Download Outflow from Perforated Pipe

Technical Note 2.105
Re: Outflow from Perforated Pipe
Date: January 2004 (Published May, 2004)
Introduction
In order to provide guidance to the engineering community in designing drainage or recharge
systems, ADS has conducted theoretical computations using an orifice equation. It should be
emphasized that ADS conducted these calculations using ADS standard perforation patterns, and
that the values are based on free outlet (no backfill) through the perforations. Infiltration is
assumed to be equal to the calculated exfiltration rate.
When designing storm water drainage or recharge systems, the goal in mind is to calculate the
amount of storm water which can escape the pipe and replenish the ground water. Although
some may believe that the controlling parameter is the free outflow from the perforated pipe, this
is not often the case. A perforated pipe can only discharge water at a rate at which the surrounding soil will accept it.
Procedure
The goal is to calculate the free outflow from the perforations in a pipe. Knowing the perforation
hole diameter and hole pattern, a simple orifice equation can be used to calculate the flow rate in
cubic feet per second.
Orifice equation
Q P = C d A 2gH
Where
QP = free out fall flow rate through one perforation (ft3/sec)
Cd = Coefficient of discharge = 0.60
A = Cross sectional area of one perforation (ft2)
g = Gravimetric constant = 32.2 ft/sec2
H = Height of water above perforation, head (ft)
Having the orifice equation, the location of the perforations with respect to the invert of the pipe
and the size of perforations, the free outflow at any elevation in the pipe can be calculated. To
calculate the amount of flow per foot of pipe, or unit length, simply multiply the free outflow in
one valley by the number of valleys per foot of pipe.
With the above procedure, we can calculate the free outflow at any given elevation provided the
perforation orientation is known. Looking at a typical curve inside a pipe cross section, (Chart 1.)
the curve is somewhat jumpy and not uniform throughout the pipe cross section. As the water
head increases, however, the curve becomes more uniform and looks much more like a curve
produced from using the orifice equation, Chart 2. The non-uniform part of the curve is due to
the additional perforations holes at higher elevations inside the pipe cross-section, producing
what can be characterized as hydraulic jumps.
4640 TRUEMAN BLVD. HILLIARD, OH 43026 (800) 821-6710 http://www.ads-pipe.com
When designing a pipe in typical storm sewer design, the pipe is assumed to be flowing full. For
the purposes of this technical note, charts have been provided showing the relationship between
free outflow and water head elevation when the pipe is full. Placed on these charts is a second
order polynomial which best describes the data. This polynomial may be used to estimate the
free outfall at various head elevations.
The designer should keep in mind that, for some applications and some pipe sizes, the free outfall
from the pipe perforations may be larger than the flow rate of the pipe itself and thus the pipe
may not flow full. This, however, will only exist in applications where the water is purely in a
free outflow state and is not inhibited by the surrounding soil.
The determining factor for recharge systems is the surrounding soil’s ability to accept water, not
the pipe’s ability to deliver water. Although the perforations in the pipe determine the allowable
area at which water can be released, it is the soil’s ability to accept the water that is the
determining factor in designing recharge systems. This can best be described with the following
example:
Example
A 12” diameter drainage pipe is used to recharge the ground water table through very permeable
backfill envelope (coefficient of permeability, K = 1,000 m/d = 0.0375 ft/s). The ground water
table is 3 feet below the pipe. The 12” diameter pipe has a total of 36 - 0.375” diameter holes per
foot of pipe (area at which water enters the backfill envelop, A = 0.0276 ft2/foot of pipe).
Assume the pipe is full; determine the outfall rate of storm water through the pipe alone, (no
backfill) and the acceptance rate of the soil envelope.
A) The outfall rate of the 12” pipe has been determined using the aforementioned procedure
for determining the free outflow of a perforated pipe. Q pipe free = 0.086 ft3/s/ft = 38.7
gpm./foot of pipe.
∆
Figure 1.
B).Using Darcy’s Law one can solve for the flow through the soil.
Q s = KiA
Where, Q = Flow rate through soil, ft3/s
K = The permeability of the soil = 0.0375 ft/s
i = Hydraulic gradient (∆H/L), ft/ft
A = Area (sum of the areas from the perforations) = 0.0276 ft2
Q s = 0.0375
ft 4 ft
ft 3
x
x 0.0276 ft 2 = 0.0014
per foot of soil along the pipe
s 3 ft
s
Or
Q s = 0.63
gallons
per foot of soil along the pipe , Q s << Q P
min.
As the example shows, the flow rate through the soil is much less than the flow rate through the
pipe perforations. Although the area at which water can reach the soil is determined by the pipe
perforations, the surrounding soil determines the flow rate through the soil. When designing
drainage or recharge systems, one should reference the minimum inlet areas listed in ADS
Product Note 3.106, AASHTO M294, or contact the pipe manufacturer for a detailed explanation
of its pipe’s perforation pattern.
OUTFLOW - ADS PIPE
PIPE NOT FULL
120
FLOW (GPM/FT)
100
80
60
40
20
0
0
2
4
6
8
10
12
HEAD (INCHES)
Chart 1.
14
16
18
20
22
ORIFICE EQUATION
14
12
FLOW (CFS)
10
8
6
4
2
0
0
5
10
15
HEAD (FEET)
Chart 2.
20
25
30
OUTFLOW - ADS PIPE
3" CLASS II TYPE CP
FULL FLOW
180
160
y = -0.0304x2 + 4.142x + 25.629
3" Class 2 CP
Poly. (3" Class 2 CP)
140
FLOW (GPM/FT)
120
100
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
HEAD (INCHES)
32
34
36
38
40
42
44
46
48
50
52
54
56
OUTFLOW - ADS PIPE
4" CLASS II TYPE CP AND SP
FULL FLOW
180
160
4" Class 2 CP & SP
Poly. (4" Class 2 CP & SP)
2
y = -0.0263x + 3.8693x + 29.597
140
FLOW (GPM/FT)
120
100
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
HEAD (INCHES)
32
34
36
38
40
42
44
46
48
50
52
54
56
OUTFLOW - ADS PIPE
5" CLASS II TYPE CP
FULL FLOW
200
180
2
y = -0.0261x + 4.1523x + 34.766
5" class 2 CP
Poly. (5" class 2 CP)
160
FLOW (GPM/FT)
140
120
100
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
HEAD (INCHES)
34
36
38
40
42
44
46
48
50
52
54
56
58
OUTFLOW - ADS PIPE
6" CLASS II TYPE SP AND CP
FULL FLOW
200
2
y = -0.0258x + 4.169x + 32.912
180
6" Class 2 CP & SP
Poly. (6" Class 2 CP & SP)
160
FLOW (GPM/FT)
140
120
100
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
HEAD (INCHES)
34
36
38
40
42
44
46
48
50
52
54
56
58
60
OUTFLOW - ADS PIPE
8" CLASS II TYPE SP AND CP
FULL FLOW
200
180
8" Class 2 CP & SP
Poly. (8" Class 2 CP & SP)
160
2
y = -0.0237x + 3.9369x + 29.577
FLOW (GPM/FT)
140
120
100
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
HEAD (INCHES)
34
36
38
40
42
44
46
48
50
52
54
56
58
60
OUTFLOW - ADS PIPE
10" CLASS II TYPE SP AND CP
FULL FLOW
160
2
y = -0.0167x + 3.0052x + 23.075
140
10" Class 2 CP & SP
Poly. (10" Class 2 CP & SP)
FLOW (GPM/FT)
120
100
80
60
40
20
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
HEAD (INCHES)
36
38
40
42
44
46
48
50
52
54
56
58
60
62
64
OUTFLOW - ADS PIPE
12" CLASS II CP SLOT
FULL FLOW
100
2
y = -0.0107x + 1.9688x + 14.155
90
80
12" Class 2 CP Slot
Poly. (12" Class 2 CP Slot)
FLOW (GPM/FT)
70
60
50
40
30
20
10
0
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
HEAD (INCHES)
44
46
48
50
52
54
56
58
60
62
64
OUTFLOW - ADS PIPE
12" CLASS II TYPE SP AND CP
FULL FLOW
140
2
y = -0.0173x + 3.0082x + 12.273
120
12" Class 2 CP & SP
Poly. (12" Class 2 CP & SP)
FLOW (GPM/FT)
100
80
60
40
20
0
14
16
18
20
22
24
26
28
30
32
34
36
38
40
HEAD (INCHES)
42
44
46
48
50
52
54
56
58
60
62
OUTFLOW - ADS PIPE
15" CLASS II TYPE SP AND CP
FULL FLOW
120
15" Class 2 CP & SP
Poly. (15" Class 2 CP & SP)
100
2
y = -0.0124x + 2.2553x + 5.4732
FLOW (GPM/FT)
80
60
40
20
0
14
16
18
20
22
24
26
28
30
32
34
36
38
40
HEAD (INCHES)
42
44
46
48
50
52
54
56
58
60
62
64
OUTFLOW - ADS PIPE
18" CLASS II TYPE SP AND CP
FULL FLOW
120
18" Class 2 CP & SP
Poly. (18" Class 2 CP & SP)
100
2
y = -0.0109x + 2.1202x + 3.777
FLOW (GPM/FT)
80
60
40
20
0
18
20
22
24
26
28
30
32
34
36
38
40
42
44
HEAD (INCHES)
46
48
50
52
54
56
58
60
62
64
66
68
OUTFLOW - ADS PIPE
24" CLASS II TYPE SP AND CP
FULL FLOW
90
2
y = -0.0088x + 1.8439x - 3.0525
80
24" Class 2 CP and SP
Poly. (24" Class 2 CP and SP)
70
FLOW (GPM/FT)
60
50
40
30
20
10
0
24
26
28
30
32
34
36
38
40
42
44
46
48
50
52
HEAD (INCHES)
54
56
58
60
62
64
66
68
70
72
74
76
OUTFLOW - ADS PIPE
30" CLASS II TYPE SP
FULL FLOW
70
2
30" Class 2 SP
Poly. (30" Class 2 SP)
y = -0.0063x + 1.4143x - 6.4484
60
FLOW (GPM/FT)
50
40
30
20
10
0
30
35
40
45
50
55
60
HEAD (INCHES)
65
70
75
80
85
OUTFLOW - ADS PIPE
36" CLASS II TYPE SP
FULL FLOW
60
2
y = -0.0046x + 1.1164x - 8.4316
36" Class 2 SP
Poly. (36" Class 2 SP)
50
FLOW (GPM/FT)
40
30
20
10
0
34
39
44
49
54
59
64
HEAD (INCHES)
69
74
79
84
89
OUTFLOW - ADS PIPE
42" CLASS II TYPE SP
FULL FLOW
60
42" Class 2 SP
Poly. (42" Class 2 SP)
2
y = -0.0044x + 1.1378x - 12.073
50
FLOW (GPM/FT)
40
30
20
10
0
40
45
50
55
60
65
70
HEAD (INCHES)
75
80
85
90
95
OUTFLOW - ADS PIPE
48" CLASS II TYPE SP
FULL FLOW
60
48" Class 2 SP
Poly. (48" Class 2 SP)
50
2
y = -0.0042x + 1.1346x - 15.562
FLOW (GPM/FT)
40
30
20
10
0
46
51
56
61
66
71
76
HEAD (INCHES)
81
86
91
96
101
OUTFLOW - ADS PIPE
60" CLASS II TYPE SP
FULL FLOW
60
60" Class 2 SP
Poly. (60" Class 2 SP)
2
y = -0.0034x + 1.0124x - 20.276
50
FLOW (GPM/FT)
40
30
20
10
0
58
63
68
73
78
83
88
HEAD (INCHES)
93
98
103
108
113