, actual flow velocity; (iii) Flow number, pipe diameter, backwater level, finished level; depending on which checking step, i.e. capacity checking, velocity checking or backwater calculation, is currently being activated. Besides, in a colour monitor, the above information will be displayed in different colours, namely, the pipe capacity checking will be in white text, the velocity checking will be in blue text while the backwater computation will be in yellow text,
Fig. 4. Screen during data input integrating with some default values. so that a ready distinction of the current status during the program execuation can be reckoned by the user.
ALGORITHM OF MATHEMATICAL MODEL The flow chart of the overall program is depicted in Fig. 6. Computer simulation to conventional manual design of a stormwater drainage network in Hong Kong is implemented through the following design procedure. A plan of the area under consideration is divided into the natural and developed catchments and the routing of the pipelines is laid out. Each manhole is then numbered in a definite order: a) upstream manhole at the main branch; b) downstream manhole at the main branch; c) upstream manhole at the secondary branch nearest the
COMPUTER-AIDED DESIGN PACKAGE FOR ~
MUNICIPAL STORMWATER DRAINAGE NETWORKS ~
EFI5 FLOW NO. 15
300
0.189
FLG~ NO. 15
300
2.456
FLO~ NO. 15
300
3.456
i. 234
COMPUTER-AIDED DESIGN PACKAGE FOR ~
MUNICIPAL STORMWATER DRAINAGE NETWORKS -
NO. OF MANHOLE:8 - -
MANHOLE NUMBER:8 - -
TYPE OF MANHOLE: -I-
-
4.567
FINISHED SURFACE LEVEL (mP.D.):4.91
Fig. 3. Screen showing data input of manholes,
. . . . . . . . . . . . . . . .
Fig. 5. Screen during execution of program within the main computational domain.
46
K. W. Chau
[ ACC.JlIA
F ~[s HO
~s
~~
¥[S ~
~0~
~0
Fig. 6. Overall flow chart of computer-aided design package for municipal stormwater drainage networks. outfall ... and so on. The basic design data, manhole numbers, increment catchment areas and the pipe lengths are entered by the user. A pipe size and gradient are assumed by the user and the time of concentration is computed. Where sewers join, the time of concentration is taken to be the greater time entailed for flow to the manhole concerned. The rainfall intensity corresponding to the time of concentration and frequency Of storm is computed from the simulated Intensity-Duration-Frequency equations. The expected peak runoff in the pipe is then obtained by the Rational Method. Inverted levels, based on the assumption that soffit-by-soffit pipe connections are effected at all manholes, are calculated. The assumed pipe sizes are checked to see if the flow capacity is capable of carrying the designed runoff at each pipe or if the actual flow
velocity is less than 4 m/s, and if not, the particular pipe size is adjusted and iterations are made until the pipe sizes are sufficient. The details of this subroutine for capacity checking are shown in Fig. 7. The assumed pipe sizes are then checked to see if the backwater level is below the proposed ground level at each manhole location, and if not, iterations are similarly initiated. The checking is proceeded from the downstream end of the network towards the upstream end. If at any manhole the backwater level is higher than the finished ground level, the pipe directly downstream of that particular manhole and all downstream pipes with the same diameter will be upgraded by one commercial size. The process will be continued iteratively until the backwater level criteria is satisfied. The algorithm of this subroutine for backwater checking is shown in Fig. 8.
A robust computer-aided design package for municipal stormwater drainage networks
47
I'l )
Y|S
I
~zs
¥~$
~0
c~tc~- | ATI01~
]
NO T[$ ¥I$
Fig. 7. Flow chart of subroutine for pipe capacity checking. THEORETICAL CONSIDERATIONS C o l e b r o o k Formula for pipe flow
Colebrook Formula (eqn (1)) is used to describe the flow velocity within the whole range of smooth, transitional and rough turbulent flow 1/x/A : - 2 log [e/3"7D + 2.51/(Rex/A)]
(1)
The variation of the kinematic viscosity of water at different temperatures 5 has been incorporated in the computer program. For instance, within the usual temperature range, kinematic viscosity of water is 1-308 × 10 -6, 1.141 × 10 -6 and 1-007 × 10-6m2/s at 10°C, 15°C and 20°C respectively. After some simple rearrangement, eqn (1) becomes:
.]
2.51~ v = -2(2gDs) ~/2 log _I ~ ~ -~ Dv/(ZgDs)j
(2)
from which the water velocity for uniform and steady pipe flow can be calculated, provided D, s and e are known since the hydraulic gradient will be equal to the gradient of drainage pipe in this case. The pipe capacity Qp, for circular sections flowing full, is related with
.0/~,\ ~ 1~I$
)
Fig. 8. Flow chart of subroutine for backwater computatxons. water velocity v by straight multiplication with the cross-sectional area of the pipe. Estimation of time of concentration (t c)
The computer program includes both designs for catchments with man-made elements and for the natural area. For developed areas, the time of concentration is estimated as the summation of the time of entry (te), which is input by the user, and the time of
48
K. W. Chau
flow (tf), which is computed automatically based on the pipe length and flow velocity. In accordance with H o n g K o n g practice, it is recommended that a minimum te of 1 minute should be adopted on slopes while a minimum te of 5 minutes may be used elsewhere. tc-
0-14465L H0.2A0.1
(3)
Intensity-Duration-Frequency curves The choice of designed rainfall intensity is based on the duration of a rainstorm and on the statistical frequency of recurrence to be used. Rainfall intensity curves 6 have been based on the statistical analysis of long term rainfall records from the Royal Observatory of H o n g Kong. The equations of the rainfall intensity curves are assumed to be second order polynomial equation i = al + a 2 t + a3 t2, where t is the duration of rainstorm, i is the rainfall intensity and coefficients al, a2 & a 3 are functions of return periods to be determined. By applying the least squares method to approximate the equations, the residuals R are defined to be:
N
Et
Ei
~,t
Zt 2
Eit
~t 2
~t 3
Eit 2
Et
Et 2
El 2 ~t 3
Et 3 ~t 4
a3~--N
~t ~t 2
(8)
The algorithm of the subroutine for the least squares method is shown in Fig. 9. In order to minimize the errors to represent the equations by second order polynomials, each intensity duration curve at a particular return period is fitted by three polynomials with time of concentration ranging from (i) 1-Tmin; (ii) 7 - 1 5 m i n ; and (iii) 15-120min.
(4)
R = al + a2t + a3 t2 - i
The residuals, which are required to be minimized, are first squared and then summed. The derivative is then taken with respect to each coefficient and the resulting equations are set to zero. The following system of equations are resulted:
El
~t 2 ~t 31
a2
~t 2
Et 3
a3
~]t4J
=
Eit
(5)
L~it 2
from which the unknown coefficients can be determined. By using Cramer's Rule, ~;t
~tEt2 ~t 2 Et 3
Eit 2
Et 3
Et 4
N Et
Et Et 2
Et 2 Et 3
Et 2
~t 3
Et 4
N
Ei
Et 2
Et
Eit
Et 3
Et 2
Eifl
Et 4
ItS
al =
a2 --
N Et
Et Et 2
Et 2 Et 3
Et ~
~t 3
Et 4
(6)
NO ~I 1~I$+
(7)
(-) Fig. 9. Flow chart of subroutine in simulation of IntensityDuration-Frequency Curves in Hong Kong.
A robust computer-aided design package for municipal stormwater drainage networks Table 1. Approximation of the Intensity-Duration-Frequency curves in Hong Kong by second order polynomials (Equations of the fitting curves: i = a~ + a2t + a3tz) Return period (year)
Duration a
aI
a2
a3
X Y Z
218.9 188'1 132'4
-21.0 -8"6 -1'8
1.40 0.23 0.01
X Y Z
264-3 215-9 164-8
-24.3 -8.1 -2.1
1.65 0.20 0.01
X Y Z
294.4 240-7 182"2
-28-6 -8"5 -2.2
2.02 0.20 0.01
X Y Z
319.6 269.6 207.2
-29-5 -10"6 -2.6
2-01 0-28 0.02
X Y Z
358"8 291.4 223.8
-33.3 -9-7 -2.4
2.26 0.22 0.02
100
X Y Z
382-3 303-2 251-0
-34.4 -8.5 -3.1
2.27 0.16 0.02
200
X Y Z
411.1 349.8 268.8
-36-9 -13.0 -3.2
2-46 0.34 0.02
500
X Y Z
444.3 370'8 289'6
-39-1 -12-8 -3.1
2-58 0-32 0-02
1000
X Y Z
471'9 412.7 306.6
-42.3 -17.0 -3.3
2.96 0.50 0.02
2
5
10
20
50
aLegend:
.
x
~1~
v
_h
z
zoo
~tu~ ~r~od
l~
l~
(year=}
~
10~ N
1~ ~0 ~ 1~
~
$
~
5~ I~
2 1.5
~
3
4 5 6 7 8 910 15 20 30 ~ration,Ti~ of Concentration, t(min)
40
50
~ ~0~l~lZ0
F~g. 10. The Intensity-Duration-Frequency Curves of rains t o ~ in Hong Kong. H o n g Kong, which are shown in Fig. 10, it can be readily adapted to cater for other conditions.
Capacity checking of drainage pipe Rational Method is often used for estimation of designed peak runoff to be conveyed in the municipal drainage system of H o n g Kong. This method is relatively simple and straight forward and produces satisfactory results for the small catchment generally under consideration in H o n g Kong. The peak runoff Q in litres/s is related to the runoff coefficient K, the design ~1 33
~
31
4
Table 1 tabulates the computed unknown coefficients in the fitting Intensity-Duration-Frequency curves for various combinations of return periods and times of concentration. The accuracy of the fitting curves is very high and the m a x i m u m error in approximating the rainstorm intensity is less than 5%, which is considered adequate for design purposes. The Civil Engineering Manual 7 published by the H o n g K o n g Lands and Works Branch requires the following designed rainstorm frequencies to be used:
5 \ 24
| ~7
L
LEGEND:
21
35
3~ ~
~
~ 0 ~
~
OUTFALL ~
Although this program is tailored for design based on the Intensity-Duration-Frequency rainfall curves in
'l
~oo 35o .~ 31~ ~ zso
i. Duration X represents 1 to 7 minutes; ii. Duration Y represents 7 to 15 minutes; iii. Duration Z represents 15 to 120 minutes.
a. for nullahs and main stormwater drains through developed areas and for important land drainage, the frequency should be I in 200 years; b. for stormwater drainage networks in developed areas, the frequency should be 1 in 50 years; c. for unimportant land drainage, the frequency should be 1 in 10 years.
49
(WZ~ ~ )
~7
F ~ W DI~CTION
~i~. II. D ~ n a ~ ¢ layout ~oc wfi~cafion o£ compu[¢r-aid¢d dcs~n package.
K.W. Chau
50
Table 2. Listing of computer input of the verification example No.
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 28 29 30 31 32 33 34 35 36 37 38
Manhole
Area (m2)
Dia (mm)
Grad (1 in)
Pipe class
Manhole no.
Type
to
Length (m)
Bedding
from
Finished level (mPD)
Pipe type
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 14 19 20 12 12 23 12 25 26 27 10 9 30 7 32 4 34 4 20 37 23 39 26
609-0 976"0 250.0 0"0 950'0 950.0 6470'0 1 972.0 0"0 0"0 0.0 0.0 0-0 0-0 72 563'0 1 796.0 2386'0 0.0 0.0 3262.0 1 285.0 1 607.0 764.0 550'0 0"0 3 800'0 1 719.0 1 281.0 0"0 678-0 8O8-0 1 112-0 115-0 1 583.0 800"0 0"0 604.0 586.0
20"5 21"5 9'0 26"0 46"5 22"5 30'5 52-5 72"5 70'0 16"0 11"0 64"0 51'5 13'5 31'0 16'0 35'0 37'0 22.0 39'0 48.5 44.0 38.0 36.5 32'0 30'0 40'0 36.0 26.5 33-5 22-5 29"5 5.0 16.0 18"0 28.0 30.0
300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
417"00 357'00 357"00 455"00 333'00 500-00 333'00 417"00 370"00 417-00 294-00 294-00 294'00 455'00 143"00 27"00 238"00 125'00 125"00 100"00 417"00 133'00 238"00 313"00 125"00 87"00 167"00 250-00 250-00 238'00 313"00 313"00 313"00 313"00 71'00 71"00 125'00 125'00
H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H
B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B
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 28 29 30 31 32 33 34 35 36 37 38 39
E E E E 1 1 1 I I I I I I J K O 1 2 E E 1 E 1 E E E 1 1 E E E E E E 1 O E E E
4'600 4.950 4'700 4.700 4'800 4.650 4"450 4-910 4.750 4.840 4"750 4'660 4.600 4.405 4'405 4.405 4'405 4.690 4.750 4.810 4.600 4'780 4.750 4.580 4-800 4"580 4.550 4.750 4"460 4"580 4.500 4.660 4.750 4.400 4.800 4"900 4.700 4.750 4.830
4 1 1 2 1 2 2 2 2 2 2 2 2 1 2 3 4 4 2 2 4 4 2 4 1 2 2 4 4 2 4 2 4 2 4 4 2 4 2
m e a n rainfall intensity i in m m / h r a n d the c a t c h m e n t area A in m 2. The estimation of the design m e a n rainfall intensity in general entails at first the d e t e r m i n a t i o n of the time of c o n c e n t r a t i o n a n d the return period of the rainstorm. The pipe size is first selected for the a c c u m u l a t e d runoff at each inlet of m a n h o l e a s s u m i n g that the pipe is just barely flowing full. The pipe diameter will be a u t o m a t i c a l l y adjusted such that the pipe capacity Qp is large e n o u g h to convey the peak discharge Q. The c o r r e s p o n d i n g actual flow velocity in the drainage pipe is c o m p u t e d from the peak discharge by dividing with the pipe cross-sectional area. The p r o g r a m also checks that the actual flow velocity should n o t be too large, say, less t h a n 4 m / s .
Head losses along the flow F o r steady a n d u n i f o r m t u r b u l e n t incompressible flow in conduits, the m a j o r energy losses are due to the friction dissipation between the pipe wall a n d the flow. It is assumed that the pipe frictional loss over the length is equal to the pipe length multiplied by the hydraulic gradient. Moreover, head losses occurring at bends a n d m a n h o l e s are expressed as the multiplication of the head loss coefficient a n d the velocity head. The values of the head loss coefficients rely on the type of m a n h o l e , i.e. the head loss coefficients are 0" 1, 0"3 a n d 1-0 for m a n h o l e w i t h o u t bend, m a n h o l e with b e n d a n d m a n h o l e at exit respectively.
A robust computer-aided design package for municipal stormwater drainage networks
51
Table 3. Computer output for capacity checking procedure of the verifieatlon example Manhole
Area
from
(m2)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
to
ACC A R E A
2 609-0 3 976"0 4 250-0 5 0'0 6 950"0 7 950'0 8 6470"0 9 1 972"0 10 0"0 11 0"0 12 0-0 13 0"0 14 0"0 15 0"0 16 72563-0 14 1 796-0 19 2386"0 20 0"0 12 0"0 12 3262"0 23 1 285"0 12 1 607'0 25 764.0 26 550-0 27 0"0 10 3800"0 9 1 719.0 30 1 281-0 7 0-0 32 678"0 4 808"0 34 1 112"0 4 115-0 20 1 583"0 37 800"0 23 0"0 39 604.0 26 586.0
(~ll2)
Cap (m3/s)
Vel (m/s)
Time flow (min)
Time conc (min)
609"0 1 585'0 1 835"0 4548-0 5498'0 6448'0 14 199"0 16 171"0 17 890-0 24 194'0 24 194'0 35 117"0 35 117-0 36913"0 109476'0 1 796'0 2386"0 2386'0 3969'0 3262'0 1 285'0 3 692"0 764'0 1 314"0 2504"0 6304-0 1 719.0 1 281"0 1 281'0 678.0 1 486"0 1 112.0 1 227.0 1 583.0 800"0 800"0 604.0 1 190.0
0"054 0'170 0'170 0'320 0-375 0"548 1'086 1.196 1"271 2"060 2"457 2'457 2.457 2"683 8'113 0'214 0"208 0-288 0-288 0.323 0"097 0'280 0.072 0.112 0"178 0"519 0.154 0.126 0"126 0'072 0"112 0"112 0"112 0"112 0"132 0"132 0-099 0.099
0"762 1"068 1'068 1"133 1.326 1-242 1"709 1'603 1.703 1-823 2-174 2"174 2'174 1'876 3"796 3"034 1'311 1.814 1"814 2'030 0"879 1"758 1"012 1"016 1"616 2"399 1"397 1.139 1"139 1"012 1.016 1"016 1"016 1'016 1"865 1"865 1-402 1"402
0-45 0-34 0"14 0"38 0"58 0"30 0-30 0"55 0'71 0-64 0"12 0"08 0"49 0'46 0-06 0"17 0"20 0-32 0-34 0"18 0"74 0"46 0"72 0"62 0"38 0"22 0"36 0"59 0"53 0"44 0"55 0-37 0-48 0"08 0.14 0"16 0"33 0"36
5"45 5'78 5.92 6'31 6-89 7"19 7'49 8"04 8"75 9"39 9'51 9'59 10"08 10-54 10'60 5"17 5"20 5"52 5'86 5"18 5'74 6"20 5"72 6"35 6.72 6'95 5"36 5"59 6"11 5"44 5-99 5-37 5"85 5"08 5"14 5'30 5'33 5"69
Calculation of backwater effect
1
2(2Dg)'/2 ~
[ e log [3.--~-+
244"6 241-9 241"0 238"8 236"8 233-2 231"2 227"8 223"6 220"0 219-3 218'9 216"3 213-9 213"6 247'1 246"8 243"9 241"4 247"0 242'2 239"4 242"4 238"6 237"2 236"7 245"4 243-4 239"8 244.7 240"6 245'3 241.4 248"0 247"4 245'9 245"6 242"6
Run IN LEVEL off (-mPD) (ma/s) 0-041 0"107 0-123 0.302 0'362 0.418 0"912 1.023 1.111 1"479 1"474 2"135 2"110 2"193 6-496 0"123 0"164 0.162 0.266 0'224 0.086 0"245 0'051 0.087 0.165 0.415 0'117 0-087 0"085 0"046 0.099 0.076 0'082 0.109 0.055 0"055 0'041 0.080
2-906 2"707 2"646 2"471 2'414 2.124 1"929 1"763 1"637 1"216 1"048 0"994 0"956 0"589 0"175 2"787 2'387 2"320 2"040 1'964 2"277 2'108 3"082 2"822 2"701 2"259 2"417 2"758 2'598 2'990 2'803 2'862 2'790 2'131 2'737 2'512 3'240 3'016
OUT_LEVEL (mPD) 2-857 2-646 2-621 2"414 2"274 2"079 1"838 1"637 1"441 1'048 0'994 0'956 0"739 0"475 0-081 1.639 2"320 2'040 1-744 1"744 1'183 1"744 2"897 2-701 2.409 1"891 2"237 2"598 2-454 2"878 2'696 2.790 2"696 2"115 2.512 2"258 3"016 2'776
Cover Depth in out (m) (m) 1"362 1.755 1-566 1-581 1"738 1.722 1"560 2-109 2'075 2'348 2'426 2"390 2"368 2"390 2.478 1-286 1"815 1.942 2.282 2"148 2.093 2"154 1'166 1.568 1.469 1.722 1"923 1.292 1-572 1"178 1.447 1"478 1"200 2-259 1.831 1"856 1.178 1.482
1-761 1'566 1"591 1"738 1.728 1-567 2-112 2.075 2"361 2'426 2"390 2'368 2"390 2"504 2'573 2.434 1"942 2"282 2.428 2"428 2.157 2"428 1"571 1.469 1.731 2"380 2"103 1'572 1.586 1"450 1"594 1-200 1"594 2"285 1.856 2"160 1'482 1.472
The tolerance limit for the trial a n d e r r o r process is 1 x 10 -6 in the c o m p u t e r model.
T h e w a t e r b a c k s up into the inlet to a d e p t h a b o v e the pipe equal to the outflow velocity h e a d plus the inlet lateral e n t r a n c e loss. Hence, in this c o m p u t a t i o n a l p r o c e d u r e , the d i a m e t e r o f the pipes at m a n h o l e s are r e q u i r e d to be a d j u s t e d until the b a c k w a t e r levels are always lower t h a n the finished levels so t h a t flooding will n o t be incurred. In checking b a c k w a t e r levels at each m a n h o l e location, the actual h y d r a u l i c g r a d i e n t is c a l c u l a t e d by a p p l y i n g the C o l e b r o o k F o r m u l a . Since the actual flow velocity has been f o u n d in the f o r m e r steps f r o m the actual runoff, the actual h y d r a u l i c g r a d i e n t s, which is f o u n d on b o t h sides o f the following e q u a t i o n , can be d e t e r m i n e d by trial a n d error: x/s--
Inten (mm/hr)
2"51u
D~s)J
] (9)
NUMERICAL
VERIFICATION OF MODEL
A typical m u n i c i p a l s t o r m w a t e r d r a i n a g e n e t w o r k is chosen for verification o f the c o m p u t e r - a i d e d design p a c k a g e . F i g u r e 11 depicts the n e t w o r k in d e v e l o p e d areas c o m p r i s i n g 39 m a n h o l e s with m a n y s e c o n d a r y as well as tertiary branches. T a b l e 2 t a b u l a t e s the i n p u t d a t a for the d r a i n a g e system. The designed frequency o f storm, a c c o r d i n g to the H o n g K o n g Civil Engineering M a n u a l , is 1 in 50 years. A r o u g h n e s s value o f 0.6 m m is a d o p t e d for all the concrete d r a i n pipes. All the pipes are initially a s s u m e d to have a d i a m e t e r o f 300 m m in o r d e r to d e m o n s t r a t e the c a p a b i l i t y o f the c o m p u t e r p r o g r a m . T a b l e 3 a n d T a b l e 4 d i s p l a y the c o m p u t e r o u t p u t s c o r r e s p o n d i n g to the pipe c a p a c i t y checking s u b r o u t i n e
K.W. Chau
52
Table 4. Computer output for backwater computation procedure of the verification example Manhole from To 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 14 19 20 12 12 23 12 25 26 27 10 9 30 7 32 4 34 4 20 37 23 39 26
Length (m)
Discharge (m3/s)
Pipe size (mm)
Actual grad (1 in)
Flow vel (m/s)
Frictional loss (m)
Manhole loss (m)
Manhole no.
Backwater level (mPD)
Finished level (mPD)
20"50 21.50 9.00 26.00 46.50 22"50 30'50 52.50 72.50 70'00 16"00 11-00 64"00 51.50 13'50 31"00 16-00 35"00 37.00 22.00 39.00 48.50 44'00 38.00 36"50 32.00 30"00 40.00 36"00 26'50 33.50 22-50 29"50 5.00 16.00 18"00 28.00 30.00
0.041 0-107 0.123 0.302 0.362 0.418 0.912 1-023 1.111 1.479 1.474 2-135 2-110 2.193 6-496 0.123 0.164 0.162 0-266 0.224 0.086 0.245 0.051 0.087 0-165 0.415 0.117 0-087 0-085 0-046 0.099 0.076 0.082 0.109 0.055 0'055 0.041 0.080
300 450 450 600 600 750 900 975 975 1 200 1 200 1 200 1 200 1 350 1 650 300 450 450 450 450 375 450 300 375 375 525 375 375 375 300 375 375 375 375 300 300 300 300
698'1 893.3 675.2 511.3 357-3 856.5 470.9 568.0 482-6 805.0 809-9 388.6 398.0 678'7 222-6 81.0 384'0 393.0 146'6 206'5 522-9 172.0 455"5 515.4 146-0 136"0 287-3 521.1 536.5 565.2 398.1 677.9 576"3 331'0 399"6 404-6 703'6 189-9
0.586 0.670 0"773 1-068 1-280 0.946 1.434 1.371 1-489 1'308 1.304 1.889 1.866 1'533 3.040 1.745 1'029 1.017 1.674 1.408 0-783 1.544 0.728 0.789 1-495 1.916 1.061 0.785 0.773 0.652 0.900 0.686 0.745 0"988 0-778 0.773 0.583 1.135
0'029 0.024 0'013 0'051 0-130 0.026 0"065 0'092 0-150 0-087 0"020 0.028 0.161 0'076 0-061 0.383 0'042 0.089 0.252 0"107 0"075 0'282 0.097 0"074 0-250 0-235 0"104 0'077 0"067 0-047 0'084 0'033 0"051 0'015 0'040 0-044 0.040 0.158
0.002 0.002 0-009 0-006 0.025 0.014 0.031 0.029 0.034 0'026 0.026 0.055 0.018 0'036 0.471 0.016 0.016 0.016 0.043 0"030 0-009 0-036 0"003 0.010 0.034 0.056 0.017 0.009 0.009 0'007 0.012 0.007 0"008 0.015 0-009 0-009 0.005 0.020
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 28 29 30 31 32 33 34 35 36 37 38 39
4"297 4-266 4.240 4"217 4.160 4.005 3-965 3'869 3.748 3"564 3'451 3.405 3'322 3"143 3.032 2.500 3"542 3"863 3-805 3"700 3"542 3.807 3.723 4"322 4.223 4"139 3'855 3'869 4-128 4.042 4"367 4"314 4'317 4-277 3-730 3.826 3"777 4.362 4'317
4"600 4-950 4-700 4-700 4'800 4.650 4.450 4-910 4.750 4.840 4.750 4.660 4.600 4.405 4.405 4.405 4.405 4-690 4"750 4-810 4.600 4.780 4"750 4.580 4'800 4.580 4.550 4.750 4.460 4'580 4.500 4.660 4.750 4-400 4.800 4-900 4.700 4.750 4.830
a n d the b a c k w a t e r c o m p u t a t i o n s u b r o u t i n e respectively. T h e results have been verified with the c o n v e n t i o n a l m a n u a l calculations, f r o m which excellent a g r e e m e n t s have been o b t a i n e d . Besides, one o f the c o m m e r c i a l l y available p a c k a g e s has been used to validate the p r o g r a m , especially on the b a c k w a t e r subroutine, a n d c o m p a r a b l e results have been acquired.
CONCLUSIONS T h e c o m p u t e r - a i d e d design p r o g r a m for m u n i c i p a l s t o r m w a t e r d r a i n a g e n e t w o r k s , t a i l o r e d for use on I B M / P C / X T or P C / A T m i c r o c o m p u t e r s which is readily available in design offices, has been d e v e l o p e d a n d r i g o r o u s l y verified. By using the c o m p u t e r p a c k a g e , pipe d i a m e t e r s are a d j u s t e d a u t o m a t i c a l l y to filfull the flow criteria that the pipe c a p a c i t y is sufficient a n d that
the b a c k w a t e r effect will n o t incur flooding. Besides, the flow velocity is limited to be less t h a n 4 m/s. The user m a y c h o o s e either one o f the i n p u t m o d e s , namely, the interactive m o d e or the datafile m o d e . C u r r e n t l y , the m a x i m u m n u m b e r o f m a n h o l e s for this m o d e l is limited to 50 only. H o w e v e r , by a p p l y i n g o p t i m i z a t i o n in the p r o g r a m m i n g technique including the use o f c o m m o n block, pointer, m o r e s u b r o u t i n e procedures, etc., it w o u l d be c a p a b l e o f h a n d l i n g m o r e t h a n 100 m a n h o l e s . The a p p l i c a t i o n o f this m o d e l in s t o r m w a t e r d r a i n a g e design is p r o m i s i n g due to the n a t u r e o f the c o n v e n t i o n a l m a n u a l design m e t h o d which is b o t h m o n o t o n o u s a n d iterative. T h e source codes o f one o f the m o s t i m p o r t a n t subroutines for this c o m p u t e r model, namely, Back_water_check, is listed in the A p p e n d i x . T h e c o m p l e t e listing o f the p r o g r a m can be o b t a i n e d from the a u t h o r .
A robust computer-aided design package for municipal stormwater drainage networks REFERENCES 1. AckerscP. Charts for the hydraulic design of channels and pipes, CIRIA, 1973. 2. Borland Inc. User's Guide to TURBO PASCAL version 5.0, Borland International Inc., 1987. 3. Hergert, D. Mastering TURBO PASCAL 5.0, SYBEX, 1989. 4. Gottfried, B.S. Theory and Problems of Programming with PASCAL, McGraw-Hill, 1975. 5. Streeter, V.L. & Wylie, E.B. Fluid Mechanics, McGrawHill, 1987. 6. Peterson & Kwong A design rainstorm profile for Hong Kong, Technical Note No. 58, Hong Kong Royal Observatory, 1981. 7. Hong Kong Government, Civil Engineering Manual, Vol. IV - - Sewerage and Drainage, Hong Kong Public Works Department, 1984.
APPENDIX T H E LISTING OF T H E S O U R C E C O D E S FOR SUBROUTINE BACK_WATER_CHECK. PROCEDURE BACK_WATER_CHECK;
{Caleulatlon of bmok~ator lev~l,)
VAR I,J,II,JI,J2,KI:INTNGER; DIA1,LI:REAL; S,BI,S2,A,B,CoKll:REAL; BEGIN IF OUTPALL~WATER~EVNL THEB BEGI~ POE I:=I TO HE DO BEGIB WITH P[I] DO BEGIN DIAI:=DIA/IO00; KII:=K/IO00~ ACT_VEL:=EUN_~PF/(3.14*$@E(DIAI)~D.25); S:=I/G~D; A:=KII/(3.T*DIAI); REPEAT
B:=(2.51*K_VIB)/(DIA1*S@NT(2*B.81*DIAl*S)); C:=(-2)*(I/ACT_VEL)~S@ET(2~9.81*DIAI)*O.434*SE(A+B); SI:=I/S~R(C); $2:=S; S:=SI; UNTIL ABS(S1-S2)P[II+I].PEOH_RO ERD ERD EHD BED END; BNGIN ELOW_CALCU; INTENSITY; RUN_ORE; IBVERT~EVEL; BACK_WATER_CHECK EHD;
53
~.~.i. v'~"
A robust computer-aided design package for municipal stormwater drainage networks K.W. Chau Department of Civil & Structural Engineering, Hong Kong Polytechnic, Kowloon, Hong Kong
In this paper a computer model for automation in the design of the municipal stormwater drainage system is developed and rigorously verified. Although the program is tailored for application and use in Hong Kong, it can be readily adapted to other situations. The numerical model, which is designed for use on IBM/PC/XT or PC/AT microcomputers, is written in PASCAL language and is compiled by PC software TURBO PASCAL version 5"0 due to the various advantages of the integrated programming environment supported. The computer-aided design package for flow prediction and drainage design applies the Colebrook Formula and the Rational Method to route pipe flows through tree-type drainage networks. By using the computer package, drainage pipe diameters are adjusted automatically to fulfill the flow criteria, namely, that the pipe capacities are large enough to convey the peak runoffs and that the backwater levels are not higher than the finished levels and hence ensure that flooding will not be resulted at all locations. The monotonous and iterative conventional method for designing municipal stormwater drainage networks can be taken over by this model. During the execution of the user-friendly and easily operated computer program, adequate user oriented information will be furnished. Its verification is effected by application of the program for municipal stormwater drainage design in a typical example.
Key words." computer-aided design, municipal stormwater drainage networks, backwater effect, flood prevention, pipe flow. NOTATION A D g H i K L N Q Qp R
Re
s t tc te
the catchment area in m 2 the diameter of the pipe the gravitational co0stant (= 9.81 m/s 2) the average fall f r o m summit of catchment to the point of design in m / 1 0 0 m the design mean rainfall intensity in m m / h r the runoff coefficient the longest distance on the line of flow to the design point in m number of pairs of values for the least square method peak runoff in litres/s at particular pipe section ( : KiA/3600) pipe capacity (= ~rDZv/4) the residuals in the least square method Reynold's number (= vD/u)
tf v ~ A u
the hydraulic gradient the duration of rainstorm in minutes time of concentration (-- te ÷ tf) the time of entry the time of flow the flow velocity the roughness value of the pipe the Darcy-Weisbach friction factor (= 2gDs/u 2) kinematic viscosity of water
INTRODUCTION The aims of modern municipal stormwater drainage networks are to prevent significant damage to life and property arising from surface runoffs as outcomes of any rainstorms and, at the same time, to be able to commission and operate against any worst foreseeable stormwater runoff of a designed return period, with a view to ensuring that a greater runoff event will not incur during the design life of the infrastructure.
Advances in Engineering Software 0965-9978/92/$05.00 © 1992 Elsevier Science Publishers Ltd. 43
44
K. W. Chau
The conventional design of stormwater drainage systems is effected by referring to design charts. ~ In the process, the pipe diameters are required to be adjusted by trial and error and hence enormously laborious work is usually entailed. Moreover, mistakes are easily incurred in the time consuming procedure. As such, there is a necessity to develop a user-friendly computer model coupled with automation of the design process in order to avoid the troublesome manual computations and to design the municipal drainage networks speedily as well as precisely. The program for municipal stormwater drainage design is written in T U R B O PASCAL language version 5.0, 2 for use on personal computers which are readily available in design offices. The mathematical model is developed to serve the purpose of systematic hydraulic design of the pipe sizes of a new drainage system, or of extensions and modifications to an existing drainage system, with prescribed design inflows. By using the computer package, drainage pipe diameters are adjusted automatically to fulfill the flow criteria, namely, that the pipe capacities are large enough to convey the peak runoffs and that the backwater levels are not higher than the finished levels and hence ensure that flooding will not be resulted at all times. Furthermore, the maximum actual flow velocities are limited to be not greater than 4m/s. The computer program will automatically adjust pipe diameters to appropriate magnitudes attaining the above criteria and hence any arbitrary pipe diameter can be initially assumed. During the execution of the user-friendly and easily operated computer program, adequate user oriented information will be furnished. The verification of the model is effected by subjecting it to application in a typical urban drainage system. The rainfall Intensity-Duration-Frequency curves in Hong Kong are approximated and represented by second order polynomial equations based on statistical records. The unknown coefficients of the simulated polynomial equations are computed by the least squares method. Although the computer program is tailored for application in Hong Kong, it can be readily adapted to other situations.
of units that provide many useful procedures and functions. Besides, it comprises a built-in full-screen editor and a debugger that allows any syntax error in the program to be detected easily. 3'4
COMPUTER PACKAGE FOR MUNICIPAL STORMWATER DRAINAGE NETWORK DESIGN
By simply executing the compiled file on the microcomputer, user-friendly and self-explanatory instructions will be displayed for the step-by-step data input procedure. The user may choose either one of the input modes, i.e. the interactive mode or the datafile mode, so that a fresh user can follow the guided instructions in the interactive mode to provide the input data whilst a more experienced user can save time by preparing datafiles directly in the fixed format before execution of the program. The main menu screen for the program and a sub-menu for input of flow line data are shown in Fig. 1 and Fig. 2 respectively. Figure 3 shows the screen during data input of the manhole. Only the commerically available pipe diameters are allowed, i.e. multiple increments of 75 mm from 150 mm to 1200mm and multiple increments of 150mm from 1200 mm to 2100 mm. Any other arbitrary input of pipe diameters not included in the above will prompt an error message 'This pipe size is not used'. The type of bedding required depends on the pipes under fields or under roads while the strength classes required depend on the depth of cover as well as the total design loads on pipes under fields, gardens, lightly trafficked access tracks and main traffic routes. Besides, some default designed values are applied if < E N T E R > is keyed in instead of other numerical values. These include kinematic viscosity of 1.141 x 10-6m2/s, runoff coefficient of 1.0,
COMPUTER-AIDED ~
MUNICIPAL
DESIGN
STORMWATER
PACKAGE
D R.~ AINAGE
FOR
NETWORKS
~
MAIN MENU CREATE A N E W FILE
RATIONALE FOR E M P L O Y I N G T U R B O PASCAL LANGUAGE
READ FROM EXIST FILE MODIFY A RECORD
The programming language PASCAL is used for the engineering program to automate the design of stormwater drainage networks while the compilation of the model is effected through PC software T U R B O PASCAL version 5.0 tailored for use on IBM/PC/XT or PC/AT microcomputers. There are a number of advantages in adopting T U R B O PASCAL as the programming tool. It is a fast, versatile and powerful version of the PASCAL language and possesses a library
INPUT D A T A
PRINT O U T P U T D A T A QUIT
USE T ~ ~-- ~
TO SELECT THE OPTION AND PRESS
Fig. 1. Main menu screen of computer-aided design package for municipal stormwater drainage networks.
A robust computer-aided design package for municipal stormwater drainage networks COMPUTER-AIDED DESIGN PACKAGE FOR ~
COMPUTER-AIDED DESIGN PACKAGE FOR
MUNICIPAL STORMWATER DRAINAGE NETWORKS ~
FLOW NO.: _3_ F R O M
~
MUNICIPAL STORMWATER DRAINAGE NETWORKS ~
VALUE OF ROUGHNESS ( m m ) : _ _
MANHOLE OF NO.:3 _ _
TO MANHOLE OF NO.:4 _ _
45
VALUE OF KINEMATIC VISCOSITY(m^s):I.141*IOE-6
RUNOFF COEFFICIENT (I OR 0.8):I__
CATCHMENT AREA (m^2):250
OUTFALL INVERT LEVEL (mP.D.):
LENGTH OF FLOW (m):9~
BACKWATER LEVEL AT OUTFALL (mP.D.):2.5
DIAMETER OF PIPE (mm):30__0
D E S I G N E D
GRADIENT
NO.
P I P E
(1 IN):357
CLASS: (N, M OR L ) : H
BEDDING: (A OR B):B _ _
RAINSTORM RETURN PERIOD (1-9):__
NO.
YEARS
NO.
YEARS
1
2
2
5
3
i0
4
20
5
50
6
lO0
7
200
8
500
9
i 0 0 0
Fig. 2. Sub-menu screen for input of flow line data. existing backwater level at outfall of 2.5 mP.D., etc. The recommended design values of roughness in mm are 0.003, 0"006, 0.015, 0-03, 0.06, 0.15, 0.3, 0"6, 1-5, and 3 which cover a wide range of pipe surface. Figure 4 depicts the screen during data input integrating with some default values. When the program is being executed, the screen, as depicted in Fig. 5, will show the key parameters for that particular step in either one of the following forms: (i)
Flow number, pipe diameter, flow capacity, peak runoff; (ii) Flow number, pipe diameter, actual flow velocity; (iii) Flow number, pipe diameter, backwater level, finished level; depending on which checking step, i.e. capacity checking, velocity checking or backwater calculation, is currently being activated. Besides, in a colour monitor, the above information will be displayed in different colours, namely, the pipe capacity checking will be in white text, the velocity checking will be in blue text while the backwater computation will be in yellow text,
Fig. 4. Screen during data input integrating with some default values. so that a ready distinction of the current status during the program execuation can be reckoned by the user.
ALGORITHM OF MATHEMATICAL MODEL The flow chart of the overall program is depicted in Fig. 6. Computer simulation to conventional manual design of a stormwater drainage network in Hong Kong is implemented through the following design procedure. A plan of the area under consideration is divided into the natural and developed catchments and the routing of the pipelines is laid out. Each manhole is then numbered in a definite order: a) upstream manhole at the main branch; b) downstream manhole at the main branch; c) upstream manhole at the secondary branch nearest the
COMPUTER-AIDED DESIGN PACKAGE FOR ~
MUNICIPAL STORMWATER DRAINAGE NETWORKS ~
EFI5 FLOW NO. 15
300
0.189
FLG~ NO. 15
300
2.456
FLO~ NO. 15
300
3.456
i. 234
COMPUTER-AIDED DESIGN PACKAGE FOR ~
MUNICIPAL STORMWATER DRAINAGE NETWORKS -
NO. OF MANHOLE:8 - -
MANHOLE NUMBER:8 - -
TYPE OF MANHOLE: -I-
-
4.567
FINISHED SURFACE LEVEL (mP.D.):4.91
Fig. 3. Screen showing data input of manholes,
. . . . . . . . . . . . . . . .
Fig. 5. Screen during execution of program within the main computational domain.
46
K. W. Chau
[ ACC.JlIA
F ~[s HO
~s
~~
¥[S ~
~0~
~0
Fig. 6. Overall flow chart of computer-aided design package for municipal stormwater drainage networks. outfall ... and so on. The basic design data, manhole numbers, increment catchment areas and the pipe lengths are entered by the user. A pipe size and gradient are assumed by the user and the time of concentration is computed. Where sewers join, the time of concentration is taken to be the greater time entailed for flow to the manhole concerned. The rainfall intensity corresponding to the time of concentration and frequency Of storm is computed from the simulated Intensity-Duration-Frequency equations. The expected peak runoff in the pipe is then obtained by the Rational Method. Inverted levels, based on the assumption that soffit-by-soffit pipe connections are effected at all manholes, are calculated. The assumed pipe sizes are checked to see if the flow capacity is capable of carrying the designed runoff at each pipe or if the actual flow
velocity is less than 4 m/s, and if not, the particular pipe size is adjusted and iterations are made until the pipe sizes are sufficient. The details of this subroutine for capacity checking are shown in Fig. 7. The assumed pipe sizes are then checked to see if the backwater level is below the proposed ground level at each manhole location, and if not, iterations are similarly initiated. The checking is proceeded from the downstream end of the network towards the upstream end. If at any manhole the backwater level is higher than the finished ground level, the pipe directly downstream of that particular manhole and all downstream pipes with the same diameter will be upgraded by one commercial size. The process will be continued iteratively until the backwater level criteria is satisfied. The algorithm of this subroutine for backwater checking is shown in Fig. 8.
A robust computer-aided design package for municipal stormwater drainage networks
47
I'l )
Y|S
I
~zs
¥~$
~0
c~tc~- | ATI01~
]
NO T[$ ¥I$
Fig. 7. Flow chart of subroutine for pipe capacity checking. THEORETICAL CONSIDERATIONS C o l e b r o o k Formula for pipe flow
Colebrook Formula (eqn (1)) is used to describe the flow velocity within the whole range of smooth, transitional and rough turbulent flow 1/x/A : - 2 log [e/3"7D + 2.51/(Rex/A)]
(1)
The variation of the kinematic viscosity of water at different temperatures 5 has been incorporated in the computer program. For instance, within the usual temperature range, kinematic viscosity of water is 1-308 × 10 -6, 1.141 × 10 -6 and 1-007 × 10-6m2/s at 10°C, 15°C and 20°C respectively. After some simple rearrangement, eqn (1) becomes:
.]
2.51~ v = -2(2gDs) ~/2 log _I ~ ~ -~ Dv/(ZgDs)j
(2)
from which the water velocity for uniform and steady pipe flow can be calculated, provided D, s and e are known since the hydraulic gradient will be equal to the gradient of drainage pipe in this case. The pipe capacity Qp, for circular sections flowing full, is related with
.0/~,\ ~ 1~I$
)
Fig. 8. Flow chart of subroutine for backwater computatxons. water velocity v by straight multiplication with the cross-sectional area of the pipe. Estimation of time of concentration (t c)
The computer program includes both designs for catchments with man-made elements and for the natural area. For developed areas, the time of concentration is estimated as the summation of the time of entry (te), which is input by the user, and the time of
48
K. W. Chau
flow (tf), which is computed automatically based on the pipe length and flow velocity. In accordance with H o n g K o n g practice, it is recommended that a minimum te of 1 minute should be adopted on slopes while a minimum te of 5 minutes may be used elsewhere. tc-
0-14465L H0.2A0.1
(3)
Intensity-Duration-Frequency curves The choice of designed rainfall intensity is based on the duration of a rainstorm and on the statistical frequency of recurrence to be used. Rainfall intensity curves 6 have been based on the statistical analysis of long term rainfall records from the Royal Observatory of H o n g Kong. The equations of the rainfall intensity curves are assumed to be second order polynomial equation i = al + a 2 t + a3 t2, where t is the duration of rainstorm, i is the rainfall intensity and coefficients al, a2 & a 3 are functions of return periods to be determined. By applying the least squares method to approximate the equations, the residuals R are defined to be:
N
Et
Ei
~,t
Zt 2
Eit
~t 2
~t 3
Eit 2
Et
Et 2
El 2 ~t 3
Et 3 ~t 4
a3~--N
~t ~t 2
(8)
The algorithm of the subroutine for the least squares method is shown in Fig. 9. In order to minimize the errors to represent the equations by second order polynomials, each intensity duration curve at a particular return period is fitted by three polynomials with time of concentration ranging from (i) 1-Tmin; (ii) 7 - 1 5 m i n ; and (iii) 15-120min.
(4)
R = al + a2t + a3 t2 - i
The residuals, which are required to be minimized, are first squared and then summed. The derivative is then taken with respect to each coefficient and the resulting equations are set to zero. The following system of equations are resulted:
El
~t 2 ~t 31
a2
~t 2
Et 3
a3
~]t4J
=
Eit
(5)
L~it 2
from which the unknown coefficients can be determined. By using Cramer's Rule, ~;t
~tEt2 ~t 2 Et 3
Eit 2
Et 3
Et 4
N Et
Et Et 2
Et 2 Et 3
Et 2
~t 3
Et 4
N
Ei
Et 2
Et
Eit
Et 3
Et 2
Eifl
Et 4
ItS
al =
a2 --
N Et
Et Et 2
Et 2 Et 3
Et ~
~t 3
Et 4
(6)
NO ~I 1~I$+
(7)
(-) Fig. 9. Flow chart of subroutine in simulation of IntensityDuration-Frequency Curves in Hong Kong.
A robust computer-aided design package for municipal stormwater drainage networks Table 1. Approximation of the Intensity-Duration-Frequency curves in Hong Kong by second order polynomials (Equations of the fitting curves: i = a~ + a2t + a3tz) Return period (year)
Duration a
aI
a2
a3
X Y Z
218.9 188'1 132'4
-21.0 -8"6 -1'8
1.40 0.23 0.01
X Y Z
264-3 215-9 164-8
-24.3 -8.1 -2.1
1.65 0.20 0.01
X Y Z
294.4 240-7 182"2
-28-6 -8"5 -2.2
2.02 0.20 0.01
X Y Z
319.6 269.6 207.2
-29-5 -10"6 -2.6
2-01 0-28 0.02
X Y Z
358"8 291.4 223.8
-33.3 -9-7 -2.4
2.26 0.22 0.02
100
X Y Z
382-3 303-2 251-0
-34.4 -8.5 -3.1
2.27 0.16 0.02
200
X Y Z
411.1 349.8 268.8
-36-9 -13.0 -3.2
2-46 0.34 0.02
500
X Y Z
444.3 370'8 289'6
-39-1 -12-8 -3.1
2-58 0-32 0-02
1000
X Y Z
471'9 412.7 306.6
-42.3 -17.0 -3.3
2.96 0.50 0.02
2
5
10
20
50
aLegend:
.
x
~1~
v
_h
z
zoo
~tu~ ~r~od
l~
l~
(year=}
~
10~ N
1~ ~0 ~ 1~
~
$
~
5~ I~
2 1.5
~
3
4 5 6 7 8 910 15 20 30 ~ration,Ti~ of Concentration, t(min)
40
50
~ ~0~l~lZ0
F~g. 10. The Intensity-Duration-Frequency Curves of rains t o ~ in Hong Kong. H o n g Kong, which are shown in Fig. 10, it can be readily adapted to cater for other conditions.
Capacity checking of drainage pipe Rational Method is often used for estimation of designed peak runoff to be conveyed in the municipal drainage system of H o n g Kong. This method is relatively simple and straight forward and produces satisfactory results for the small catchment generally under consideration in H o n g Kong. The peak runoff Q in litres/s is related to the runoff coefficient K, the design ~1 33
~
31
4
Table 1 tabulates the computed unknown coefficients in the fitting Intensity-Duration-Frequency curves for various combinations of return periods and times of concentration. The accuracy of the fitting curves is very high and the m a x i m u m error in approximating the rainstorm intensity is less than 5%, which is considered adequate for design purposes. The Civil Engineering Manual 7 published by the H o n g K o n g Lands and Works Branch requires the following designed rainstorm frequencies to be used:
5 \ 24
| ~7
L
LEGEND:
21
35
3~ ~
~
~ 0 ~
~
OUTFALL ~
Although this program is tailored for design based on the Intensity-Duration-Frequency rainfall curves in
'l
~oo 35o .~ 31~ ~ zso
i. Duration X represents 1 to 7 minutes; ii. Duration Y represents 7 to 15 minutes; iii. Duration Z represents 15 to 120 minutes.
a. for nullahs and main stormwater drains through developed areas and for important land drainage, the frequency should be I in 200 years; b. for stormwater drainage networks in developed areas, the frequency should be 1 in 50 years; c. for unimportant land drainage, the frequency should be 1 in 10 years.
49
(WZ~ ~ )
~7
F ~ W DI~CTION
~i~. II. D ~ n a ~ ¢ layout ~oc wfi~cafion o£ compu[¢r-aid¢d dcs~n package.
K.W. Chau
50
Table 2. Listing of computer input of the verification example No.
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 28 29 30 31 32 33 34 35 36 37 38
Manhole
Area (m2)
Dia (mm)
Grad (1 in)
Pipe class
Manhole no.
Type
to
Length (m)
Bedding
from
Finished level (mPD)
Pipe type
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 14 19 20 12 12 23 12 25 26 27 10 9 30 7 32 4 34 4 20 37 23 39 26
609-0 976"0 250.0 0"0 950'0 950.0 6470'0 1 972.0 0"0 0"0 0.0 0.0 0-0 0-0 72 563'0 1 796.0 2386'0 0.0 0.0 3262.0 1 285.0 1 607.0 764.0 550'0 0"0 3 800'0 1 719.0 1 281.0 0"0 678-0 8O8-0 1 112-0 115-0 1 583.0 800"0 0"0 604.0 586.0
20"5 21"5 9'0 26"0 46"5 22"5 30'5 52-5 72"5 70'0 16"0 11"0 64"0 51'5 13'5 31'0 16'0 35'0 37'0 22.0 39'0 48.5 44.0 38.0 36.5 32'0 30'0 40'0 36.0 26.5 33-5 22-5 29"5 5.0 16.0 18"0 28.0 30.0
300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
417"00 357'00 357"00 455"00 333'00 500-00 333'00 417"00 370"00 417-00 294-00 294-00 294'00 455'00 143"00 27"00 238"00 125'00 125"00 100"00 417"00 133'00 238"00 313"00 125"00 87"00 167"00 250-00 250-00 238'00 313"00 313"00 313"00 313"00 71'00 71"00 125'00 125'00
H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H
B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B B
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 28 29 30 31 32 33 34 35 36 37 38 39
E E E E 1 1 1 I I I I I I J K O 1 2 E E 1 E 1 E E E 1 1 E E E E E E 1 O E E E
4'600 4.950 4'700 4.700 4'800 4.650 4"450 4-910 4.750 4.840 4"750 4'660 4.600 4.405 4'405 4.405 4'405 4.690 4.750 4.810 4.600 4'780 4.750 4.580 4-800 4"580 4.550 4.750 4"460 4"580 4.500 4.660 4.750 4.400 4.800 4"900 4.700 4.750 4.830
4 1 1 2 1 2 2 2 2 2 2 2 2 1 2 3 4 4 2 2 4 4 2 4 1 2 2 4 4 2 4 2 4 2 4 4 2 4 2
m e a n rainfall intensity i in m m / h r a n d the c a t c h m e n t area A in m 2. The estimation of the design m e a n rainfall intensity in general entails at first the d e t e r m i n a t i o n of the time of c o n c e n t r a t i o n a n d the return period of the rainstorm. The pipe size is first selected for the a c c u m u l a t e d runoff at each inlet of m a n h o l e a s s u m i n g that the pipe is just barely flowing full. The pipe diameter will be a u t o m a t i c a l l y adjusted such that the pipe capacity Qp is large e n o u g h to convey the peak discharge Q. The c o r r e s p o n d i n g actual flow velocity in the drainage pipe is c o m p u t e d from the peak discharge by dividing with the pipe cross-sectional area. The p r o g r a m also checks that the actual flow velocity should n o t be too large, say, less t h a n 4 m / s .
Head losses along the flow F o r steady a n d u n i f o r m t u r b u l e n t incompressible flow in conduits, the m a j o r energy losses are due to the friction dissipation between the pipe wall a n d the flow. It is assumed that the pipe frictional loss over the length is equal to the pipe length multiplied by the hydraulic gradient. Moreover, head losses occurring at bends a n d m a n h o l e s are expressed as the multiplication of the head loss coefficient a n d the velocity head. The values of the head loss coefficients rely on the type of m a n h o l e , i.e. the head loss coefficients are 0" 1, 0"3 a n d 1-0 for m a n h o l e w i t h o u t bend, m a n h o l e with b e n d a n d m a n h o l e at exit respectively.
A robust computer-aided design package for municipal stormwater drainage networks
51
Table 3. Computer output for capacity checking procedure of the verifieatlon example Manhole
Area
from
(m2)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
to
ACC A R E A
2 609-0 3 976"0 4 250-0 5 0'0 6 950"0 7 950'0 8 6470"0 9 1 972"0 10 0"0 11 0"0 12 0-0 13 0"0 14 0"0 15 0"0 16 72563-0 14 1 796-0 19 2386"0 20 0"0 12 0"0 12 3262"0 23 1 285"0 12 1 607'0 25 764.0 26 550-0 27 0"0 10 3800"0 9 1 719.0 30 1 281-0 7 0-0 32 678"0 4 808"0 34 1 112"0 4 115-0 20 1 583"0 37 800"0 23 0"0 39 604.0 26 586.0
(~ll2)
Cap (m3/s)
Vel (m/s)
Time flow (min)
Time conc (min)
609"0 1 585'0 1 835"0 4548-0 5498'0 6448'0 14 199"0 16 171"0 17 890-0 24 194'0 24 194'0 35 117"0 35 117-0 36913"0 109476'0 1 796'0 2386"0 2386'0 3969'0 3262'0 1 285'0 3 692"0 764'0 1 314"0 2504"0 6304-0 1 719.0 1 281"0 1 281'0 678.0 1 486"0 1 112.0 1 227.0 1 583.0 800"0 800"0 604.0 1 190.0
0"054 0'170 0'170 0'320 0-375 0"548 1'086 1.196 1"271 2"060 2"457 2'457 2.457 2"683 8'113 0'214 0"208 0-288 0-288 0.323 0"097 0'280 0.072 0.112 0"178 0"519 0.154 0.126 0"126 0'072 0"112 0"112 0"112 0"112 0"132 0"132 0-099 0.099
0"762 1"068 1'068 1"133 1.326 1-242 1"709 1'603 1.703 1-823 2-174 2"174 2'174 1'876 3"796 3"034 1'311 1.814 1"814 2'030 0"879 1"758 1"012 1"016 1"616 2"399 1"397 1.139 1"139 1"012 1.016 1"016 1"016 1'016 1"865 1"865 1-402 1"402
0-45 0-34 0"14 0"38 0"58 0"30 0-30 0"55 0'71 0-64 0"12 0"08 0"49 0'46 0-06 0"17 0"20 0-32 0-34 0"18 0"74 0"46 0"72 0"62 0"38 0"22 0"36 0"59 0"53 0"44 0"55 0-37 0-48 0"08 0.14 0"16 0"33 0"36
5"45 5'78 5.92 6'31 6-89 7"19 7'49 8"04 8"75 9"39 9'51 9'59 10"08 10-54 10'60 5"17 5"20 5"52 5'86 5"18 5'74 6"20 5"72 6"35 6.72 6'95 5"36 5"59 6"11 5"44 5-99 5-37 5"85 5"08 5"14 5'30 5'33 5"69
Calculation of backwater effect
1
2(2Dg)'/2 ~
[ e log [3.--~-+
244"6 241-9 241"0 238"8 236"8 233-2 231"2 227"8 223"6 220"0 219-3 218'9 216"3 213-9 213"6 247'1 246"8 243"9 241"4 247"0 242'2 239"4 242"4 238"6 237"2 236"7 245"4 243-4 239"8 244.7 240"6 245'3 241.4 248"0 247"4 245'9 245"6 242"6
Run IN LEVEL off (-mPD) (ma/s) 0-041 0"107 0-123 0.302 0'362 0.418 0"912 1.023 1.111 1"479 1"474 2"135 2"110 2"193 6-496 0"123 0"164 0.162 0.266 0'224 0.086 0"245 0'051 0.087 0.165 0.415 0'117 0-087 0"085 0"046 0.099 0.076 0'082 0.109 0.055 0"055 0'041 0.080
2-906 2"707 2"646 2"471 2'414 2.124 1"929 1"763 1"637 1"216 1"048 0"994 0"956 0"589 0"175 2"787 2'387 2"320 2"040 1'964 2"277 2'108 3"082 2"822 2"701 2"259 2"417 2"758 2'598 2'990 2'803 2'862 2'790 2'131 2'737 2'512 3'240 3'016
OUT_LEVEL (mPD) 2-857 2-646 2-621 2"414 2"274 2"079 1"838 1"637 1"441 1'048 0'994 0'956 0"739 0"475 0-081 1.639 2"320 2'040 1-744 1"744 1'183 1"744 2"897 2-701 2.409 1"891 2"237 2"598 2-454 2"878 2'696 2.790 2"696 2"115 2.512 2"258 3"016 2'776
Cover Depth in out (m) (m) 1"362 1.755 1-566 1-581 1"738 1.722 1"560 2-109 2'075 2'348 2'426 2"390 2"368 2"390 2.478 1-286 1"815 1.942 2.282 2"148 2.093 2"154 1'166 1.568 1.469 1.722 1"923 1.292 1-572 1"178 1.447 1"478 1"200 2-259 1.831 1"856 1.178 1.482
1-761 1'566 1"591 1"738 1.728 1-567 2-112 2.075 2"361 2'426 2"390 2'368 2"390 2"504 2'573 2.434 1"942 2"282 2.428 2"428 2.157 2"428 1"571 1.469 1.731 2"380 2"103 1'572 1.586 1"450 1"594 1-200 1"594 2"285 1.856 2"160 1'482 1.472
The tolerance limit for the trial a n d e r r o r process is 1 x 10 -6 in the c o m p u t e r model.
T h e w a t e r b a c k s up into the inlet to a d e p t h a b o v e the pipe equal to the outflow velocity h e a d plus the inlet lateral e n t r a n c e loss. Hence, in this c o m p u t a t i o n a l p r o c e d u r e , the d i a m e t e r o f the pipes at m a n h o l e s are r e q u i r e d to be a d j u s t e d until the b a c k w a t e r levels are always lower t h a n the finished levels so t h a t flooding will n o t be incurred. In checking b a c k w a t e r levels at each m a n h o l e location, the actual h y d r a u l i c g r a d i e n t is c a l c u l a t e d by a p p l y i n g the C o l e b r o o k F o r m u l a . Since the actual flow velocity has been f o u n d in the f o r m e r steps f r o m the actual runoff, the actual h y d r a u l i c g r a d i e n t s, which is f o u n d on b o t h sides o f the following e q u a t i o n , can be d e t e r m i n e d by trial a n d error: x/s--
Inten (mm/hr)
2"51u
D~s)J
] (9)
NUMERICAL
VERIFICATION OF MODEL
A typical m u n i c i p a l s t o r m w a t e r d r a i n a g e n e t w o r k is chosen for verification o f the c o m p u t e r - a i d e d design p a c k a g e . F i g u r e 11 depicts the n e t w o r k in d e v e l o p e d areas c o m p r i s i n g 39 m a n h o l e s with m a n y s e c o n d a r y as well as tertiary branches. T a b l e 2 t a b u l a t e s the i n p u t d a t a for the d r a i n a g e system. The designed frequency o f storm, a c c o r d i n g to the H o n g K o n g Civil Engineering M a n u a l , is 1 in 50 years. A r o u g h n e s s value o f 0.6 m m is a d o p t e d for all the concrete d r a i n pipes. All the pipes are initially a s s u m e d to have a d i a m e t e r o f 300 m m in o r d e r to d e m o n s t r a t e the c a p a b i l i t y o f the c o m p u t e r p r o g r a m . T a b l e 3 a n d T a b l e 4 d i s p l a y the c o m p u t e r o u t p u t s c o r r e s p o n d i n g to the pipe c a p a c i t y checking s u b r o u t i n e
K.W. Chau
52
Table 4. Computer output for backwater computation procedure of the verification example Manhole from To 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 14 19 20 12 12 23 12 25 26 27 10 9 30 7 32 4 34 4 20 37 23 39 26
Length (m)
Discharge (m3/s)
Pipe size (mm)
Actual grad (1 in)
Flow vel (m/s)
Frictional loss (m)
Manhole loss (m)
Manhole no.
Backwater level (mPD)
Finished level (mPD)
20"50 21.50 9.00 26.00 46.50 22"50 30'50 52.50 72.50 70'00 16"00 11-00 64"00 51.50 13'50 31"00 16-00 35"00 37.00 22.00 39.00 48.50 44'00 38.00 36"50 32.00 30"00 40.00 36"00 26'50 33.50 22-50 29"50 5.00 16.00 18"00 28.00 30.00
0.041 0-107 0.123 0.302 0.362 0.418 0.912 1-023 1.111 1.479 1.474 2-135 2-110 2.193 6-496 0.123 0.164 0.162 0-266 0.224 0.086 0.245 0.051 0.087 0-165 0.415 0.117 0-087 0-085 0-046 0.099 0.076 0.082 0.109 0.055 0'055 0.041 0.080
300 450 450 600 600 750 900 975 975 1 200 1 200 1 200 1 200 1 350 1 650 300 450 450 450 450 375 450 300 375 375 525 375 375 375 300 375 375 375 375 300 300 300 300
698'1 893.3 675.2 511.3 357-3 856.5 470.9 568.0 482-6 805.0 809-9 388.6 398.0 678'7 222-6 81.0 384'0 393.0 146'6 206'5 522-9 172.0 455"5 515.4 146-0 136"0 287-3 521.1 536.5 565.2 398.1 677.9 576"3 331'0 399"6 404-6 703'6 189-9
0.586 0.670 0"773 1-068 1-280 0.946 1.434 1.371 1-489 1'308 1.304 1.889 1.866 1'533 3.040 1.745 1'029 1.017 1.674 1.408 0-783 1.544 0.728 0.789 1-495 1.916 1.061 0.785 0.773 0.652 0.900 0.686 0.745 0"988 0-778 0.773 0.583 1.135
0'029 0.024 0'013 0'051 0-130 0.026 0"065 0'092 0-150 0-087 0"020 0.028 0.161 0'076 0-061 0.383 0'042 0.089 0.252 0"107 0"075 0'282 0.097 0"074 0-250 0-235 0"104 0'077 0"067 0-047 0'084 0'033 0"051 0'015 0'040 0-044 0.040 0.158
0.002 0.002 0-009 0-006 0.025 0.014 0.031 0.029 0.034 0'026 0.026 0.055 0.018 0'036 0.471 0.016 0.016 0.016 0.043 0"030 0-009 0-036 0"003 0.010 0.034 0.056 0.017 0.009 0.009 0'007 0.012 0.007 0"008 0.015 0-009 0-009 0.005 0.020
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 28 29 30 31 32 33 34 35 36 37 38 39
4"297 4-266 4.240 4"217 4.160 4.005 3-965 3'869 3.748 3"564 3'451 3.405 3'322 3"143 3.032 2.500 3"542 3"863 3-805 3"700 3"542 3.807 3.723 4"322 4.223 4"139 3'855 3'869 4-128 4.042 4"367 4"314 4'317 4-277 3-730 3.826 3"777 4.362 4'317
4"600 4-950 4-700 4-700 4'800 4.650 4.450 4-910 4.750 4.840 4.750 4.660 4.600 4.405 4.405 4.405 4.405 4-690 4"750 4-810 4.600 4.780 4"750 4.580 4'800 4.580 4.550 4.750 4.460 4'580 4.500 4.660 4.750 4-400 4.800 4-900 4.700 4.750 4.830
a n d the b a c k w a t e r c o m p u t a t i o n s u b r o u t i n e respectively. T h e results have been verified with the c o n v e n t i o n a l m a n u a l calculations, f r o m which excellent a g r e e m e n t s have been o b t a i n e d . Besides, one o f the c o m m e r c i a l l y available p a c k a g e s has been used to validate the p r o g r a m , especially on the b a c k w a t e r subroutine, a n d c o m p a r a b l e results have been acquired.
CONCLUSIONS T h e c o m p u t e r - a i d e d design p r o g r a m for m u n i c i p a l s t o r m w a t e r d r a i n a g e n e t w o r k s , t a i l o r e d for use on I B M / P C / X T or P C / A T m i c r o c o m p u t e r s which is readily available in design offices, has been d e v e l o p e d a n d r i g o r o u s l y verified. By using the c o m p u t e r p a c k a g e , pipe d i a m e t e r s are a d j u s t e d a u t o m a t i c a l l y to filfull the flow criteria that the pipe c a p a c i t y is sufficient a n d that
the b a c k w a t e r effect will n o t incur flooding. Besides, the flow velocity is limited to be less t h a n 4 m/s. The user m a y c h o o s e either one o f the i n p u t m o d e s , namely, the interactive m o d e or the datafile m o d e . C u r r e n t l y , the m a x i m u m n u m b e r o f m a n h o l e s for this m o d e l is limited to 50 only. H o w e v e r , by a p p l y i n g o p t i m i z a t i o n in the p r o g r a m m i n g technique including the use o f c o m m o n block, pointer, m o r e s u b r o u t i n e procedures, etc., it w o u l d be c a p a b l e o f h a n d l i n g m o r e t h a n 100 m a n h o l e s . The a p p l i c a t i o n o f this m o d e l in s t o r m w a t e r d r a i n a g e design is p r o m i s i n g due to the n a t u r e o f the c o n v e n t i o n a l m a n u a l design m e t h o d which is b o t h m o n o t o n o u s a n d iterative. T h e source codes o f one o f the m o s t i m p o r t a n t subroutines for this c o m p u t e r model, namely, Back_water_check, is listed in the A p p e n d i x . T h e c o m p l e t e listing o f the p r o g r a m can be o b t a i n e d from the a u t h o r .
A robust computer-aided design package for municipal stormwater drainage networks REFERENCES 1. AckerscP. Charts for the hydraulic design of channels and pipes, CIRIA, 1973. 2. Borland Inc. User's Guide to TURBO PASCAL version 5.0, Borland International Inc., 1987. 3. Hergert, D. Mastering TURBO PASCAL 5.0, SYBEX, 1989. 4. Gottfried, B.S. Theory and Problems of Programming with PASCAL, McGraw-Hill, 1975. 5. Streeter, V.L. & Wylie, E.B. Fluid Mechanics, McGrawHill, 1987. 6. Peterson & Kwong A design rainstorm profile for Hong Kong, Technical Note No. 58, Hong Kong Royal Observatory, 1981. 7. Hong Kong Government, Civil Engineering Manual, Vol. IV - - Sewerage and Drainage, Hong Kong Public Works Department, 1984.
APPENDIX T H E LISTING OF T H E S O U R C E C O D E S FOR SUBROUTINE BACK_WATER_CHECK. PROCEDURE BACK_WATER_CHECK;
{Caleulatlon of bmok~ator lev~l,)
VAR I,J,II,JI,J2,KI:INTNGER; DIA1,LI:REAL; S,BI,S2,A,B,CoKll:REAL; BEGIN IF OUTPALL~WATER~EVNL THEB BEGI~ POE I:=I TO HE DO BEGIB WITH P[I] DO BEGIN DIAI:=DIA/IO00; KII:=K/IO00~ ACT_VEL:=EUN_~PF/(3.14*$@E(DIAI)~D.25); S:=I/G~D; A:=KII/(3.T*DIAI); REPEAT
B:=(2.51*K_VIB)/(DIA1*S@NT(2*B.81*DIAl*S)); C:=(-2)*(I/ACT_VEL)~S@ET(2~9.81*DIAI)*O.434*SE(A+B); SI:=I/S~R(C); $2:=S; S:=SI; UNTIL ABS(S1-S2)
53