Cu06997 the basics_26052013


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Cu06997 the basics_26052013

  1. 1. Course CU06997 Fluid DynamicsThe 13 situations you are able tocalculate at the end of this course1
  2. 2. WaterStagnantnot flowingu = 0 m/sIn motionflowingu > 0 m/sHydrostatics Fluid dynamicsPipes Open channel[Gesloten leidingen] [Open water]1
  3. 3. Classification of flows.1. Steady uniform flow [Eenparig uniform]example: pipe with constant D and Qexample: channel with constant A and Q2. Steady non-uniform flowexample: pipe with different D and constant Qexample: channel with different A and constant Q3. Unsteady uniform flow[Niet eenparig , uni..]example: pipe with constant D and different Qexample: channel with constant A and different Q4. Unsteady non-uniform flowexample: pipe with different D and Qexample; channel with different A and Q1
  4. 4. Basics 𝑄 = 𝑒 βˆ™ 𝐴 PAR ο€½212222211122 Hguzyguzyu1Reference /datum [m] [Referentie]Surface level [m] [Waterstand]Total head H [m] [Energiehoogte]P1z1y1u12/2g Velocity head [m] [Snelheidshoogte]y = Pressure head [m] [drukhoogte]z = Potential head [m] [plaatshoogte]1
  5. 5. Turbulent or laminar flow[Turbulente of laminaire stroming]𝑅𝑒 =𝑉. 4π‘…πœˆSubcritical or Supercritical flow[Stromend of Schietend water]𝑦𝑐 =𝑄2𝑔 βˆ™ 𝐡23𝑉𝑐 = 𝑔 βˆ™ 𝑦𝑐2πΉπ‘Ÿ =𝑉𝑉𝑐1
  6. 6. DownstreamUpstreamCross-section CulvertHeadLossLength CulvertVelocity1. Discharge culvert [Debiet duiker]2. Dimensions culvert[Afmetingen duiker]2
  7. 7. DownstreamUpstreamCross-section CulvertHeadLossLength CulvertVelocityCulvert,submerged [Duiker,volledig gevuld]211i1ο€½oRLf4οƒ—ο€½ [m]2gu)ΞΎΞΎΞΎ(ΔΗ2culvertoficulvert 2
  8. 8. DownstreamUpstreamCross-sectionLength CulvertFlow velocity3. Discharge partly submerged Culvert[Debiet gedeeltelijk gevulde duiker]2
  9. 9. DownstreamUpstreamCross-sectionLength CulvertFlow velocityCulvert, partly filled[Duiker, gedeeltelijk gevuld]Is a broad crested weir[Is een lange overlaat]2
  10. 10. Free flow broad crested weir[Volkomen lange overlaat]23HBcq vv οƒ—οƒ—ο€½Total Head or Energy line HFree flow broad crested weirSuper critical flowHydraulic Jump2
  11. 11. Submerged broad crested weir flow[Onvolkomen lange overlaat])(2 33 hHghBcq olv ο€­οƒ—οƒ—οƒ—οƒ—ο€½Total Head or Energy line HSubmerged broad crested weirBottom eddy2
  12. 12. Bed SlopeDepthHeadLossCross-sectionProfile4. Discharge open channel5. Dimensions open channel6. Equilibrium depth open channel3
  13. 13. Bed SlopeDepthHeadLossCross-sectionProfileOpen channel, bed slope > 0[Open watergang, bodemverhang > 0]𝑉 =𝑅23 βˆ™ 𝑆 𝑏12𝑛𝑉 = 𝐢 βˆ™ 𝑅 βˆ™ 𝑆 𝑏𝑆 𝑏 = 𝑆𝑓𝑦𝑛 =π‘ž2𝑏2 βˆ™ 𝐢2 βˆ™ 𝑆 𝑏33
  14. 14. DepthDepthHeadLossHydraulic gradientHorizontal bedCross-sectionProfile7. Hydraulic Gradient open channel[Energieverhang open watergang]3
  15. 15. DepthDepthHeadLossHydraulic gradientHorizontal bedCross-sectionProfileOpen channel, bed slope <= 0[Open watergang, bodemverhang <=0]𝑉 =𝑅23 βˆ™ 𝑆𝑓12𝑛𝑉 = 𝐢 βˆ™ 𝑅 βˆ™ 𝑆𝑓3
  16. 16. SpecificHeadWidthWeirHydraulic GradientCross-sectionProfile8. Upstream water level Weir9. Dimensions Weir [Afmetingen stuw]3
  17. 17. SpecificHeadWidthWeirHydraulic GradientCross-sectionProfileShort crested weir [Korte overlaat, meetstuw]𝑄 = π‘š βˆ™ 𝐡 βˆ™ 𝐻323
  18. 18. Hydraulic GradientHeadLossWater levelCross-sectionProfileSubmerged Pipe10. Flow rate Pipe [Debiet buis]11. Dimensions Pipe [Afmetingen buis]4
  19. 19. Hydraulic GradientHeadLossWater levelCross-sectionProfileSubmerged PipeFlow rate Pipe [Debiet buis]𝑉 = 𝐢 βˆ™ 𝑅 βˆ™ 𝑆𝑓 𝐢 = 18 βˆ™ π‘™π‘œπ‘”12π‘…π‘˜π‘†π‘“ =Ξ”H𝐿4
  20. 20. WaterdepthWaterpressureWallWater levelProfile12. Force by water [Kracht door water]4
  21. 21. WaterdepthWaterpressureWallWater levelProfileForce by water [Kracht door water]𝑝 = 𝜌 βˆ™ 𝑔 βˆ™ 𝑦 [π‘ƒπ‘Ž] F = p βˆ™ A [N]4
  22. 22. CulvertEmptyGround water levelCross-section13. Buoyancy [Opdrijving]4
  23. 23. CulvertEmptyGround water levelCross-sectionBuoyancy, [Opdrijving]Upward force = weight of fluid displaced by the body4