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Engineering Low-Head Dams for Function and Safety

Engineering Low-Head Dams for Function and Safety. Fritz R. Fiedler Department of Civil Engineering University of Idaho. What is a Low-Head Dam?. A dam that is typically less than 15 feet tall Used to pond water behind them but not control flow

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Engineering Low-Head Dams for Function and Safety

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  1. Engineering Low-Head Dams for Function and Safety Fritz R. Fiedler Department of Civil Engineering University of Idaho

  2. What is a Low-Head Dam? • A dam that is typically less than 15 feet tall • Used to pond water behind them but not control flow • Head: a term that refers to elevation, which can be related to fluid pressure and energy

  3. Why are they dangerous? • Low-head dams cause water to recirculate, thus trapping buoyant objects

  4. y V w Flow in rectangular channels • Side view • Front view Variables: y = flow depth (L) w = channel width (L) A = flow area = yw (L2) V = flow velocity (L/T) Q = discharge = VA (L3/T) q = Q/w (L2/T) Example: y = 2 ft w = 1.5 ft A = 3 ft2 V = 3 ft/s Q = 9 ft3/s q = 6 ft2/s Q

  5. States of flow in open channels • For a given Q, flow in open channels can be subcritical, supercritical, or critical • Subcritical: disturbances on water surface will travel upstream (flow velocity less than wave velocity); high y, low V • Supercritical: disturbances will not travel upstream (flow velocity greater than wave velocity); low y, high V • Critical: flow velocity equals wave velocity

  6. Hydraulic Jump Hydraulic Jump 2 Q = V1A1 = V1y1w 1 Q = V2A2 = V2y2w Image source: http://www.engineering.usu.edu/classes/cee/3500/openchannel.htm Note: Q is constant, so V1y1 = V2y2 (if w constant also)

  7. Froude Number • Ratio of inertia forces to gravity forces • F = V / (gy)0.5 • G = gravitational acceleration • Subcritical flow: F < 1 (gravity forces larger) • Supercritical flow: F > 1 (inertia forces larger) • Critical flow: F = 1

  8. Froude Number Hydraulic Jump 2 1 F1 = V1 / (gy1)0.5 F1 > 1 F2 = V2 / (gy2)0.5 F2 < 1 Image source: http://www.engineering.usu.edu/classes/cee/3500/openchannel.htm

  9. Initial and Sequent Depths • Relationship between depths before (initial) and after (sequent) a hydraulic jump • If y1 and V1 are known, can compute y2

  10. Flow over a dam (weir) As water flows over dam, goes through critical depth, yc at which F = 1 subcritical H yc Hydraulic Jump y0 subcritical P supercritical y1 y2 Q = CwH1.5 or q = CH1.5 where C is a weir coefficient that varies with dam type and H – but we are going to find and measure yc

  11. Critical Flow • At critical flow, F = 1 = Vc / (gyc)0.5 • Vc = (gyc)0.5 • Measure yc at dam, compute Vc then • Q = Vcycw • How is the location of yc found?

  12. Submerged Hydraulic Jump H yc y0 P y1 y2 yt • When yt exceeds y2 the jump becomes submerged • Degree of Submergence = S = (yt – y2) / y2 • When S < 0, jump occurs downstream • When S > 0, jump is submerged • If yt becomes large enough, dam will be submerged too • In the flume, we can control yt

  13. waves travel up waves travel down H yc y0 Dy P y1 y2 yt

  14. Project Steps • Analysis • Measure variables at two discharges • With and without tailwater submergence • Design • Objectives: maintain upstream depth, allow safe passage, create surf wave, minimize cost • Method: simple calculations, physical model studies and testing

  15. Analysis • At low discharge • With no tailwater • Measure: H, P (dam height), yc (must locate), y1, y2, Dy • Compute: Vc, Q, q, F1, C • Evaluate: measurement accuracy, sequent depth equation, floating object passage • With tailwater submerging jump • Measure: yt, Dy, and compute S • Evaluate: measurements, floating object passage • Repeat 1., a., b., … for high discharge

  16. Notes • We can mark, with tape and markers, the water levels right on the flume • Mark the height of the tailwater gate • We will keep flume slope, discharges constant throughout semester • Group Assignment: create a data sheet based on previous slide before next class.

  17. Design • Conceptual • What makes the hydraulic dangerous? • Uniformity, Dy, reverse flow velocity, aeration • How can this knowledge be used to meet objectives? • Analytical / Mathematical • Difficult! • Computer models • Simple equations (e.g., V-notch weir) • Physical models…

  18. Physical Models Image source: http://www.usbr.gov/pmts/hydraulics_lab/about/index.html

  19. Physical Model Testing • Measure variables as in Analysis (and more?) • What has changed? • Compare upstream pool elevations • Aim for little or no difference at both discharges • Test object passage • Surf spot? • Describe the hydraulic • Iterative process! (a.k.a., trial and error)

  20. Practicality and Economics • What types of materials would be required to build your design? (concrete, rip rap, …) • How and when could it be constructed? • If volume of material added is the primary cost, and the cost of this material per unit volume is known – how much would it cost? • Minimum volume = minimum cost: estimate the volume change in your design

  21. Other (Important) Considerations • Water Quality • Sediment and contaminants • Physical • Sediment and stream morphology • Dissolved oxygen • flooding • Ecological • Fish passage • Effects on aquatic life

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