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The Stage-Discharge Rating

The Stage-Discharge Rating. D. Phil Turnipseed, P.E. Hydrologist USGS-FERC Streamgaging Seminar Washington, D.C. June 6-7, 2006. Ratings developed by making discharge measurements.

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The Stage-Discharge Rating

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  1. The Stage-Discharge Rating D. Phil Turnipseed, P.E. Hydrologist USGS-FERC Streamgaging Seminar Washington, D.C. June 6-7, 2006

  2. Ratings developed by making discharge measurements

  3. A straight line on rectilinear paper is of the form:y = mx + bwhere: m = slope of line and: b is the y intercept

  4. Logarithmic Coordinate System • Many hydraulic relations are linear in log form • Examples include: • Discharge equations for weirs • Open-channel flow equations, with simplifying assumptions • This means SEGMENTS of ratings may be linear in log space

  5. Stage-Discharge Relations for Artificial Controls

  6. Q = C B h 1.5 Equations commonly used to relate water discharge to hydraulic head (h) RECTANGULAR WEIR where: C = a discharge coefficient B = top width of weir or length of weir crest normal to flow

  7. V-NOTCH WEIR (90 degrees) 2.5 Q = 2.5 h Equations commonly used to relate water discharge to hydraulic head (h)

  8. 2.50 Water Surface h Relation between water discharge (Q) and Head (h) for a v-notch weir (pzf at gage height = 0.0) 4 2.5 Q = 2.5 h 3 Gage Height 2 1 0

  9. RATING CURVE FOR A V-NOTCH WEIR(PZF at GH = 0.0, therefore h = ght) Q = 2.5h 2.5 Gage Height (e=0) Discharge

  10. 3.50 Water Surface h Relation between water discharge (Q) and head (h) for a v-notch weir (pzf at gage height = 1.0) 5 2.5 h = GH - e Q = 2.5 h 4 3 Gage Height 2 1 Will be scale e offset 0

  11. Rating if no offset used (Gage height plotted against discharge) Rating if offset used (Head plotted against discharge) Rating for a V-notch weir when PZF = 1.0 ft. Gage height Discharge

  12. Gage Height PZF Example of relation between PZFand gage height Head = GH - PZF or about 0.37 (2.55 - 2.18)

  13. Include Velocity Head Measuring Point of Zero Flow Flow Gage Pool Control Section Flow Deepest Point on Control Gage Pool Control Section Perpendicular to Flow

  14. Stage-Discharge Relations for Natural Controls

  15. Section Controls

  16. Section Controls

  17. Common equations used to relate water discharge to channel conditions Section Control Q = a(GH-e)b where: a = coefficient b = slope of the relations (b is almost always greater than 2)

  18. 1 >2 1 <2 1 >2 Rating curve shapes Overbank Channel Control Gh - e Section Control Section Control Q = a(GH-e)b

  19. Channel Controls

  20. Common equations used to relate water discharge to channel conditions Channel Control Q = 1.49 A R 2/3 S 1/2 n Where: A = cross section area R = hydraulic radius (area/wetted perimeter) S = energy slope n = Manning’s “n” (roughness coefficient)

  21. 1 >2 1 <2 1 >2 Rating curve shapes Overbank Channel Control Gh - e Section Control Channel Control Q = CD 1.67(Manning’s Eq.)

  22. Different Controls, Same Site Section control Channel control or partial channel control

  23. 1 >2 1 <2 1 >2 Rating curve shapes Overbank Channel Control Gh - e Section Control Overbank Control Q = CD (>2)(Manning’s Eq.)

  24. Open-Channel Flow: • Types of Flow • States of Flow • Regimes of Flow

  25. Open-Channel Flow: • Types of Flow • States of Flow • Regimes of Flow • Basic equations

  26. Temporal flow classifications Steady Unsteady Depth and velocity are constantwith time Depth and velocitychangewith time

  27. Spatial flow classifications Uniform Varied Constantdepth and velocityalong the channel length Changingdepth and velocity along the channel length

  28. Spatial flow classifications Uniform Gradually Varied water-surface slope = channel SlopeSw = So water-surface slope = friction SlopeSw = Sf

  29. Gradually Varied Flow

  30. Flow-Classification Summary: • Steady flow • Uniform flow • Varied flow • Gradually varied flow • Rapidly varied flow • Unsteady flow • Unsteady uniform flow (rare) • Unsteady flow (i.e., unsteady varied flow) • Gradually varied unsteady flow • Rapidly varied unsteady flow From Chow, 1959

  31. Open-Channel Flow: • Types of Flow • States of Flow • Regimes of Flow

  32. State of Flow: • State of flow governed by effects of viscosity and gravity relative to the inertial forces of the flow

  33. States of Flow: • Viscosity vs. inertia: Reynold’s NumberR = VL/ע where V = velocity of flow L = hydraulic radius ע = kinematic viscosity of water • Laminar flow: R< 500 • Turbulent flow: R> 2000 • Laminar flow rare in open channels

  34. States of Flow: • Gravity vs. inertia: Froude NumberF = V/(gL)1/2 where V = velocity of flow L = hydraulic radius (depth) g = acceleration of gravity • F = 1: V = (gD)1/2 Critical flow Equilibrium • F < 1: V < (gD)1/2 Sub-critical flow Gravity dominates • F > 1: V > (gD)1/2 Super-critical flow Inertia dominates

  35. States of Flow: • Critical velocity (gD)1/2 known as the “wave celerity”– velocity of a gravity wave generated by a local disturbance in shallow water • Ability of a gravity wave to propagate upstream is a criterion for identifying sub-critical or super-critical flow • Flow in most channels is controlled by gravity Sub-critical

  36. States of Flow flow flow Sub-critical (tranquil) flow Supercritical (rapid) flow F < 1.0 F >1.0 F = 1.0 critical flow

  37. Open-Channel Flow: • Types of Flow • States of Flow • Regimes of Flow • Basic equations

  38. Regimes of Flow: • Combined effect of viscosity and gravity 4 regimes of flow1) Sub-critical – laminar: F < 1; R < 5002) Super-critical – laminar: F > 1; R < 5003) Sub-critical – turbulent: F < 1; R > 20004) Super-critical – turbulent: F > 1; R > 2000

  39. Regimes of Flow: From Chow, 1959

  40. Downstream view Upstream view Upstream Natural Control Upstream control- Flow past gage is supercritical

  41. Rating and controls, San Francisquito Cr. PZF = 0.07

  42. Rating and controls, San Francisquito Cr. (cont.) Measurement at moderate flow G.H. = 5.4

  43. Rating and Controls, San Francisquito Cr. (cont.) Channel Control beginning to dominate at this stage (6.25 feet)

  44. Rating and controls, San Francisquito Cr. (cont.)

  45. Shifting Controls

  46. Shifting Control The non-cohesive streambed in this photo is subject to scour and fill, as well as changing vegetation conditions.  Unstable channel

  47. Shifts • Shift is a “temporary rating” • Generally used for a temporary change in the control • Case 1: Assumes control will move back to the rating • Case 2: Control changes so frequently, shifts applied to avoid always making a new rating

  48. Shift Corrections • Change the shape and/or position of the rating curve • Creates a “temporary rating” • By time • Simple • By stage • Variable shift or V-shift diagrams • A better reflection of what actually happens in stream • Combination of both

  49. Template for Content Slide

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