|
Note: In subdivisions with no through streets, a fifty-five
(55) foot pavement radius and a sixty-seven (67) foot right-of-way
radius will be required on at least one (1) cul-de-sac in order to
facilitate school bus circulation. For individual cul-de-sacs the
fifty-five (55) foot pavement radius and sixty-seven (67) foot right-of-way
radius shall only be required if the cul-de-sac exceeds one thousand
three hundred (1,300) feet in length.
|
|
Flow quantities. Flow quantities are to be
calculated by the "rational method" in which:
| |
|
Q = API
| |
|
Where:
| |
|
Q = runoff in cubic feet per second
| |
|
A = tributary area in acres
| |
|
I = average intensity of rainfall (inches per hour) for a given
period and a given frequency
| |
|
P = runoff factor based on runoff from previous and impervious
surfaces
| |
|
P (Runoff Factors) for various impervious conditions are shown in Table 4-1 following this Section 400.220.
| |
|
P.I. values for various impervious conditions are shown in Tables 4-2 to 4-4 following this Section 400.220.
|
Percent Imperviousness
|
20 Minute Duration
| ||
---|---|---|---|
15 Year
|
20 Year
| ||
5
|
1.7
|
1.8
| |
10
|
1.8
|
1.9
| |
20
|
2.0
|
2.1
| |
30
|
2.2
|
2.3
| |
40
|
2.4
|
2.5
| |
50
|
2.6
|
2.7
| |
90
|
3.4
|
3.5
| |
100
|
3.5
|
3.7
| |
*Roofs
|
4.2
|
6.0
| |
*For direct connection to sewer
|
Area (Abscissas)
|
"Ka" (Ordinates)
| |
---|---|---|
300 to 449 acres
|
1.00
| |
450 to 549 acres
|
.99
| |
550 to 749 acres
|
.98
| |
750 to 999 acres
|
.97
| |
1,000 to 1,280 acres
|
.96
| |
1,281 to 1,600 acres
|
.95
| |
1,601 to 1,920 acres
|
.92
| |
1,921 to 2,240 acres
|
.91
|
|
hf = L x Sh
| |
|
Where:
| |
|
hf = difference in water surface elevation or head in feet in
length L
| |
|
L = length in feet of pipe or channel
| |
|
Sh = hydraulic slope required for a pipe
of given diameter or channel of given cross section and for a given
roughness "n", expressed as feet of slope per foot of length
| |
|
From Manning's formula: Sh = [V n / (1.486
R 0.667)] 2
| |
|
Where:
| |
|
R = hydraulic radius of pipe, conduit or channel (feet) (ratio
of flow area/wetted perimeter)
| |
|
V = velocity of flow in feet per second (fps)
| |
|
n = Manning's value for coefficient of roughness
| |
|
Use:
| |
|
n = .013 for pipes of concrete, vitrified clay and PVC pipe
| |
|
n = .012 for formed monolithic concrete, i.e., vertical wall
channels, box culverts and for R.C.P. over forty-eight (48) inches
in diameter
| |
|
n = .015 for concrete lining in ditch or channel inverts and
trapezoidal channels
| |
|
n = .020 for grouted riprap lining on ditch or channel side
slopes
| |
|
n = .033 for gabion walled channels
|
|
Hti = (V2/2g)
| |
|
Where:
| |
|
V = Velocity in flow of outgoing pipe
| |
|
g = Acceleration of gravity (32.2 ft/sec/sec)
|
Change in Direction of Flow (A)
|
Multiplier of Velocity Head of Water Being Turned (K)
| |
---|---|---|
90 degrees
|
0.7
| |
60 degrees
|
0.55
| |
45 degrees
|
0.47
| |
30 degrees
|
0.35
| |
15 degrees
|
0.18
| |
0 degrees
|
0.0
| |
Other angles
|
By interpolation
|
Formula:
| ||
|
HL = K(VL)2/2g
| |
Where:
| ||
|
HL = Feet of head lost in manhole due
to change in direction of lateral flow
| |
|
VL = Velocity of flow in lateral in ft/sec
| |
|
g = Acceleration of gravity (32.2 ft/sec/sec)
| |
|
K = Multiplier of velocity head of water being turned
|
|
Losses in a junction chamber for combining large flows shall
be minimized by setting flowline elevations so that pipe centerlines
(spring-lines) will be approximately in the same planes.
| |
|
At junction points for combining large storm flows, a manhole
with a slotted cover shall be provided.
| |
|
A computation method for determining junction chamber losses
is presented below:
| |
|
Hj = Δy + Vh1 Vh2
| |
|
Where:
| |
|
Hj = junction chamber loss (ft)
| |
|
Δy = change in hydraulic grade line through the junction
in feet
| |
|
Vhl = upstream velocity head
| |
|
Vh2 = downstream velocity head
| |
|
Where:
| |
|
Δy = [(Q2V2) - ((Q1V1) + {(Q3V3Cos e-3) + QnVnCos e-n)})]
| |
|
0.5 (A1+A2) g
| |
|
Where:
| |
|
Q2 = Discharge in cubic feet per second
(cfs) at the exiting conduit
| |
|
V2 = Velocity in feet per second (fps)
at the exiting conduit
| |
|
A2 = Cross-sectional area of flow in
square feet for the exiting conduit
| |
|
Q1 = Discharge in cfs for the incoming
pipe (main flow)
| |
|
V1 = Velocity in fps for the incoming
pipe (main flow)
| |
|
A1 = Cross sectional area of flow in
square feet for the incoming pipe (main flow)
| |
|
Q3, Qn = Discharge(s)
in cfs for the branch lateral(s)
| |
|
V3, Vn = Velocity(ies)
in fps for the branch lateral(s)
| |
|
Ө3, Өn = The angle between the axes of the exiting pipe and the branch
lateral(s)
| |
|
g = Acceleration of gravity (32.2 ft/sec/sec)
| |
|
Where:
| |
|
Ө = is the angle between the axes of the outfall and the
incoming laterals
|
|
The upstream hydraulic grade line may be calculated as follows:
| |
|
Hu = [VD2/2g] - [((Qu/QD)(1-K)(Vu2/2g))
+ ((QL1/QD)(1-K)(VL12/2g)) + ((QLN/QD)(1-K)(VLN2/2g))] + HD
| |
|
Where:
| |
|
Hu = Upstream hydraulic grade line in
feet
| |
|
Qu = Upstream main line discharge in
cubic feet per second
| |
|
QD = Downstream main line discharge in
cubic feet per second
| |
|
QLI-QN = Lateral
discharges in cubic feet per second
| |
|
Vu = Upstream main line velocity in feet
per second
| |
|
VD = Downstream main line velocity in
feet per second
| |
|
VLI-VLN = Lateral
velocities in feet per second
| |
|
HD = Downstream hydraulic grade line
in feet
| |
|
K = Multiplier of velocity of water being turned
| |
|
G = Acceleration of gravity, 32.2 ft/sec/sec
| |
|
The above equation does not apply when two (2) almost equal
and opposing flows, each perpendicular to the downstream pipe, meet
and no other flows exist in the structure. In this case the head loss
is considered as the total velocity head of the downstream discharge.
|
Sub-critical Flow:
| ||
ΔHW = 1.15 (V2/2grc) [b + D (ZL + ZR)]
| ||
Super-critical flow:
| ||
ΔHW = 2.6 (V2/2grc) [b + D (ZL + ZR)]
|
|
Sub-critical flow:
|
|
ΔHW = (V2b/2grc)
|
|
Super-critical flow:
|
|
ΔHw = (V2b/grc)
|
|
Where:
|
|
ΔHw = Change in water height above
the centerline water surface
|
|
V = Average velocity of design flow in Fps
|
|
g = Acceleration of gravity (32.2 ft/sec/sec)
|
|
rc = Radius of curve on horizontal alignment
in feet
|
|
b = Base width of channel in feet
|
|
D = Depth of flow in straight channel
|
|
ZL = Left side slope (ft/ft)
|
|
ZR = Right side slope (ft/ft)
|
|
Ht = Kt ΔHH
| |
|
Where:
| |
|
Ht = Conversion loss
| |
|
Kt = Coefficient of head loss in transition
| |
|
ΔHH = Absolute change in velocity
head
|
|
Average design values for Kt are presented
in the table below:
|
Type of Transition
|
Contracting Section
|
Expanding Section
| |
---|---|---|---|
Warped
|
0.10
|
0.20
| |
Wedge
|
0.20
|
0.50
| |
Cylinder-quadrant
|
0.15
|
0.25
| |
Straight line
|
0.30
|
0.50
| |
Square end
|
0.40
|
0.75
|
See Figure 4-4 for sketches of each type of transition.
|
HLe = Ke (V2/2g)
| ||
Where:
| ||
Ke = Coefficient of head loss for enlargements
= 1
| ||
V = Change in velocities between incoming and outgoing sections
| ||
g = Acceleration of gravity (32.2 ft/sec/sec)
| ||
The flow in a sudden contraction is first contracted and then
expanded resulting in high losses as compared to a sudden enlargement.
Thus the head loss at a sudden contraction, HLc is:
| ||
HLc = Kc(ΔV2/2g)
| ||
Where:
| ||
Kc = Coefficient of head loss for contractions
= 0.5
| ||
V = Change in velocities between incoming and outgoing sections
| ||
g = Acceleration of gravity, ft/sec/sec
|