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Chapter 12

Chapter 12. Hydrologic Statistics and Hydraulics. Storm Hydrograph. Stream Hydrographs: A plot of discharge (= flow rate) or stage (= water level) versus time. Stormflow Hydrograph: A plot of discharge or stage before, during, and after a specific storm. Rising Limb:

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Chapter 12

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  1. Chapter 12 Hydrologic Statistics and Hydraulics

  2. Storm Hydrograph

  3. Stream Hydrographs: • A plot of discharge (= flow rate) or stage (= water level) versus time. • Stormflow Hydrograph: • A plot of discharge or stage before, during, and after a specific storm. • Rising Limb: • The steep advance portion of the hydrograph that reflects the onset of runoff • Falling Limb: • Flow that tapers off gradually following the peak.

  4. Peak Stormflow: • Generally produced by surface runoff, either by partial area contribution or Hortonian overland flow as well as direct precipitation on the channels. • Interflow: • Flow that takes longer to reach the channel • Dominates the falling limb of the hydrograph. • Baseflow: • The flow before and after the storm • Generated principally by ground water discharge and unsaturated interflow. • Stormflow Volume: • Total volume of streamflow associated with that storm • It can be determined from the area under the hydrograph when the hydrograph plots flow (not stage) vs time.

  5. Hydrographfor 1997 Homecoming Weekend Storm

  6. Stream Hydrograph

  7. Flow behavior for different streams

  8. Hydrograph Behavior

  9. Hydrograph Behavior:Also related to channel patterns

  10. Streamflow Variability

  11. Measurement Units • cfs: cubic feet per second • gpm: gallons per minute • mgd: million gallons per day • AF/day: Acre-Feet per day • cumec: cubic meters per second • Lps: liters per second • Lpm: liters per minute

  12. Useful Conversions • 1 cfs  • 2 AF/day • 450 gpm • 28.3 Lps • 1 m3/s = 35.28 cfs • 1 mgd  1.5 cfs • 1 gpm = 3.785 Lpm

  13. Weir Construction

  14. Weir Types

  15. Weir Equations • Submerged Pipe: • Q = c  r2 h1/2 • Rectangular Weir: • Q = c W h3/2 • V-notch Weir: • Q = c h5/2 • where • Q is flow, cfs • c are weir coefficients • h is stage, ft • r is the pipe diameter, ft • W is the weir width, ft

  16. Field Velocity Measurements • Flow Equation: • Q = v A • where • Q is the discharge, cfs • v is the water velocity, ft/s • A is the flow cross-sectional area, ft2

  17. Discharge Measurements

  18. Manning's Equation • v = (1.49/n) R2/3 S1/2 • where • v is the water velocity, ft/s • n is the Manning's hydraulic roughness factor • R = A / P is the hydraulic radius, ft • A is the channel cross-sectional area, ft2 • P is the channel wetted perimeter, ft • S is the water energy slope, ft/ft

  19. Manning’s Equation

  20. River Stage: • The elevation of the water surface • Flood Stage • The elevation when the river overtops the natural channel banks. • Rating Curve • The relationship between river stage and discharge

  21. Rating Curve

  22. Hydrologic Statistics: • Trying to understand and predict streamflow • Peak Streamflow Prediction: • Our effort to predict catastrophic floods • Recurrence Intervals: • Used to assign probability to floods • 100-yr flood: • A flood with a 1 chance in 100 years, or a flood with a probability of 1% in a year.

  23. Return Period • Tr = 1 / P • Tr is the average recurrence interval, years • P is exceedence probability, 1/years • Recurrence Interval Formulas: • Tr = (N+1) / m • Gringarten Formula: Tr = (N+1-2a) / (m-a) • where • N is number of years of record, • a = 0.44 is a statistical coefficient • m is rank of flow (m=1 is biggest)

  24. Flood Prediction

  25. Peak Flows in Ungaged Streams • Qn = a Ax Pn • where • A is the drainage area, and • Pn is the n-year precipitation depth • Qn is the n-year flood flow • Q2 = 182 A0.622 • Q10 = 411 A0.613 • Q25 = 552 A0.610 • Q100 = 794 A0.605

  26. Bankfull DischargeQbkf = 150 A0.63

  27. Curve Number Method • Most common method used in the U.S. for predicting stormflow peaks, volumes, and hydrographs for precipitation events. • It is useful for designing ditches, culverts, detention ponds, and water quality treatment facilities.

  28. Curve Number Method

  29. P = Precipitation, usually rainfall • Heavy precipitation causes more runoff than light precipitation • S = Storage Capacity • Soils with high storage produce less runoff than soils with little storage. • F = Current Storage • Dry soils produce less runoff than wet soils

  30. r = Runoff Ratio => how much of the rain runs off? • r = Q / P • r = 0 means that little runs off • r = 1 means that everything runs off • r = F / S • r = 0 means that the bucket is empty • r = 1 means that the bucket is full • F = P - Q • the soil fills up as it rains • Combining equations yields: • Q = P (P - Q) / S • Solving for Q yields: • Q = P2 / (P + S)

  31. S is maximum available soil moisture • S = (1000 / CN) - 10 • CN = 100 means S = 0 inches • CN = 50 means S = 10 inches • F is actual soil moisture content • F / S = 1 means that F = S, the soil is full • F / S = 0 means that F = 0, the soil is empty • Land Use CN S, inches • Wooded areas 25 - 83 2 - 30 • Cropland 62 - 71 4 - 14 • Landscaped areas 72 - 92 0.8 - 4 • Roads 92 - 98 0.2 - 0.8

  32. Curve Number Procedure • First we subtract the initial abstraction, Ia, from the observed precipitation, P • Adjusted Rainfall: Pa = P - Ia • No runoff is produced until rainfall exceeds the initial abstraction. • Ia accounts for interception and the water needed to wet the organic layer and the soil surface. • The initial abstraction is usually taken to be equal to 20% of the maximum soil moisture storage, S, => Ia = S / 5

  33. The runoff depth, Q, is calculated from the adjusted rainfall, Pa , and the maximum soil moisture storage, S, using: • Q = Pa2 / (P_a + S) • or by using the graph and the curve number • We get the maximum soil moisture storage, S, from the Curve Number, CN: • S = 1000 / CN - 10 • CN = 1000 / (S + 10) • We get the Curve Number from a Table.

  34. Examples • A typical curve number for forest lands is CN = 70, so the maximum soil storage is: • S = 1000 / 70 - 10 = 4.29" • A typical curve number for a landscaped lawn is 86, and so • S = 1000 / 86 - 10 = 1.63"

  35. A curve number for a paved road is 98, • so S = 0.20” • Why isn’t the storage equal to zero for a paved surface? • The roughness, cracks, and puddles on a paved surface allow for a small amount of storage. • The Curve Number method predicts that Ia = S / 5 = 0.04 inches of rain must fall before a paved surface produces runoff.

  36. Another CN Example • For a watershed with a curve number of 66, how much rain must fall before any runoff occurs? • Determine the maximum potential storage, S: • S = 1000 / 66 - 10 = 5.15" • Determine the initial abstraction, Ia • Ia = S / 5 = 5.15” / 5 = 1.03" • It must rain 1.03 inches before runoff begins. • If it rains 3 inches, what is the total runoff volume? • Determine the effective rainfall, Pa • Pa = P - Ia = 3" - 1.03" = 1.97" • Determine the total runoff volume, Q • Q = 1.972 / (1.97 + 5.15) = 0.545"

  37. Unit Hydrographs

  38. Unit Hydrograph

  39. Flood Routing

  40. Unit Area Hydrographs

  41. Unit Hydrograph Example • A unit hydrograph has been developed for a 100 hectare watershed • The peak flow rate for a storm that produces 1 mm of runoff is 67 L/s • What is the peak flow rate for this same watershed if a storm produces 3 mm of runoff? • The unit hydrograph method assumes that the hydrograph can be scaled linearly by the amount of runoff and by the basin area. • In this case, the watershed area does not change, but the amount of runoff is three times greater than the unit runoff. • Therefore, the peak flow rate for this storm is three times greater than it is for the unit runoff hydrograph, or 3 x 67 L/s = 201 L/s.

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