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July 30-130-Ken Kagy2

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2019 SWCS International Annual Conference
July 28-31, 2019
Pittsburgh, Pennsylvania

Publicado en: Medio ambiente
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July 30-130-Ken Kagy2

  1. 1. AN EVALUATION OF ESTIMATING PEAK RUNOFF with Tc for GREEN INFRASTRUCTURE TC Equation Relationship to Rational Method Peak Flow
  2. 2. Rational Method Equation and Variables: Q = C i A Where: Q = Maximum Rate of Runoff (cfs) C = Runoff Coefficient i = Average Rainfall Intensity (in/hr) A = Drainage Area (in acres) The EQUATION (Q)
  3. 3. Rational Method Equation and Variables: Where: C = Runoff Coefficient R = Total Depth of Runoff (in) P = Total Depth of Precipitation (in) RUNOFF COEFFICIENT (C) Rossmiller (1981) C = 7.210-7 CN3 T0.05 (0.01CN)-0.6s-.02 ((0.001CN)1.48 )0.15 – 0.1I ((P+1)/2) 0.7 Where: CN is the Soil Conservation Service Curve Number; T is the recurrence interval (years); S is the average land slope (%); I is the intensity (in/hr); and P is percent imperviousness. C = 𝑅 𝑑 𝑃 𝑑
  4. 4. Rational Method Equation and Variables: RAINFALL INTENSITY (i) The determination of rainfall intensity (i) for use in the Rational Formula involves consideration of three factors: • Average frequency of occurrence • Intensity-duration characteristics for a selected rainfall frequency. • The time of concentration (tc).
  5. 5. Rainfall Intensities Based upon I-D-F Curves As the Tc goes up, the “I” goes down. Rainfall Intensities are obtained by entering the Log-Log nomograph with the Time of Concentration along the abscissa, intersecting the Storm Return Period Curve, and proceeding horizontally to the Rainfall Intensity. http://hdsc.nws.noaa.gov/hdsc/pfds/index.html
  6. 6. Rational Equation with an “R” Runoff Ratio: Where: q = Maximum Rate of Runoff (cfs), c = Runoff Coefficient, i = Average Rainfall Intensity (in/hr), A = Drainage Area (acres) 𝐑𝐚𝐭𝐢𝐨𝐧𝐚𝐥 Equation 𝐀𝐫𝐫𝐚𝐧𝐠𝐞𝐝 to ‘c’ Coeff. & ‘A’ Area 𝐜 = 𝐪(𝐜𝐟𝐬) 𝐢 ∗ 𝐀 𝐀 = 𝐪(𝐜𝐟𝐬) 𝐢 ∗ 𝐜 𝐑𝐮𝐧𝐨𝐟𝐟 𝐑𝐚𝐭𝐢𝐨 = 𝐝𝐢𝐬𝐜𝐡𝐚𝐫𝐠𝐞 𝐫𝐚𝐭𝐞 𝐢𝐧𝐭𝐞𝐧𝐬𝐢𝐭𝐲 = 𝐑 = 𝐪(cfs) 𝐢 ( in hr ) R = 2 cfs/4 in. = 2.0 Or R= 4 cfs/2 in. = 0.5 c = R A Now A = R c & Where:
  7. 7. Plotting the Rational Equation using “R” Runoff Ratio with “c” coefficient
  8. 8. Plotting the Rational Equation using “R” Runoff Ratio with “A” area
  9. 9. Rational Method Assumptions & Limitations • Maximum watershed area has a 200 acre limit • The method is applicable when the time of concentration (tc) for the drainage area is less than the duration of peak rainfall intensity. • The time of concentration (tc) is the time required for water to travel from the hydraulically most remote point of the basin to the point of interest within the basin.
  10. 10. • The calculated runoff is directly proportional to the rainfall intensity. • Rainfall intensity is uniform throughout the duration of the storm. • The frequency of occurrence for the peak discharge is the same as the frequency of the rainfall producing that event. Rational Method Assumptions & Limitations
  11. 11. • Rainfall is distributed uniformly over the drainage area. • The minimum duration to be used for computation of rainfall intensity is 10 Minutes. (Several jurisdictions use a 5 minute minimum) • The rational method does not account for storage in the drainage area. Available storage is assumed to be filled. Rational Method Assumptions & Limitations
  12. 12. Rational Method Equation and Variables: TIME OF CONCENTRATION (tc) • If the chosen storm duration > tc, then the rainfall intensity will be less than that at tc (Peak discharge < optimal value). • If the chosen storm duration < tc, then the watershed is not fully contributing runoff to the outlet for that storm length (i.e. optimal value will not be realized). • Therefore, use storm duration = tc for peak discharge.
  13. 13. Unified TC Equation for Channelization using ‘C’ Tc = 𝟏−𝑪avg 𝟑 𝒔 𝟏𝟐𝟓 𝑳 + 𝟑 𝒔 𝟏𝟒 • Tc = Time of Concentration (minutes) • 𝑳 = Length of Flow Path (feet) • 𝑪avg = Rational method’s average runoff coefficient • 𝒔 = % Slope of Flow Path (decimal format) • Equation Limits: 1 to 225 acres for drainage basin 1 to 12 percent slope for flow path 0.10 to 0.95 rational runoff coefficient
  14. 14. ‘C’ Relationships for Soil Types using a 10yr. Storm Event
  15. 15. Unified Tc ‘C’ Equation uses an average ‘C‘ coefficient (near B soil type) Basin weighed ‘C’ value is attained by adjusting ‘C’ soil types to a ‘Cavg’ type Cavg = 𝑪𝒕𝒚𝒑𝒆 𝟐𝟏+𝟎.𝟕𝒙+𝟎.𝟏𝟓𝒙 𝟐 −𝒙+𝟏.𝟓 𝟐𝟐.𝟓 Cavg = Average C values used in Kirpich-Velocity Eq. 𝑪𝒕𝒚𝒑𝒆 = Rational method’s runoff coefficient per soil type 𝒙 = NRCS’s soil type factor shown below Type A Soil: x = 0 Type B Soil: x = 1 Type C Soil: x = 2 Type D Soil: x = 3
  16. 16. Mockus (USDA 1973) developed an empirical relationship between flow length and drainage area using data from Agricultural Research Service (ARS) watersheds. Time of Concentration’s Flow Length and Drainage Area Relationship National Engineering Handbook 630.1502 Methods for estimating time of concentration Eq. 15-5 𝒍 = 𝟐𝟎𝟗 𝑨 𝟎.𝟔 Where: l = length of runoff flow, (ft) A = drainage area, (acres)
  17. 17. Kirpich Equation compared to NRCS Equation by Area of Drainage Basin
  18. 18. Tc = 𝟏−𝑪avg 𝟑 𝒔 𝟏𝟐𝟓 209 𝑨 0.6 + 𝟑 𝒔 𝟏𝟒 Unified TC Equation with ‘C’ for a Basin Area UTC Equation arranged for Rational Runoff Coefficient ‘c’ for Basin Areas at 5 & 10 Minutes 𝟓 𝐨𝐫 𝟏𝟎 𝐦𝐢𝐧. 𝐓 𝐜 = 1 − 𝑪 3 𝒔 125 209 𝑨0.6 + 3 𝒔 14 𝒄 = 1 − 5 3 𝒔 125 209 𝑨0.6 + 3 𝒔 14 𝒄 = 1 − 10 3 𝒔 125 209 𝑨0.6 + 3 𝒔 14 5 min. Runoff Coefficient ‘c’ 10 min. Runoff Coefficient ‘c’
  19. 19. Total Hydraulic Time Calculations (TR55, Velocity, or SCS Method) Sheet Flow Tt = 0.007(nL)0.8/(P2 0.5S0.4) Shallow Concentrated Flow Tt = L /3600V Open Channel Flow Tt= (L*n) /(1.49R0.67S 0.5) (Manning’s Equation) Where Hydraulic Radius = conveyance flow depth then: Manning’s equation becomes Tt = L/3600V Total Watershed Time of Concentration tc=STt L= ft., Tt = hr., S= % slope, R= ft., P= in.(2yr.24hr.) , V= ft./sec.
  20. 20. Sheet Flow TR-55 Sheet Flow—The sheet flow time computed for each area of sheet flow that requires the following input data: Hydraulic Length—Defined flow length for the sheet flow. Manning's n—Manning's roughness value of the sheet flow. Slope— The defined slope of the sheet flow/catchment. Precipitation Infiltration Kinematic Wave Eq.
  21. 21. Technical Paper No. 40 Rainfall Frequency Atlas of the U.S. for a 2 yr. Return Period with 24 hr. Storm Duration
  22. 22. Kirpich Equation compared to NRCS Equation with a P2 Sheet Flow of 2 inches Equations Confluence
  23. 23. Kirpich Equation compared to NRCS Equation with a P2 Sheet Flow of 4 inches Equations Confluence
  24. 24. Kirpich Equation compared to NRCS Equation with a P2 Sheet Flow of 6 inches Equations Confluence
  25. 25. Unified TC ‘C’ Equation compared to Kirpich & NRCS’s P2 Sheet Flow of 2” UTC & Kirpich Confluence
  26. 26. Unified TC ‘C’ Equation compared to Kirpich & NRCS’s P2 Sheet Flow of 4” UTC & Kirpich Confluence
  27. 27. Unified TC ‘C’ Equation compared to Kirpich & NRCS’s P2 Sheet Flow of 6” UTC & Kirpich Confluence
  28. 28. Unified TC Equation Plotted to Rational Equation Runoff Ratio ‘R’ per Basin Area
  29. 29. Unified TC Equation Plotted to Rational Equation Runoff Ratio ‘R’ per ‘c’ Coefficient
  30. 30. UTC Eq. for 2% Slope Plotted to Rational Eq. Runoff Ratio ‘R’ per ‘c’ Coefficient
  31. 31. UTC Eq. for 10% Slope Plotted to Rational Eq. Runoff Ratio ‘R’ per ‘c’ Coefficient
  32. 32. UTC Equation Plotted to Rational Runoff Ratio ‘R’ per a ‘c’ Coefficient Variable
  33. 33. A Graphical Representation & Significance of a 5 Minute UTC Equation Intersection to a Rational Ratio‘R’ Equation
  34. 34. A Graphical Representation & Significance of a 10 Minute UTC Equation Intersection to a Rational Ratio‘R’ Equation
  35. 35.  Area #1: The rational equation can be used without checks. No verification of rainfall intensity or time of concentration reassessment.  Area #2: The rational equation is limited only by the Tc time. Time of concentration verification is necessary to confirm the total time is less than Tc.  Area #3: The rational equation is limited by rainfall intensity. There is an iterative process to verification rainfall intensity or a Tc reassessment. These Areas Offer Insight to the Rational Equation’s Restrictions on Runoff Calculations in the Following: What are the 3 Areas Under the Curves?
  36. 36. Rational ‘c’ Equivalent Values for the Rational Equation & 5 minute Tc Equation Where: C = Runoff Coefficient s = Average flow path slope (ft./ft.) (decimal) (with Slope limits from 2% to 12%) R = Rational Ratio 𝐑 = 𝐪(cfs) / 𝐢 (in./hr.) (with R limit ratios from 0.2 to 10) An Equation for a 5 minute Balance ‘c’ 𝒄 = 0.82 𝑹 4.8 𝒔 + 𝑹
  37. 37. Rational ‘c’ Equivalent Values for the Rational Equation & 10 minute Tc Equation An Equation for a 10 minute Balance ‘c’ 𝒄 = 0.76 𝑹 13.7 𝒔 + 𝑹Where: C = Runoff Coefficient s = Average flow path slope (ft./ft.) (decimal) (with Slope limits from 2% to 12%) R = Rational Ratio 𝐑 = 𝐪(cfs) / 𝐢 (in./hr.) (with R limit ratios from 0.2 to 10)
  38. 38. Rational ‘c’ Equivalent Values for the Rational Equation & a Calculated UTC Tc A Balance ‘c’ Equation for UTC and Rational Eq. Where: C = Runoff Coefficient S = Average flow path slope (ft./ft.) (decimal) (with Slope limits from 2% to 12%) R = Rational Ratio 𝐑 = 𝐪(cfs) / 𝐢 (in./hr.) (with R limit ratios from 0.2 to 10) Tc = Time of Concentration (minutes) (5-20 min.) 𝒄 = )(𝒕 𝒄 −0.12 𝑹 0.5 𝒕 𝒄 1.46 𝒔 + 𝑹
  39. 39. Previous Equations are Established for Green Infrastructure on Small Basins • The TC comparisons are graphed to the rational empirical equation that convey runoff with a related surface rational ‘c’ coefficient. • These empirical equations provide runoff estimations for homogenous rainfall intensities and a uniform watershed surface coefficient. • Runoff time calculations are estimated for small drainage basins of 60 acres or less and maintain a primary pattern of a dominate “surface” flow attribute.
  40. 40. Ken Kagy, P.E., CFM, CPSWQ, CPESC (678) 242-2543 ken.kagy@cityofmiltonga.us  Understand each required variable in the time of concentration equation.  Understand the limits to each time of concentration equation’s variables.  Understand the basin’s flow path with its flow type, length, depth, and slope.  Apply acceptable surface roughness Tc coefficients that correlate to equivalent hydrology’s surface roughness conditions used to calculate the hydrograph. Time of Concentration Equations Improve Accuracy with the following: The End

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