Glenn E. Moglen Department of Civil & Environmental Engineering Virginia Tech Course Introduction, the Rational Method, and Inlet Design CEE 5734 – Urban Hydrology and Stormwater Management Week 1

Introductions Safety Statement Overview of Course Begin Course Material Rational Method IDF curves Inlet Design Pipe Design Today’s Agenda

Please read: “1 page Emergency Preparedness Document.doc” Designation of Emergency Assembly Point: Falls Church: Picnic tables between NVC building and parking lot. Blacksburg: Other sites: Safety Statement

Hydrology: literally the “study of water” We are interested in both scientific understanding (analysis) and engineering issues (design). We are interested in both water quantity and water quality. Urban: emphasis on issues with urban infrastructure How does the presence of urban structures affect the hydrology? (Analysis question) How do we build structures to convey stormwater in an urban setting? (Design question) Overview: What is Urban Hydrology?

What is urbanization? Definition: Urbanization is the transition of land use from forest or agriculture to residential and commercial purposes. Hallmarks: Land is cleared of vegetation Impervious surfaces (roads, parking lots, rooftops) are added Drainage “improvements”are constructed (e.g. curb & gutter, storm sewers, channel re-alignments or linings)

Hydrology 101… Horizontal axis: time (minutes, hours, days) depends on scale of watershed (e.g. Potomac crested at 2pm September 23 after Hurricane Isabel (which hit on September 18-19) Vertical axis: discharge (Q) in units of ft 3 /s.

What are the hydrologic effects of urbanization?

As urbanization takes place: Flood hydrograph volume increases Flood peak increases Timing of hydrograph peak decreases What are the hydrologic effects of urbanization?

Land Use Change Animation Northwest Branch Watershed: Based on methods presented in Moglen and Beighley, JAWRA 2002

Urbanization - changes in daily discharge record

Water Quantity: Rational Method NRCS methods Peak Flow Control BMPs (detention basins) SWMM modeling (w/ focus on water quantity) Water Quality: Urbanization and water quality SWMM modeling (w/ focus on water quality) Water quality-oriented BMPs BMP optimization LID (time permitting) Course Overview: Topics we will examine

Rule 1: Exact numbers have infinite significant digits. Ex: A dozen eggs is exactly 12 eggs. Rule 2: Zeros used just to position the decimal point are not significant figures. Trailing zeros are not significant unless a decimal point is explicitly indicated. Ex: has 3 significant figures Ex: 20 has 1 significant figure Ex: 20. has 2 significant figures Ex has 3 significant figures For Starters: Significant Figures

Rule 3: In multiplication and division, an answer contains no more significant figures than the least number of significant figures used in the operation. Ex: For Starters: Significant Figures (cont.)

Rule 4: In addition and subtraction, the last digit retained in the sum or difference is determined by the first doubtful digit. Ex: For Starters: Significant Figures (cont.)

Fact 1: Car generally get’s between 40 and 50 mpg depending type of driving and season Fact 2: Fuel efficiency is reported on dashboard to the tenth’s place (e.g mpg) Observation: Although efficiency is reported to the tenths place, certain efficiency values are never seen. For instance, the progression of reported values between 44 and 45 mpg is: 44.2, 44.4, 44.6, 44.9 (you’ll never see 44.1, 44.3, 44.5, 44.7, 44.8) Explain? Significant Digits: Real World Example: Dr. Moglen’s Honda Civic Hybrid

Dr. Moglen’s theory: Fuel efficiency is actually calculated internally in units of km/liter and truncated to 1 decimal place (e.g 18.6 km/liter). The conversion factor from km/liter to mpg is 2.352…. = 2.4 (to two significant digits) Thus: Significant Digits: Real World Example: Dr. Moglen’s Honda Civic Hybrid (cont’d.) Question: if using 2.4 conversion factor, how many sig. figs. should be used to report fuel efficiency?

Significant Figures – WARNING! Significant figures are important. Hydrology is a science with considerable uncertainty (small precision). I reserve the right to subtract percent from any answer with an inappropriate number of significant figures. Use significant figures you report to convey your certainty about a value.

Peak discharge is: where: Q p : peak discharge in [ft 3 /s] c : runoff coefficient (function of land use, slope, etc.) i : rainfall intensity in [in/hr] A : drainage area in [acres] Rational Method

Note odd combination of units. To make it dimensionally homogeneous: Rational Method – cocktail party chatter…

The rainfall intensity used in Rational equation depends on the time of concentration (t c ) of the system being studied. Typically the Kirpich (1940) equation is used to estimate this quantity: where: t c : time of concentration in [minutes] L : flow length in [feet] S : average watershed slope in [ft/ft] If channel flow path is concrete, divide by 5. Rational Method – getting time of concentration

Rainfall (depth or intensity) data are obtained from precipitation frequency studies. The best source used to be TP-40 (Hershfield, 1961). A better (and more current) source is NOAA Atlas 14. Rational Method – getting rainfall data

“IDF curves”: classic source for precipitation depth information NOAA Atlas 14 data presentation renders IDF curves obsolete, but concept is still important. Rational Method – getting rainfall data (cont.) Increasing Return Period 2-yr 1000-yr “average recurrence interval” (ARI) and “annual exceedance probability” (AEP) – how do they differ?

Inlet Rule: For each inlet area at the headwater of a drainage area, the Rational method is used to compute the peak discharge. Pipe Rule: For locations where drainage is arriving from two or more inlets, the pipe discharge is determined as follows: The longest time of concentration is used to find the design rainfall intensity A weighted runoff coefficient is computed Total drainage area is used in the Rational Method computation Inlet/Pipe Design Discharges with the Rational Method

Pipe sizes (diameters): 8, 10, 12, 15, 16, 18 inches 3 inch increments between 18 and 36 inches 6 inch increments between 3 feet and 10 feet Inlet or Outlet Control? (see details on following pages) Inlet: conditions at upstream end of pipe dominate Outlet: conditions at downstream end of pipe dominate Simplified: for expediency, we’ll assume (for now) that pipe flows just full but with no pressure. Pipe Sizing

A culvert flowing in inlet control has shallow, high velocity flow categorized as "supercritical." For supercritical flow, the control section is at the upstream end of the barrel (the inlet) Inlet Control

A culvert flowing in outlet control will have relatively deep, lower velocity flow termed "subcritical" flow. For subcritical flow the control is at the downstream end of the culvert (the outlet). Outlet Control

Mathematics of inlet capacity depend on shape and style of inlet. Weir: typical C w = 3.0 to 3.2 Orifice: typical C o = 0.6 Safety factors are commonly applied that reduce intercepted flow by 50 to 80 percent Inlet Sizing

Manning’s equation applies to a pipe flowing full but without pressure: Re-arranging for D : Manning’s n values: use to for concrete to for corrugated metal Simplified Pipe Sizing

Runoff to Inlet 1: From Blacksburg IDF curve, precipitation intensity is: 3.79 in/hr (for 10-year, 15 minute duration) Sample Rational Method Calculation – Area 1 A 1 = 5.3 C 1 = 0.20 T c,1 = 15 min A 2 = 7.2 C 2 = 0.40 T c,2 = 9 min A 3 = 6.4 C 3 = 0.60 T c,3 = 7 min L 1-2 = 600 ft T t,1-2 = ??? L 2-3 = 500 ft T t,2-3 = ??? Pipe 1-2 Pipe 2-3 Pipe 3…

Design Inlet: Assume head, h, at inlet is 4.0” (could be calculated from Manning’s equation if pavement slope, roughness, and geometry were known ) Assume 50% factor of safety, f s (inlet only allows 50% of theoretical inflow. If weir inlet: If orifice inlet: Design of Inlet for Area 1

Pipe 1-2 carries 4.0 ft 3 /s. Determine diameter: Nearest size pipe is 27 inches in diameter. Sample Rational Method Calculation – Pipe 1-2 A 1 = 5.3 C 1 = 0.20 T c,1 = 15 min A 2 = 7.2 C 2 = 0.40 T c,2 = 9 min A 3 = 6.4 C 3 = 0.60 T c,3 = 7 min L 1-2 = 600 ft S 1-2 = n = L 2-3 = 500 ft T t,2-3 = ??? Pipe 1-2 Pipe 2-3 Pipe 3…

Need to get velocity in 27 inch pipe. Use circular geometry table (see website): From table, y/d = (also note that A/d 2 = ), therefore: Travel time in pipe is 600 ft / 1.2 ft/s = 500 s (8.3 min) Sample Rational Method Calculation – Pipe 1-2 (cont.)

Sample Rational Method Calculation – Area 2 Runoff to Inlet 2: From Blacksburg IDF curve, precipitation intensity is: 4.72 in/hr (for 10-year, 9 minute duration- interpolated) A 1 = 5.3 C 1 = 0.20 T c,1 = 15 min A 2 = 7.2 C 2 = 0.40 T c,2 = 9 min A 3 = 6.4 C 3 = 0.60 T c,3 = 7 min L 1-2 = 600 ft T t,1-2 =8.3 min L 2-3 = 500 ft T t,2-3 = ??? Pipe 1-2 Pipe 2-3 Pipe 3…

You might think Pipe 2-3 carries = 18 ft 3 /s. But longest T c controls. T c coming from Area 1 is = 23 minutes T c coming from Area 2 is 9 minutes. T c = 23 minutes controls. Sample Rational Method Calculation – Pipe 2-3 A 1 = 5.3 C 1 = 0.20 T c,1 = 15 min A 2 = 7.2 C 2 = 0.40 T c,2 = 9 min A 3 = 6.4 C 3 = 0.60 T c,3 = 7 min L 1-2 = 600 ft T t,1-2 =8.3 min L 2-3 = 500 ft T t,2-3 = ??? Pipe 1-2 Pipe 2-3 Pipe 3…

Calculated weighted c value: For T c = 23 minutes, i = 3.23 in/hr Since 14 ft 3 /s from Area 2 alone is greater than the combined area, 14 ft 3 /s is the design discharge for pipe. Sample Rational Method Calculation – Pipe 2-3 (cont.)

Sizing of pipe for 14 ft 3 /s (assume S 2-3 = 0.001, n = 0.030): How do we do this? Ans. D = 48 inches Velocity in pipe: How do we do this? Ans. v = 1.7 ft/s Travel time along Pipe 2-3 : How do we do this? Ans. T t,2-3 = L 2-3 /v = 4.9 min Sample Rational Method Calculation – Pipe 2-3 (cont.)

Review of Inlet and Pipe Design: Analysis and Synthesis AnalysisSynthesis Inlet“1”: Use rational method to analyze/determine discharge to inlet. “2”: Use discharge from “1” as input parameter to inlet design problem. Pipe“3”: Use controlling T c to analyze/determine discharge pipe must carry. “4”: Use discharge from “3” along with re-arranged Manning’s equation to design appropriate pipe diameter.