Basic Hydrology Time of Concentration Methodology

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 T C for both Flow Paths?
Path “B” T C = 0.39 Hours, Path “A” T C = 0.20 Hours

What is the difference in Q PEAK 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 T C Flow Path
“B” represents an underestimation
of Q PEAK 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 T C . 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 Concentration
Sheet Flow Travel Time Component
P 2 values are obtained from NRCS 24
Hour Design Storm Rainfall Depths.

TR-55 Segmental Time of Concentration
Shallow Concentrated Flow and Channel Flow Component

How sensitive is the Sheet Flow equation to Manning’s “n”?
Sheet Flow Equation:
T T= (.007) x (n) 0.8 x (L) 0.8
P 2 0.5 x S 0.4
• Example: L = 125 ft.
P 2 = 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: T T= (.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: T T= (.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 Acres
Runoff Curve Number = 74
10 Year Storm Precipitation = 5.00 Inches
Additional Travel Time for Shallow Concentrated Flow Plus
Channel Flow = 0.50 Hours
T C1 = 0.136 Hours + 0.40 Hours = 0.536 Hours
T C2 = 0.475 Hours + 0.40 Hours = 0.875 Hours
Q 0.05 = 30.70 cfs (Incorrect)
Q 0.24 = 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 T C ’s
But the timing of the Peak Discharge is
different as well.
Not only is the actual
Peak Discharge
different…

A
What is the correct Manning’s n value?
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
% Decrease In Sheet Flow Tt
0.0
10.0
20.0
30.0
40.0
50.0
60.0
0.50
0.60
0.70
25 %
0.80
0.90
1.00
Ground Slope In %
1.10
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 %.
1.20
1.30
1.40
1.50
1.60
1.70
1.80
1.90
2.00

93
92
Example Time of Concentration Calculation
92
93
94
95
96
X
"D"-
93.3
Channel Flow
Shallow
Concentrated
Flow Sheet Flow
250 ft. 125 ft. 100 ft.
93 92 92 93 94 95 96 97 98 99
97
98
X
"C"-
96.0
99
100
X
"B"-
99.5
X
"A"-
100.5
Note: The individual segment lengths are not the
horizontal distances, but the linear distances along the
flow path line.

1. Compute the Sheet Flow
Travel Time Component of
the Time of Concentration:
“B” –
99.5
Example - Continued
“A” –
100.5
What surface description best categorizes this type of ground
cover for the purpose of choosing a Manning’s “n” Roughness
Coefficient ?
100
X
"B"-
99.5
Sheet Flow
100 ft.
99
X
"A"-
100.5

Which Manning’s “n” value most closely mimics this
specific ground cover?
We can immediately eliminate the
following:
Smooth Surfaces
Fallow (No Residue)
Cultivated Soil
Woods
This leaves the following choices:
Grass
Range
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:
T T = (.007) x (n) 0.8 x (L) 0.8
P 2 0.5 x S 0.4
L = 100 ft.
P2 = 3.00 In.
S = (100.5 – 99.5)/ 100 = 0.01 ft / ft
n = 0.24
T T = (.007) x (0.24) 0.8 x (100) 0.8 = 0.324 Hrs
3.0 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
“C” –
96.0
“B” –
99.5
S hallow
Concentrated
Flow S
125 ft.
X
"C"-
96.0
99
100
X
"B"-
99.5
97 98 9
Shallow Concentrated Flow is 125 ft. (non-paved) at (99.5-96.0)
/125 = 0.028 ft/ft

0.028
ft/ft
Enter Figure 3-1 to arrive at the Average Velocity
2.7 fps
T T = 125 / 3600 x 2.70 = 0.013 hrs.
The actual equation used to
determine the velocity for Shallow
Concentrated flow is based on:
T T = L * (58,084.2 * s 0.5 ) -1
-or-
T T = L
3600 x 16.1345 x S 0.5
Therefore: V = 16.1345 x S 0.5

Channel Flow Component of the Time of Concentration
“D” –
93.3
“C” –
96.0
5
96
X
"D"-
93.3
Channel Flow
250 ft.
97
98
Con
X
"C"-
96.0
95 96 97
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
1.5 ft
5 ft
Approximate channel geometry
2
1
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.
Assume a reasonable flow
depth – say 1.5 ft, and solve for
the cross sectional flow area
and the wetted perimeter.

The first step is to compute the Hydraulic Radius:
Compute the Hydraulic Radius as follows:
1.5 ft
5 ft
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?
2
1

Method used to determine Manning’s n value for earthen channels
(Not to be confused with Manning’s “n” for Sheet Flow)
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 =(n 0 + n 1 + n 2 + n 3 + n 4 ) x m 5
Where:
n = Manning’s “n” value
n 0 = the portion of the n value that represents the channel material in a straight,
uniform smooth reach
n 1 = the additional value added to correct for the effect of channel surface
irregularities
n 2 = the additional value for variations in shape and size of the channel cross section
through the reach
n 3 = the additional value for obstructions (such as beaver dams, debris dams,
stumps, downed trees, and root wads extending into the channel)
n 4 = the additional value for vegetation in the channel
m 5 = the correction factor for the meandering of the channel

Manning’s “n” values to be used for Cowan’s method for channel
roughness
Material Involved
Degree of Irregularity
Vegetation
Degree of Meandering
Channel Conditions
Variations of Channel Cross Section
Relative Effect of Obstructions
Earth
Rock cut
Fine gravel
Coarse gravel
Smooth
Minor
Moderate
Severe
Gradual
Alternating occasionally
Alternating frequently
Negligible
Minor
Appreciable
Severe
Low
Medium
High
Very high
Minor
Appreciable
Severe
n 0
n 1
n 2
n 3
n 4
m 5
Values
0.02
0.025
0.024
0.028
0
0.005
0.01
0.02
0
0.005
0.010-0.015
0
0.010-0.015
0.020-0.030
0.040-0.060
0.005-0.010
0.010-0.025
0.025-0.050
0.050-0.100
1
1.15
1.3

Compute Manning’s “n” value for the channel
n0 = Earth Channel = 0.02
n1 = Smooth Irregularity = 0.00
n2 = Gradual Section Variations = 0.00
n3 = Negligible Obstructions = 0.00
n4 = Low to Medium Vegetation = 0.01
0.03
m5 = Minor Meandering = 1.00
Manning’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
n
V = 1.486 x 0.651 2/3 x 0.0108 ½ = 3.87 fps
0.03
TT = 250 / 3600 x 3.87 = 0.0179 hours
The total Time of Concentration = T T1 + T T2 + T T3 = T C
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:
0.5 ft
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
T T = 250 / 3600 x 2.86 = 0.024 hours
Remember our original TT was 0.018 hours!!
Really, not that much of a difference.
2
1

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 postdevelopment.

Questions and (hopefully!) Answers ?