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TRANSCRIPT
Basic Hydrology
Time of Concentration Methodology
By: Paul Schiariti, P.E., CPESC
Mercer County Soil Conservation District
What is the Time of Concentration?
The time it takes for runoff to travel from the most hydraulically distant point in the watershed to a
point of interest.
What is the most Hydraulically Distant Point in the watershed?
Is it a “hydraulic distance” or a “hydraulic time”?
Is there a difference?
Hydraulically Most Distant Point?
Path “A” is 1000 ft. long with a Time of Concentration = 1.00 Hours
Path “B” is 750 ft. long with a Time of Concentration = 1.25 Hours
Where is the “Correct TC Flow Path?
What is the difference in TC for both Flow Paths?
Path “B” TC = 0.39 Hours, Path “A” TC = 0.20 Hours
What is the difference in QPEAK for the two Flow Paths & which is correct?
Approximately 9 Acres of the 10 Acres flows similar to Path “B”,
therefore this path is representative of 90% of the
drainage area, and realistically better represents the watershed
The use of TC Flow Path “B” represents an under-estimation of QPEAK by 19
to 20%.
Would this be an issue if it was the Pre-
Development analysis?
Three Components of the Segmental Time of Concentration Method
1. Sheet Flow: “Sheet flow is flow over plane surfaces. It usually occurs in the headwater of streams.”
The most sensitive component of the TC. Pay very close attention to the Manning’s Roughness Coefficient. Pay very close attention to the ground surface slope. The maximum sheet flow length should be no greater than 125 to 150 ft.
2. Shallow Concentrated Flow: “After a maximum of 300 feet, sheet flow usually becomes shallow concentrated flow.”Note: This 300 ft. value has since been revised down to a maximum of 150 ft. on very uniform surfaces. The latest version of WinTR-55 only allows up to 100 ft. of sheet flow.
3. Channel Flow: Channel flow occurs within swales, channels, streams, ditches and piped storm drainage systems. Velocities are computed for channel flow based upon Manning’s open channel flow equation.
TR-55 Segmental Time of ConcentrationSheet Flow Travel Time Component
P2 values are obtained from NRCS 24 Hour Design Storm Rainfall Depths.
TR-55 Segmental Time of ConcentrationShallow Concentrated Flow and Channel Flow Component
How sensitive is the Sheet Flow equation to Manning’s “n”?
Sheet Flow Equation:TT= (.007) x (n) 0.8 x (L) 0.8
P20.5 x S 0.4
• Example: L = 125 ft.P2 = 3.00 In.S = 0.006 ft / ft
Lets say an “n” value of 0.05 was mistakenly used when an “n” value of 0.24 was the appropriate value. What effect will this have on the Time of Concentration? What effect will this have on the peak discharge rates?
“n” = 0.05: TT= (.007) x (0.05) 0.8 x (125) 0.8 = 0.136 Hours (Incorrect)3.0 0.5 x 0.006 0.4
“n” = 0.24: TT= (.007) x (0.24) 0.8 x (125) 0.8 = 0.475 Hours (Correct)3.0 0.5 x 0.006 0.4
This represents an under-estimation of the Time of Concentration of 71%!!!
How does this effect the peak Discharge?
Drainage Area = 20.00 AcresRunoff Curve Number = 74
10 Year Storm Precipitation = 5.00 InchesAdditional Travel Time for Shallow Concentrated Flow Plus
Channel Flow = 0.50 Hours
TC1 = 0.136 Hours + 0.40 Hours = 0.536 HoursTC2 = 0.475 Hours + 0.40 Hours = 0.875 Hours
Q0.05 = 30.70 cfs (Incorrect)Q0.24 = 24.10 cfs (Correct)
Difference in Peak Discharge Rates = 6.60 cfs
Over estimates the peak discharge by 27.4% !!
Effect on the Runoff Hydrograph for the different TC’s
Not only is the actual Peak Discharge different…
But the timing of the Peak Discharge is different as well.
What is the correct Manning’s n value?
A
B
Manning’s “n” for “Maintained Turf Grass” should almost always be = 0.24
Percent Increase In The Sheet Flow Travel Time Related to Change In Ground Slope
0.0
10.0
20.0
30.0
40.0
50.0
60.0
0.50
0.60
0.70
0.80
0.90
1.00
1.10
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00
Ground Slope In %%
Dec
reas
e In
Shee
t Flo
w Tt
An over-estimation of ground slope from 1.00 % to 2.00 % results in an under-estimation in the Sheet Flow
component of the Time of Concentration by 25 %.
25 %
Example Time of Concentration Calculation
100
99989796
959493929293
93 92 92 93 94 95 96 97 98 99
"A"- 100.5
"B"- 99.5
"C"- 96.0
"D"- 93.3
X
X
X
X
Channel Flow
ShallowConcentrated Flow Sheet Flow
250 ft. 125 ft. 100 ft.
Note: The individual segment lengths are not the horizontal distances, but the linear distances along the
flow path line.
Example - Continued
1. Compute the Sheet FlowTravel Time Component of the Time of Concentration:
“A” –100.5
“B” –99.5
What surface description best categorizes this type of ground cover for the purpose of choosing a Manning’s “n” Roughness
Coefficient ?
1 0 0
9 9
" A " - 1 0 0 . 5
" B " - 9 9 . 5
X
X
S h e e t F lo w1 0 0 f t .
Which Manning’s “n” value most closely mimics this specific ground cover?
We can immediately eliminate the following:
Smooth SurfacesFallow (No Residue)
Cultivated SoilWoods
This leaves the following choices:GrassRange
Range is defined as: “An extensive tract of open land on which livestock wander and graze.”
This is not a range !
This leaves us with the grass options:
Best fit is Dense Grasses – “n” = 0.24
Compute the Sheet Flow Travel Time Component:
Sheet Flow Equation:TT= (.007) x (n) 0.8 x (L) 0.8
P20.5 x S 0.4
L = 100 ft.P2 = 3.00 In.S = (100.5 – 99.5)/ 100 = 0.01 ft / ftn = 0.24
TT= (.007) x (0.24) 0.8 x (100) 0.8 = 0.324 Hrs3.0 0.5 x 0.010 0.4
• The next component of the Time of Concentration is the shallow Concentrated flow Travel Time portion.
Shallow Concentrated Flow Component of the Time of Concentration
1 0 0
9 9
9 7 9 8 9
" B " - 9 9 .5
" C " - 9 6 .0
X
X
S h a l lo wC o n c e n t r a t e d F lo w S
1 2 5 f t .
“B” –99.5
“C” –96.0
Shallow Concentrated Flow is 125 ft. (non-paved) at (99.5-96.0) /125 = 0.028 ft/ft
Enter Figure 3-1 to arrive at the Average Velocity
0.028 ft/ft
2.7 fps
TT = 125 / 3600 x 2.70 = 0.013 hrs.
The actual equation used to determine the velocity for Shallow Concentrated flow is based on:
TT = L * (58,084.2 * s0.5) -1-or-
TT = L3600 x 16.1345 x S0.5
Therefore: V = 16.1345 x S0.5
Channel Flow Component of the Time of Concentration
9897965
95 96 97
"C"- 96.0
"D"- 93.3 X
X
Channel Flow
Con
250 ft.
“C” –96.0
“D” –93.3
The Channel Slope is 250 ft. at (96.0-93.3)/250 = 0.0108 ft/ft
Note: The channel does not have to possess a visible water surface to be considered channel flow.
Solve Manning’s equation to arrive at the Channel Velocity
Wow ! There are several unknown variables here. How
are we going to assign values to them ?
The first thing we need to know is the channel cross sectional
geometry.
21
5 ft
1.5 ft
Assume a reasonable flow depth – say 1.5 ft, and solve for
the cross sectional flow area and the wetted perimeter.
Approximate channel geometry
The first step is to compute the Hydraulic Radius:Compute the Hydraulic Radius as follows:
The Hydraulic Radius is equal to the cross – sectional flow area divided by the wetted perimeter:
A = (5.0 ft. x 1.5 ft.) + [(1.5 ft. x 2) x 1.5 ft.] = 12.0 s.f.WP = 5.0 ft. + [2 x (3.0 ft.2 + 1.5 ft.2)1/2] = 18.42 ft.
R = 12.0 s.f. / 18.42 ft. = 0.651 ft.
How do we compute the Manning’s “n” roughness coefficient?
21
5 ft
1.5 ft
SUPPLEMENT A contained within Appendix A8 of the NJ STANDARDS entitled “Method for Estimating Manning’s “n”” contains a practical methodology based upon
“Cowan's Equation”:
n =(n0 + n1 + n2 + n3 + n4) x m5
Where:n = Manning’s “n” valuen0 = the portion of the n value that represents the channel material in a straight, uniform smooth reach n1 = the additional value added to correct for the effect of channel surface irregularitiesn2 = the additional value for variations in shape and size of the channel cross sectionthrough the reach n3 = the additional value for obstructions (such as beaver dams, debris dams, stumps, downed trees, and root wads extending into the channel) n4 = the additional value for vegetation in the channel m5 = the correction factor for the meandering of the channel
Method used to determine Manning’s n value for earthen channels
(Not to be confused with Manning’s “n” for Sheet Flow)
Manning’s “n” values to be used for Cowan’s method for channel roughness
1.3Severe 1.15Appreciable
1m5Minor Degree of Meandering
0.050-0.100 Very high
0.025-0.050 High
0.010-0.025 Medium
0.005-0.010 n4Low Vegetation
0.040-0.060 Severe
0.020-0.030 Appreciable
0.010-0.015 Minor
0n3Negligible Relative Effect of Obstructions
0.010-0.015 Alternating frequently
0.005Alternating occasionally
0n2Gradual Variations of Channel Cross Section
0.02Severe
0.01Moderate
0.005Minor
0n1Smooth Degree of Irregularity
0.028Coarse gravel 0.024Fine gravel 0.025Rock cut 0.02n0Earth Material Involved
Values Channel Conditions
Compute Manning’s “n” value for the channel
n0 = Earth Channel = 0.02n1 = Smooth Irregularity = 0.00n2 = Gradual Section Variations = 0.00n3 = Negligible Obstructions = 0.00n4 = Low to Medium Vegetation = 0.01
0.03m5 = Minor Meandering = 1.00Manning’s “n” value = 0.03 x 1.00 = 0.03
Compute the Travel Time for the channel section
V = 1.486 x R 2/3 x S ½
nV = 1.486 x 0.651 2/3 x 0.0108 ½ = 3.87 fps
0.03TT = 250 / 3600 x 3.87 = 0.0179 hours
The total Time of Concentration = TT1 + TT2 + TT3 = TC
TC = 0.324 Hr. + 0.013 Hr. + 0.018 Hr. = 0.355 Hr.
What if our depth of flow assumption was incorrect?
Lets say the actual flow depth was 0.5 ft. as opposed to our original assumption of 1.5 ft:
A = (5.0 ft. x 0.5 ft.) + [(0.5 ft. x 2) x 0.5 ft.] = 3.00 s.f.WP = 5.0 ft. + [2 x (1.0 ft.2 + 0.5 ft.2)1/2] = 7.24ft.
R = 12.0 s.f. / 18.42 ft. = 0.414 ft.
V = 1.486 x 0.414 2/3 x 0.0108 ½ = 2.86 fps 0.03
TT = 250 / 3600 x 2.86 = 0.024 hoursRemember our original TT was 0.018 hours!!
Really, not that much of a difference.
21
5 ft
0.5 ft
What is the correct Manning’s “n” value for Sheet Flow ?
Is this Fallow (no residue) or Cultivated Soils: Residue Cover <
20%; n = 0.05 or 0.06 ?
What is the correct Manning’s “n” value for Sheet Flow ?
Cultivated Soils: Residue Cover > 20%; n = 0.17
What is the correct Manning’s “n” value for Sheet Flow ?
Smooth Surface (concrete, asphalt, gravel or bare soil); n = 0.011
What is the correct Manning’s “n” value for Sheet Flow ?
Woods; Light Underbrush;
n = 0.40
Summary:
1. Make sure the flow path is representative of the drainage area.
2. Check the Manning’s “n” value in the sheet flow equation.
3. Check the slope used in the sheet flow equation.
4. Do the field conditions agree with the analysis?
5. If the Tc goes up from the pre-development to the post-development, there may be an error.
6. Tc should typically go down from pre to post-development.
Questions and (hopefully!) Answers ?