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Hydraulics

Hydraulics. Open Channel Flow. Liquid (water) flow with a ____ ________ (interface between water and air) relevant for natural channels: rivers, streams engineered channels: canals, sewer lines or culverts (partially full), storm drains of interest to hydraulic engineers

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Hydraulics

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  1. Hydraulics

  2. Open Channel Flow • Liquid (water) flow with a ____ ________ (interface between water and air) • relevant for • natural channels: rivers, streams • engineered channels: canals, sewer lines or culverts (partially full), storm drains • of interest to hydraulic engineers • location of free surface • velocity distribution • discharge - stage (______) relationships • optimal channel design free surface depth

  3. Topics in Open Channel Flow • Uniform Flow • Discharge-Depth relationships • Channel transitions • Control structures (sluice gates, weirs…) • Rapid changes in bottom elevation or cross section • Critical, Subcritical and Supercritical Flow • Hydraulic Jump • Gradually Varied Flow • Classification of flows • Surface profiles normal depth

  4. Mines Avenue pump station

  5. Classification of Flows • Steady and Unsteady • Steady: velocity at a given point does not change with time • Uniform, Gradually Varied, and Rapidly Varied • Uniform: velocity at a given time does not change within a given length of a channel • Gradually varied: gradual changes in velocity with distance • Laminar and Turbulent • Laminar: flow appears to be as a movement of thin layers on top of each other • Turbulent: packets of liquid move in irregular paths (Temporal) (Spatial)

  6. Momentum and Energy Equations • Conservation of Energy • “losses” due to conversion of turbulence to heat • useful when energy losses are known or small • ____________ • Must account for losses if applied over long distances • _______________________________________________ • Conservation of Momentum • “losses” due to shear at the boundaries • useful when energy losses are unknown • ____________ Contractions We need an equation for losses Expansion

  7. Rapidly Varied FlowThe Hydraulic Jump • Use of hydraulic jumps • Specific force revisited • Sequent or conjugate depths • Types of jump

  8. Uses of Hydraulic Jumps • Hydraulic Jumps can and do occur naturally – for example, in and after “rapids” in rivers • They are also deliberately created: • To dissipate energy after a spillway etc and so prevent scouring • To recover head downstream of an obstruction • To induce mixing and aeration

  9. Specific Force Revisited • Over a short reach of channel, external friction forces can be ignored and if the slope is mild the downstream self-weight body forces can also be ignored. • Thus….

  10. and giving

  11. Sequent or Conjugate Depths • These terms refer to the depths at sections 1 and 2, before and after a hydraulic jump

  12. Evaluation of Conjugate Depths • In general form: • and F1 = F2, referring to diagram on previous slide.

  13. For a wide or rectangular channel, A=By and • Hence, dividing by B:

  14. Which leads to:

  15. These equations can be used to determine the depths upstream or downstream of a hydraulic jump. • The Froude Number Fr is used to characterize a jump.

  16. Undular Jump • Fr1 = 1.0 to 1.7 • y1 near ycr • y2/y1 low • Little energy dissipation • As Fr1 increases towards 1.7 the first undulation becomes more pronounced and will eventually break.

  17. Weak Jump • Fr1 = 1.7 to 2.5 • Little energy dissipation • Surface fairly smooth • Breaking of first undulation gives small rollers on the face of the jump.

  18. Oscillating Jump • Fr1 = 2.5 to 4.5 • High velocity entering jump. • This oscillates from bed to surface and back, producing waves of irregular period downstream • Avoid in design.

  19. Steady Jump • Fr1 = 4.5 to 9.0 • Jet oscillation disappears • Surface roller increases in length till it ends where the jet reaches the surface • 45-70% energy dissipation • Aim for in design

  20. Choppy Jump • Fr1 = >9.0 • Surface roller highly aerated • Jet penetrates for a long distance downstream, requiring a long deep stilling basin.

  21. Mines Avenue pump station

  22. Broad-crested Weir

  23. Broad Crested Weir

  24. This is the simplest device for flow measurement. • It is more suitable for large discharges. • The width of the weir is taken as the width of the waterway. • The following equations is used:

  25. The discharge coefficient Cd equals 0.89. • To design the weir, h1 is the only unknown and can be calculated from the equation. • If the characteristics of the weir are known, the discharge can be evaluated from the equation.

  26. Ogee type Weir

  27. Ogee Type weir • Ogee type weir is used as spillway for dams. • The shape of the weir is selected such that the water flow is always in contact with the face of the weir. • The shape of the weir face follows this equation:

  28. Where x and y are the coordinates and h1 is the head of water above the crest level. • The discharge can be evaluated using the following equation: Where Ce is the discharge coefficient (1.3) and bc is the crest width.

  29. San Gabriel River desilting basin spreading basin number 1 headworks Diversion Structure intake canal

  30. Mines Avenue pump station

  31. Standard Step • Given a depth at one location, determine the depth at a second given location • Step size (x) must be small enough so that changes in water depth aren’t very large. Otherwise estimates of the friction slope and the velocity head are inaccurate • Can solve in upstream or downstream direction • Usually solved upstream for subcritical • Usually solved downstream for supercritical • Find a depth that satisfies the energy equation

  32. Settling Basin / Canal • Sedimentation is a process in which the velocity of the water is lowered below the suspension velocity and the suspended particles settle out of the water due to gravity.  • The process is also known as the settling process • Accomplished in a sedimentation basin

  33. San Gabriel River desilting basin spreading basin number 1 headworks Diversion Structure intake canal

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