Basic Hydrology. Time of Concentration Methodology

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1 Basic Hydrology Time of Concentration Methodology By: Paul Schiariti, P.E., CPESC Mercer County Soil Conservation District

2 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?

3 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

4 Where is the Correct TC Flow Path?

5 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

6 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?

7 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.

8 TR-55 Segmental Time of Concentration Sheet Flow Travel Time Component P 2 values are obtained from NRCS 24 Hour Design Storm Rainfall Depths.

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

10 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 x S 0.4 Example: L = 125 ft. P 2 = 3.00 In. S = 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: n = 0.24: T T = (.007) x (0.05) 0.8 x (125) 0.8 = Hours (Incorrect) x T T = (.007) x (0.24) 0.8 x (125) 0.8 = Hours (Correct) x This represents an under-estimation of the Time of Concentration of 71%!!!

11 How does this effect the peak Discharge? Drainage Area = Acres Runoff Curve Number = Year Storm Precipitation = 5.00 Inches Additional Travel Time for Shallow Concentrated Flow Plus Channel Flow = 0.50 Hours T C1 = Hours Hours = Hours T C2 = Hours Hours = Hours Q 0.05 = cfs (Incorrect) Q 0.24 = cfs (Correct) Difference in Peak Discharge Rates = 6.60 cfs Over estimates the peak discharge by 27.4%!!

12 Effect on the Runoff Hydrograph for the different T C s Not only is the actual Peak Discharge different But the timing of the Peak Discharge is different as well.

13 What is the correct Manning s n value? B A Manning s n for Maintained Turf Grass should almost always be = 0.24

14 Percent Increase In The Sheet Flow Travel Time Related to Change In Ground Slope Ground Slope In % % Decrease In Sheet Flow 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 %.

15 Example Time of Concentration Calculation Channel Flow Shallow Concentrated Flow Sheet Flow 250 ft. 125 ft. 100 ft X "D" X "C" X "B" X "A" Note: The individual segment lengths are not the horizontal distances, but the linear distances along the flow path line.

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

17 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

18 Compute the Sheet Flow Travel Time Component: Sheet Flow Equation: T T = (.007) x (n) 0.8 x (L) 0.8 P x S 0.4 L = 100 ft. P 2 = 3.00 In. S = ( )/ 100 = 0.01 ft / ft n = 0.24 T T = (.007) x (0.24) 0.8 x (100) 0.8 = Hrs x The next component of the Time of Concentration is the shallow Concentrated flow Travel Time portion.

19 Shallow Concentrated Flow Component of the Time of Concentration B 99.5 S hallow Concentrated Flow 125 ft. S C 96.0 X "C" X "B" Shallow Concentrated Flow is 125 ft. (non-paved) at ( ) /125 = ft/ft

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

21 Channel Flow Component of the Time of Concentration C Channel Flow 250 ft Con D 93.3 X "D" X "C" The Channel Slope is 250 ft. at ( )/250 = ft/ft Note: The channel does not have to possess a visible water surface to be considered channel flow.

22 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. 1.5 ft 5 ft 2 1 Assume a reasonable flow depth say 1.5 ft, and solve for the cross sectional flow area and the wetted perimeter. Approximate channel geometry

23 The first step is to compute the Hydraulic Radius: Compute the Hydraulic Radius as follows: 1.5 ft 5 ft 2 1 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 ft. 2 ) 1/2 ] = ft. R = 12.0 s.f. / ft. = ft. How do we compute the Manning s n roughness coefficient?

24 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

25 Manning s n values to be used for Cowan s method for channel roughness Channel Conditions Values Material Involved Earth n Rock cut Fine gravel Coarse gravel Degree of Irregularity Smooth n 1 0 Minor Moderate 0.01 Severe 0.02 Variations of Channel Cross Section Gradual n 2 0 Alternating occasionally Alternating frequently Relative Effect of Obstructions Negligible n 3 0 Minor Appreciable Severe Vegetation Low n Medium High Very high Degree of Meandering Minor m 5 1 Appreciable 1.15 Severe 1.3

26 Compute Manning s n value for the channel n 0 = Earth Channel = 0.02 n 1 = Smooth Irregularity = 0.00 n 2 = Gradual Section Variations = 0.00 n 3 = Negligible Obstructions = 0.00 n 4 = Low to Medium Vegetation = m 5 = Minor Meandering = 1.00 Manning s n value = 0.03 x 1.00 = 0.03

27 Compute the Travel Time for the channel section V = x R 2/3 x S ½ n V = x /3 x ½ = 3.87 fps 0.03 T T = 250 / 3600 x 3.87 = hours The total Time of Concentration = T T1 + T T2 + T T3 = T C TC = Hr Hr Hr. = Hr.

28 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 2 1 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 ft. 2 ) 1/2 ] = 7.24ft. R = 12.0 s.f. / ft. = ft. V = x /3 x ½ = 2.86 fps 0.03 T T = 250 / 3600 x 2.86 = hours Remember our original TT was hours!! Really, not that much of a difference.

29 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?

30 What is the correct Manning s n value for Sheet Flow? Cultivated Soils: Residue Cover > 20%; n = 0.17

31 What is the correct Manning s n value for Sheet Flow? Smooth Surface (concrete, asphalt, gravel or bare soil); n = 0.011

32 What is the correct Manning s n value for Sheet Flow? Woods; Light Underbrush; n = 0.40

33 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.

34 Questions and (hopefully!) Answers?

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