HYDROLOGIC & HYDRAULIC ASPECTS of the Walnut Street Bridge over the Schuylkill River Philadelphia, PA J. Richard Weggel CAEE201 Lectures 30 April & 2 May 2007
HYDROLOGY (Natural Science) Study of the waters of the earth Oceanography Meteorology Limnology Potomology Engineering Hydrology Surface water hydrology Ground water hydrology
HYDROLOGIC CYCLE Where water exists on the earth and how it moves from place to place processes Location: Ocean Lakes, rivers, streams Below ground Atmosphere Processes: Precipitation Runoff Evaporation Transpiration Infiltration
HYDROLOGIC CYCLE
PRECIPITATION Geographic Distribution of Rainfall National Weather Service collects rainfall data all around the United States Rain gages Daily accumulations Recording gages Radar Current precipitation rates STP = storm total precipitation - for a time period
STANDARD RAINGAGE - ACCUMULATION
RECORDING RAIN GAGE Weighing type
RADAR REFLECTIVITY PROPORTIONAL TO RAINFALL INTENSITY
MEAN ANNUAL RAINFALL IN THE UNITED STATES
100-YEAR, 30 MINUTE RAINFALL
RAINFALL STATISTICS FOR THE PHILADELPHIA AREA Depth-Duration-Frequency Data - Philadelphia PA 8 100 yr 7 50 yr 6 25 yr Depth (inches) 5 4 3 10 yr 5 yr 2 yr 1 yr 2 1 0 10 100 1000 10000 Duration (minutes)
TIME OF CONCENTRATION The time it takes for water to flow from the farthest reach of a watershed to the point where discharge is measured. For times greater than the time of concentration all of the watershed is contributing to the discharge. Rainfall durations equal to or greater than the time of concentration give maximum flows.
A WATERSHED, ISOCHRONES & RUNOFF HYDROGRAPH
HYDRAULICS (Engineering Science) Moving water around (controlled flows) Pipe flow Free surface flow (open channels)
OPEN CHANNEL FLOW Overland flow sheet flow Channel flow Manning s equation for open channel flow V = velocity n = roughness coefficient R = hydraulic radius S = slope A = flow area WP = wetted perimeter Conservation of mass V = R = 1.49 n A WP Q = VA R 2 / 3 S 1/ 2
SOME n VALUES
TRAVEL TIME t = x V (x) Travel time = distance/velocity Note: Velocity can depend on where you are along the channel, x
HIGHWAY DRAINAGE Remove water from a roadway. Convey it to a stream or storm drain Reroute flow in a natural or man-made water course to accommodate a street or highway bridges culverts
DRAINAGE (continued) Lateral (overland flow) from roadway to shoulder/gutter Longitudinal along shoulder/gutter to water course or storm drain inlet or scupper Open channel flow Manning s equation
ROADWAY CROSS-SECTION (SHOWING SLOPES)
RAINFALL STATISTICS FOR THE PHILADELPHIA AREA Depth-Duration-Frequency Data - Philadelphia PA 8 100 yr 7 50 yr 6 25 yr Depth (inches) 5 4 3 10 yr 5 yr 2 yr 1 yr 2 1 0 10 100 1000 10000 Duration (minutes)
TYPICAL CURB SECTION
ASSIGNMENT Calculate how much water a bridge scupper must handle if it drains a ½ of the length of a bridge span 123 feet long. (Calculate for a 30 minute rainfall duration having return periods of 2, 5, 10, 50 and 100 years.) Calculate how much water a gutter can carry if it is filled as shown on the preceding slide and the slope is 2.14%
THE SCHUYLKILL RIVER Navigable river up to Fairmount Dam Tidal up to Fairmount Dam Drainage area above Fairmount Dam = 1,893 mi 2 Flood stage = 11.0 feet Maximum stage = 17.0 feet (4 Oct 1869)
LOOKING NORTH TOWARD CHESTNUT STREET BRIDGE
LOOKING NORTH TOWARD MARKET STREET BRIDGE
LOOKING SOUTH FROM WALNUT STREET SOUTH STREET BRIDGE
WALNUT STREET BRIDGE Navigation lights needed Channel center (360 green) Piers (180 red) Minimum clearance for ship passage (20.2 feet required, 34.9 feet provided) Tides: range = 5.2 feet Floods 50-year +13.5 feet above datum 100-year +15.75 feet above datum
SCHUYLKILL RIVER WALNUT STREET BRIDGE PIERS
NAVIGATION LIGHTS MARKING PIERS AND CHANNEL
STREAM GAGING Measurement of discharge at a location on a stream Development of a relationship between an easily measured variable and discharge Rating curve (Stage v. Discharge) Field measurements during floods to establish relationship Extrapolation to extreme events
SCHUYLKILL RIVER CROSS-SECTION @ WALNUT STREET ( v ) 0 v.2 + v average = 2 0.8 LOGARITHMIC VELOCITY DISTRIBUION
PRICE CURRENT METER VELOCITY MEASUREMENTS
RATING CURVE - SCHUYLKILL RIVER @ PHILADELPHIA 20 18 STAGE (feet above datum) 16 14 12 10 8 6 0 20,000 40,000 60,000 80,000 100,000 120,000 140,000 160,000 DISCHARGE (cfs)
USGS Water Level (Stage) Data Schuylkill River @ Philadelphia
USGS Stream Discharge Data Schuylkill River @ Philadelphia
HEADER FROM USGS DATA SHEET SCHUYLKILL RIVER @ PHILADELHIA # U.S. Geological Survey # National Water Information System # Retrieved: 2006-11-09 21:38:03 EST # # ---------------------WARNING--------------------- # The data you have obtained from this automated # U.S. Geological Survey database have not received # Director's approval and as such are provisional # and subject to revision. The data are released # on the condition that neither the USGS nor the # United States Government may be held liable for # any damages resulting from its use. # # More data may be available offline. # #For more information on these data, contact Pennsylvania NWISWeb Data Inquiries. # This file contains the annual peak streamflow data. # # This information includes the following fields: # # agency_cd Agency Code # site_no USGS station number # peak_dt format YYYY-MM-DD # peak_va Annual peak streamflow value in cfs # peak_cd Peak Discharge-Qualification codes (see explanation below) # gage_ht Gage height for the associated peak streamflow in feet # gage_ht_cd Gage height qualification codes # year_last_pk Peak streamflow reported is the highest since this year # ag_dt Date of maximum gage-height for water year (if not concurrent with peak) # ag_tm Time of maximum gage-height for water year (if not concurrent with peak # ag_gage_ht maximum Gage height for water year in feet (if not concurrent with peak # ag_gage_ht_cd maximum Gage height code # # Sites in this file include: # USGS 01474500 Schuylkill River at Philadelphia, PA
PORTION OF DATA TABLE USGS DATA FOR SCHUYLKILL RIVER @ PHILADELPHIA # agency_cd site_no peak_dt peak_tm peak_va peak_cd gage_ht 5s 15s 10d 6s 8s 27s 8s USGS 1474500 1869-10-04 135000 2,7 17 USGS 1474500 3/1/1902 98000 2,7 14.8 USGS 1474500 3/28/1932 33300 10.27 USGS 1474500 8/24/1933 96200 14.7 USGS 1474500 9/30/1934 44800 11.3 USGS 1474500 7/9/1935 82000 14.1 USGS 1474500 1/3/1936 49600 11.7 USGS 1474500 12/20/1936 17100 8.6 USGS 1474500 9/21/1938 37700 10.66 USGS 1474500 2/3/1939 42400 11.08 USGS 1474500 3/15/1940 49600 11.72 USGS 1474500 11/15/1940 22300 9.22 USGS 1474500 8/9/1942 71500 13.1 USGS 1474500 12/30/1942 47800 11.36 USGS 1474500 11/9/1943 45200 11.19
EXTREME EVENTS FLOODS Largest flow in any given water year (Annual maximum) N largest flows in N years (Extreme values) Statistical analysis Assign probability to a measured flood (plotting position formula) Probability that a given discharge will occur or be exceeded in any year, P(X x)
PLOTTING POSITION FORMULA What is the probability that the largest flood in 100 years will be equaled or exceeded in a year? P = 1 = 100 0.01 The #1 flood in 100 years. In general, P( X x) = r N + 1 r = rank (1 = biggest, 2 = second biggest, etc.) N = number of years of record
PORTION OF RANKED DATA TABLE SCHUYLKILL RIVER @ PHILADELPHIA 76 YEARS OF DATA Q (cfs) Rank P(X>x) 135000 1 0.01299-2.22660 103000 2 0.02597-1.94356 98000 3 0.03896-1.76287 96200 4 0.05195-1.62625 94600 5 0.06494-1.51461 92500 6 0.07792-1.41919 90100 7 0.09091-1.33518 89800 8 0.10390-1.25966 82000 9 0.11688-1.19071 79000 10 0.12987-1.12701
ANNUAL PEAK FLOWS - SCHUYLKILL RIVER @ PHILADELPHIA 1,000,000 PEAK DISCHARGE (cfs) 100,000 10,000-2.5-2 -1.5-1 -0.5 0 0.5 1 1.5 2 2.5 P(X>x)
ANNUAL PEAK FLOWS - SCHUYLKILL RIVER @ PHILADELPHIA 1,000,000 100-YEAR FLOOD Q = 141,400 cfs PEAK DISCHARGE (cfs) 100,000 50-YEAR FLOOD Q = 122,600 cfs y = 41814e -0.5237 x 10,000-3 -2-1 0 1 2 3 P(X>x)