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CE 356 Elements of Hydraulic Engineering

CE 356 Elements of Hydraulic Engineering. Specific Energy (Alternate Depths) Hydraulic Jump (Sequent Depths). Energy in Open Channels. Specific Energy. Specific Energy, E. E = energy (head) measured with respect to the channel bottom . E = V 2 /2g + y = q 2 /(2gy 2 ) + y.

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CE 356 Elements of Hydraulic Engineering

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  1. CE 356 Elements of Hydraulic Engineering Specific Energy (Alternate Depths) Hydraulic Jump (Sequent Depths)

  2. Energy in Open Channels Specific Energy

  3. Specific Energy, E E = energy (head) measured with respect to the channel bottom E = V2/2g + y = q2/(2gy2) + y Multiply through by y2 and arrange to find y3 – E y2 + q2/2g = 0 What kind of equation is this? How many roots? Significance of roots?

  4. Specific Energy Diagram Rectangular channel: B = 20 ft Q = 600 ft3/s. E = y Fr = 1 Fr = 2 Fr = V/(gy)0.5

  5. Example: Sluice Gate q = 30 ft2/s y = 5.6 ft y = 1.8 ft

  6. figure 1 Hydraulic jump Note that there is head loss in an hydraulic jump

  7. steady jump: 4.5<Fr < 9.0, stable and well-balanced strong jump: Fr > 9.0, rough wavy surface downstream Hydraulic jump on Rattan Creek, TX. July 2, 2002 jump

  8. classification Classification

  9. picture

  10. figure 2

  11. jump cv Now let’s consider an hydraulic jump We know that or

  12. Our momentum balance momentum balance can be written as rearranging and dividing by g: Using A=By for a rectangular channel Let’s go back to our hydraulic jump…

  13. solvable set If we have an open channel where we know Q, B, and y1, we can solve for y2

  14. Starting from rectangular Recalling the definition of the flow rate per unit width we can obtain Solving for y2 y1 solution is similar (see text)

  15. limits Now, what are the limitations of this equation? shear forces are neglected shear causes smaller head loss than turbulence in the jump requires jump occurs over a short distance rectangular channel effect of gravity downslope is neglected again requires jump to occur over a short distance neglect non-hydrostatic pressure uniform density fluid

  16. principle …and what is the fundamental principle for this equation? conservation of momentum

  17. E–M graphs

  18. head loss The more general head loss formula is Valid for any cross section

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