Partial Flow Conditions For Culverts · Partial Flow Conditions For Culverts Sewers, both sanitary...
Transcript of Partial Flow Conditions For Culverts · Partial Flow Conditions For Culverts Sewers, both sanitary...
Partial Flow Conditions For Culverts Sewers, both sanitary and storm, are designed to carry a peak flow based on anticipated land development. The hydraulic capacity of sewers or culverts constructed of precast circular concrete pipe flowing full under gravity conditions on a known slope Is readily calculated from the Manning Formula. Most sewers, however, are designed to operate under partial flow conditions. Culverts operate un-der either inlet control or outlet control. The type of control under which a particular culvert operates is dependent upon all the hydraulic factors present. Culverts operating under inlet control will always flow partially full while those operating under outlet control can flow full or partially full.
Determination of the depth and velocity of flow in pipe flowing partially full is therefore frequently necessary. This design data presents a method for determining the values of the partial flow depth and velocity in circular concrete pipe through the use of a series of partial flow curves which eliminate tedious trial and error computations.
A complete discussion of the hydraulics of sewers is presented in Design Data 4, and the hydraulics of culverts is presented in Design Data 8.
HydrauliCs oF ConCrete PiPe
The most widely accepted formula for evaluating the hydraulic capacity of nonpressure pipe is the Manning Formula. This formula is:
Q = x A x R2/3 x So1/2 (1)1.486
n
Where: Q = flow quantity, cubic foot per second n = Manning’s roughness coefficient A = cross-sectional area of flow, square feet R = hydraulic radius, feet SO = slope, feet of vertical drop per foot of horizontal distance
Tables 1-3 list the full flow area, AF, hydraulic radius, R, and a constant, C1. For a specific pipe size under full flow conditions, the first three terms of the right hand side of Manning’s Formula equal a constant [C1 = (1.486/n) x A x R2/3]. Values of C1 are presented for the more com-monly used values, 0.010, 0.011, 0.012, and 0.013, for the roughness coefficient n for precast concrete pipe. Utilizing the appropriate value of SO
1/2, and C1 from Tables 1-3, the
full flow quantity, QF, may be determined from Manning’s Formula conveniently expressed as:
QF = C1 x So 1/2 (2)
Once the full flow quantity, QF, has been determined, the average velocity, VF, for full flow conditions may be calculated from the basic hydraulic relationship:
VF = (3)
QF
AFWhere: QF = flow quantity, flowing full, cubic feet per second VF = the average velocity, flowing full, feet per second AF = cross-sectional area of flow, flowing full, square feet
Partial FloW HydrauliC eleMents
For any size of pipe, curves showing the partial flow relationship of the hydraulic elements, flow quantity, area of flow, hydraulic radius, and velocity of flow in terms of the full flow conditions can be plotted. Figures 1-4 provide such hydraulic element curves for circular, elliptical and arch concrete pipe.
design MetHod
To determine the value of any one of the partial flow hydraulic elements for circular concrete pipe, the following three step design method is suggested:
1. Determine the full flow quantity, QF, and velocity, VF, utilizing Tables 1-3 or other appropriate methods.2. Determine the value of the ratio of partial flow to full flow of the known hydraulic elements.3. Determine the values of the unknown hydraulic elements through the use of the partial flow curves.
Design Data 16
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eXaMPle 1
given: A 48-inch diameter circular concrete pipe storm sewer, with n equal to 0.012 and flowing one-third full.
Find: Slope required to maintain a minimum velocity of 3 feet per second.
solution: Enter Figure 1 on the vertical scale at Depth of Flow = 0.33 and project a horizontal line to the curved line representing velocity. On the horizontal scale directly beneath the point of intersection read a value of 0.81 which represents the proportional value for full flow:
= 0.81
VF
V
Since the actual velocity required is 3 feet per second:
VF = 0.813
VF = 3.7
Entering Table 1 at a pipe diameter of 48 inches and an n value of 0.012, the C1
value is 1556 and AF is 12.566 square feet.Combining Equations 2 and 3 and solving
for SO:
SO = C1
VFAF[
[2
SO = 1556(3.7) (12.566)[
[2SO = 0.00089 feet per foot
answer: The slope requires to maintain a minimum velocity of 3 feet per second at on-third full is 0.00089 feet per foot.
eXaMPle 2
given: A vertical elliptical concrete sewer is designed to flow 3/4 full with a design flow, Q, of 200 cubic feet per second. The slope is 0.01 and n is equal to 0.013.
Find: The required pipe size.
solution: Enter Figure 2 at a depth of flow of 0.75 on the vertical scale. Project a line to the flow curve, Q, and from the intersection, project a vertical line to the horizontal scale and read a value of 0.87 which rep- resents the proportional value for full flow:
= 0.87
QQF
Since the actual flow required is 200 cubic feet per second:
QF =2000.87
QF = 230 cubic feet per second
Using Equation 2, to calculate C1 :
C1 = QF
So1/2
C1 = 230(0.01)1/2
C1 = 2300
Entering Table 2 with C1 equal to 2300, and n equal to 0.013, the vertical elliptical pipe with a C1 value equal to, or greater that 2300 is 76 x 48-inch.
answer: Select a 76 x 48-inch vertical elliptical pipe.
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eXaMPle 3
given: A 34 x 53-inch horizontal elliptical concrete pipe storm sewer outfall has an n value assumed to be 0.012 and is to be installed on a 10 percent slope. To meet future expansion conditions, the pipe will be designed to flow 1/2 full.
Find: The outlet velocity.
solution: Entering Table 2 at a horizontal elliptical size of 34 x 53 inches and an n value of 0.012, the C1 value is 1156 and AF is 10.2 square feet. From Equation 2:
QF = C1So1/2
QF = 1156 x (0.10)1/2
QF = 366 cubic feet per second
The full flow velocity can be calculated from Equation 3:
VF = QF/AF
VF = 366/10.2
VF = 36 feet per second
Enter Figure 3 at 0.5 on the vertical scale and project a horizontal line to the velocity curves. From this intersection, project a vertical line to the horizontal scale. The ratio of partial flow V to full flow VF is 1.0:
= 1.0 VF
V = VF x 1.0
V = 36 x 1.0
V = 36 feet per second
V
answer: The outlet velocity is 36 feet per second.
eXaMPle 4
given: A 40 x 65-inch arch concrete storm sewer outfall has an n value assumed as 0.012 and is to be installed on a 10 percent slope. To meet future expansion conditions, the pipe will be designed to flow 1/2 full.
Find: The outlet velocity.
solution: Enter Table 3 at an arch size of 40 x 65 inches and an n value of 0.012, the C1 value is 1783 and AF is 14.3 square feet. From Equation 2:
QF = C1So1/2
QF = 1783 x (0.10)1/2
QF = 564 cubic feet per second
The full flow velocity can be calculated from Equation 3:
VF = QF/AF
VF = 564/14.3
VF = 39 feet per second
Enter Figure 4 at 0.5 on the vertical scale and project a horizontal line to the velocity curve, V. From this intersection, project a vertical line to the horizontal scale. The ratio of partial flow V to full flow VF is 1.04:
= 1.04 VF
V = 39 x 1.04
V = 41 feet per second
V
answer: The outlet velocity is 41 feet per second.
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DPipe
Diameter(Inches)
AArea
(Square Feet)
R Hydraulic Radius(Feet)
Value of C1
n=0.010 n=0.011 n=0.012 n=0.013
810121518
0.3490.5450.7851.2271.767
0.1670.2080.2050.3120.375
15.828.446.484.1137
14.325.842.176.5124
13.123.638.670.1114
12.121.835.764.7105
2124273033
2.4053.1423.9764.9095.940
0.4370.5000.5620.6250.688
206294402533686
187267366485624
172245335444574
158226310410530
3642485460
7.0699.62112.56615.90419.635
0.7500.8751.0001.1251.250
8671308186725573385
7881189169823253077
7221090155621312821
6661006143619672604
6672788490
23.75828.27433.18338.48544.170
1.3751.5001.6251.7501.875
43645504681583049985
39675004619575499078
36364587567969208321
33574234524263887684
96102108114120
50.26656.74563.61770.88278.540
2.0002.1252.2502.3752.500
1185019340162301875021500
1078012670147601704019540
987811620135301562017920
911910720124901442016540
126132138144
86.59095.033103.870113.100
2.6252.7502.8753.000
24480277203121034960
22260252002837031780
20400231002601029130
18830213302401026890
x A x R2/3 1.486
n
table 1 Full Flow Coefficient Values Circular Concrete Pipe
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Pipe SizeR x S (HE)S x R (VE)(Inches)
Approximate Equivalent
Circular Diameter (Inches)
AArea
(Square Feet)
R Hydraulic Radius(Feet)
Value of C1
n=0.010 n=0.011 n=0.012 n=0.013
14 x 2319 x 3022 x 3424 x 3827 x 42
1824273033
1.83.34.15.16.3
0.3670.4900.5460.6130.686
138301405547728
125274368497662
116252339456607
108232313421560
29 x 4532 x 4934 x 5338 x 6043 x 68
3639424854
7.48.810.212.916.6
0.7360.8120.8750.9691.106
8911140138618782635
8101036126017072395
746948115615652196
686875106714452027
48 x 7653 x 8358 x 9163 x 9868 x 106
6066727884
20.524.829.534.640.1
1.2291.3521.4751.5981.721
34914503568070278560
31744094516463887790
29103753473458567140
26863464437054066590
72 x 11377 x 12182 x 12887 x 13692 x 143
9096102108114
46.152.459.266.474.0
1.8451.9672.0912.2152.340
1030012220143801677019380
936511110130701524017620
858410190119801397016150
79259403110601290014910
97 x 151106 x 166116 x 180
120132144
82.099.2118.6
2.4612.7072.968
221902863036400
201802602033100
184902386030340
170702202028000
x A x R2/3 1.486
n
table 2 Full Flow Coefficient Values elliptical Concrete Pipe
Pipe SizeR x S
(Inches)
Approximate Equivalent
Circular Diameter (Inches)
AArea
(Square Feet)
R Hydraulic Radius(Feet)
Value of C1
n=0.010 n=0.011 n=0.012 n=0.013
11 x 18131/2 x 22151/2 x 2618 x 281/2
221/2 x 361/4
1518212430
1.11.62.22.84.4
0.250.300.360.450.56
65110165243441
59100150221401
5491137203368
5084127187339
265/8 x 433/4
315/18 x 511/8
36 x 581/2
40 x 6545 x 73
3642485460
6.48.811.414.317.7
0.680.800.901.011.13
7361125157921402851
6691023143519452592
613938131517832376
566866121416462193
54 x 8863 x10272 x 115
771/4 x 122871/8 x 138
72849096108
25.634.644.551.766.0
1.351.571.771.922.17
4641694196681185016430
4219631087891077014940
386757848056987213690
3569533974369112212640
967/8 x 1541061/2 x 1683/4
120132
81.899.1
2.422.65
2197528292
1997725720
1831223577
1690421763
x A x R2/3 1.486
n
table 3 Full Flow Coefficient Values arch Concrete Pipe
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Figure 1 relative Velocity and Flow in Circular Pipe for any design depth or Flow
Figure 2 relative Velocity and Flow in Vertical elliptical Pipe for any depth of Flow
FLOW, Q
AREA OF FLOW, A
VELOCITY, V
EXAMPLE 1
HYDRAULIC RADIUS, R
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
DE
PT
H O
F F
LOW
HYDRAULIC ELEMENTS - RATIO, PARTIAL FLOW TO FULL FLOW
EXAMPLE 2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
DE
PT
H O
F F
LOW
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
HYDRAULIC ELEMENTS - RATIO, PARTIAL FLOW TO FULL FLOW
FLOW, Q
AREA OF FLOW, A
VELOCITY, V
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Figure 3 relative Velocity and Flow in Horizontal elliptical Pipe for any depth of Flow
Figure 4 relative Velocity and Flow in arch Pipe for any depth of Flow
EXAMPLE 3
DE
PT
H O
F F
LOW
HYDRAULIC ELEMENTS - RATIO, PARTIAL FLOW TO FULL FLOW
FLOW, Q
AREA OF FLOW, A
VELOCITY, V
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
DE
PT
H O
F F
LOW
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2
HYDRAULIC ELEMENTS - RATIO, PARTIAL FLOW TO FULL FLOW
FLOW, Q
AREA OF FLOW, A
VELOCITY, V
EXAMPLE 4
Technical data herein is considered reliable, but no guarantee is made or liability assumed.
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