Time of Concentration - Hydrology - Lecture Slides, Slides of Water and Wastewater Engineering

Download Time of Concentration - Hydrology - Lecture Slides and more Slides Water and Wastewater Engineering in PDF only on Docsity! Time of Concentration 1 Docsity.com Objectives • Know how to calculate time of concentration • Know why it’s important to be able to determine the time of concentration 2 Docsity.com Importance • Rational method – Calculate time of concentration, tc – Set duration = tc – Use IDF curve to find rainfall intensity • TR-55 Method – Calculate time of concentration, tc – Look up unit peak discharge on the appropriate Exhibit 4-# 5 Docsity.com Typical Values for Tc < 50 Acres • 5 minutes to 30 minutes 6 Docsity.com Water can move through a watershed as: • Sheet flow (max of 300 ft; ---usually 100 ft) • Shallow concentrated flow • Open channel flow – Gutter – Ditch – Swale – Creek • Some combination of above 7 Docsity.com Sheet Flow 1. Manning’s Kinematic Solution – See TR-55, pg 3-3 & equation 3-3 2. Kinematic Wave Equation 3. FAA Method 4. Nomograph – See appendix C-2 of your book 10 Docsity.com Manning’s Kinematic Solution • Tt=[0.007(nL).8]/[P2.5 S.4] • Tt is travel time (hrs) • n-Manning’s coefficient for sheet flow (dimensionless - must use Table 3-1 in TR-55) • L is flow length (ft) • P2 is 2-yr, 24-hr rainfall (in) – TR-55 Appendix B, Figure B-3 or – Local IDF curve (change intensity to inches) • S is slope (decimal format) 11 Docsity.com Kinematic Wave Equation • tco=[56(Lo).6 (n).6]/[So.3 i.4] • tco is travel time (sec) • n-Manning’s coefficient (dimensionless) • Lo is overland flow length (ft) • i is rainfall intensity for a desired frequency (in/hr) – TR-55 Appendix B (change inches to intensity) or – Local IDF curve • So is overland slope (decimal format) 12 Docsity.com FAA Equation • t=[1.8(1.1-C)(Lo).5 ]/[S.333] • t is travel time (min) • C-rational coefficient (dimensionless) – See Appendix C-1 of your book • Lo is overland flow length (ft) • So is overland slope (decimal format) 15 Docsity.com Nomograph • Your book – C-2 – Length – Ground character • Paved • Bare soil • Poor, average or dense grass – Percent slope 16 Docsity.com Example • Dense Grass (n=0.24, C=0.2) • Flow Length (200 ft) • Location (SUNYIT; 2-yr 24-hr duration) • Slope (3%) 17 Docsity.com Example: Kinematic Wave Equation • tco=[56(Lo).6 (n).6]/[So.3 i.4] • Assume 1-hr; 2-yr frequency (i=1”/hr) • tco=[56(200).6 (.24).6]/[.03.3*1.4] • tco=1640 seconds = 27 minutes • Intensity for 30-min; 2-yr storm =1.6”/hr • Intensities don’t match; try again 20 Docsity.com Kinematic Wave-Trial/Error (Tc=9 minutes) Assumed I Time of Conc. Actual i 1 in/hr 28 minutes 1.6 in/hr 1.6 17 2.4 2.4 11 3.1 3.1 9 3.1 21 Docsity.com Example: FAA Equation • t=[1.8(1.1-C)(Lo).5 ]/[S.333] • t=[1.8(1.1-.2)(200).5 ]/[.03.333] • C=.2 • Lo=200 ft • So = .03 • t = 41 min 22 Docsity.com Shallow Concentrated Flow • TR-55 – page 3-2; Figure 3-1 – page 3-3; Explanation – Appendix F - formulas • Derived from Manning’s equation • Determine average velocity (Fig 3-1) • Divide flow length by average velocity to obtain travel time 25 Docsity.com Watercourse slope (fvft) 50 20 10 06 e = 04 sf gs EY 02 O71 005 1 4 6 10 20 Average velocity (vsec} 26 Docsity.com Shallow Concentrated Flow • Equations – Velocity=16.1345*S0.5 Unpaved – Velocity=20.8282*S0.5 Paved • Assumptions – Unpaved: n=.05; hydraulic radius=0.4 – Paved: n=.025; hydraulic radius=0.2 27 Docsity.com Uniform Flow in Open Channels • Water depth, flow area, discharge and velocity distribution at all sections throughout the entire channel reach remains unchanged. • The energy grade line, water surface line, and the channel bottom lines are all parallel to each other • No acceleration (or deceleration) 30 Docsity.com Manning’s Equation: Flow---English • Q=A(1.49/n)(Rh2/3)(S).5 • Q is flow rate (cfs) • n-Manning’s coefficient (dimensionless) • Rh is hydraulic radius (ft) – Wetted area / wetted perimeter • S is slope (decimal format) 31 Docsity.com Manning’s Equation: Flow---Metric • Q=A(1/n)(Rh2/3)(S).5 • Q is flow rate (cms) • n-Manning’s coefficient (dimensionless) • Rh is hydraulic radius (m) – Wetted area / wetted perimeter • S is slope (decimal format) 32 Docsity.com Manning’s Coefficient Typical Values • Appendix A-1 from your book • Other ref: – http://www.fhwa.dot.gov/bridge/wsp2339.pdf – http://www.lmnoeng.com/manningn.htm 35 Docsity.com Hydraulic Radius • Wetted area / wetted perimeter • Easy to calculate for circular pipes full or half- full • Use trig to calculate triangular or trapezoidal channels 36 Docsity.com SOKaUSA0U LINQ SCaVGNVLIS ONISGSENIDNG weSCE ‘OO Feng Aw FOIANAS NOLLVAYASNOD TIOS AUALINGINOY 10 LNUWLAvagd “Ss ‘Oo wiva “9 ‘LSaHS €¢-sSs3 ‘ON ‘OMG CU¥GNYLS Section Areg Wetted Perimeter |Hydraulre Rodius | Top Mmiath g Pp r ei Ss bd +202 ‘ » ! bdtad? bt edhe? 4/ San bt2ed . 1 eg bt2oV224/ Trapezoid 8 = ~77q ba a ba bt42d eee b Rectong!le F od S| 4 2 gd z z zd 2d Ve2+/ 220 : ae ; 2Va%T ; Triangle T 2 8a? 2aT? 3a BOT T+ 37 57? 48a% 2 Parekhala LL ie (2 Dsin g y a) ee. -sin@) DO 62/22. sin no) 2 Lt 2 180 360 or 2Yd(D-¢) Circle <2 full 12 T ., @ eS ee i> 2 4 Osin v Kb) 2 (er-L2, sine) ro (360-2) ersind) ? 8 180 360 ee meal "80 or 2Vai{D-a) Circle > le futt 2. LL Satisfactory goproximea tion for rhe ipterval o<Z When Lr, ase use p= Ip Wied®+72 +g re Ei sinh" 2 \2 @=dsin™| 13 G2deos Wap $ SE O.25 Insert @ in cegrees Ze above equations Docsity SNOILOAS TANNVHS 40 SLNAW3S13 :SOImINWHaAH com Time of Concentration Calculations • For this class (homework, projects, etc.) use worksheet from the TR-55 Document • Page D-3 (to print out blank form) • Also show picture of lengths 40 Docsity.com Worksheet 3: Time of Concentration (T¢) or travel time (Tt) Project By Date Tecan Checked Dale checkone: Cl present (1) peveioped cneckone: Cts C]tyintougn sunarea, Notes: Space foras many as two segments per flow type can be used for each worksheet, Include a map, schematic, or deecription of flow segments, Segment ID . Surface description (table 9-1) Manning's roughness coefficient, n (table 2-1). Flow length, L (total L 1300 Two-year 24-hour raintal, P 2 Land slope, 9 6. Tp=_.007 iny"* Compute Ty. Pots gpd ne em +] eel CRs Segment ID 7. Surface description (paved or unpaved) 8. Flow keeth, L 9. Watercourse slope, ¢ 10, Average welocity, V (figure 3-1) 4. =k Compute Ty ... 3600 Segment ID fut tus hr 42. Croga sectional flow area, @. esses 43. Watted perimeter, pw. 44. Hychaulls radius, = Computer. 415Channel etope, ¢ .... 48. Manning's roughness coefficient, n 47. 4.49 PO g 12 Compune V tis, 48. Phowtenath, L tt 49. Tet _ Compute Tr hr v 20, Watershed or subarea T,, or Ty (add 7; in steps 6, 14, and 49) .. (2U.V-TRIG Second Bd, June 16) be 41 Docsity.com Next Lecture • Rational Method for Determining Peak Flow 42 Docsity.com