1 / 31

Problem 4.

Problem 4. Hydraulic Jump. Problem. When a smooth column of water hits a horizontal plane, it flows out radially. At some radius, its height suddenly rises. Investigate the nature of the phenomenon. What happens if a liquid more viscous than water is used?. Experiment. Obtaining the effect

aretha-lowery
Download Presentation

Problem 4.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Problem 4. Hydraulic Jump

  2. Problem When a smooth column of water hits a horizontal plane, it flows out radially. At some radius, its height suddenly rises. Investigate the nature of the phenomenon. What happens if a liquid more viscous than water is used?

  3. Experiment • Obtaining the effect • Parameters: • Liquid density • Liquid viscosity • Flow rate • Jet height

  4. Experiment cont. • Measurements: • Dependence of flow velocity on radius • Dependence of jump radius on flow rate • Dependence of jump radius on viscosity • Dependence of jump radius on jet height • Jump structure in dependence on velocity

  5. Apparatus container p l a t e pump

  6. Apparatus cont.

  7. Viscosity variation • Water was heated from 20˚C to 60˚C • The achieved viscosity change was over 50% • Dependence of viscosity on temperature: S. Gleston, Udžbenik fizičke hemije, NKB 1967

  8. Viscosity variation cont. thermometer heater

  9. Velocity measurement • A Pitot tube was used v – flow velocity H – water height in tube ΔH – cappilary correction H

  10. Explanation • Hydraulic jump – sudden slow-down and rising of liquid because of turbulence • The turbulence appears when the viscous boundary layer reaches the flow surface • Boundary layer detachment appears and a vortex is formed • The vortex spends flow energy and slows it

  11. Explanation cont. • Due to turbulenceenergy is lost in the jump •  Flow before the jump is slower than behind • Water level is higher due to continuity jump ˝Nonviscous˝ layer Boundary layer

  12. Explanation cont. • Tasks for the theory: • Dependence of jump radius on parameters • Dependence of flow velocity on radius • Jump structure • Governing equations: • Continuity and energy conservation • Navier – Stokes equation

  13. Critical radius • Critical radius – jump formation radius • Condition for obtaining critical radius: h – flow height rk – critical radius Δ– boundary layer thickness

  14. Critical radius cont. • Continuity equation: • Energy conservation: Q – flow rate v – flow velocity r – distance from jump centre z – vertical axis J – kinetc energy pro unit time Jot – friction power

  15. Critical radius cont. • Flow velocity is approximately linear in height because of hte small flow height: ξ – constant z – vertical coordinate • The constant is obtained from continuity: Q – flow rate r – radius h – flow height

  16. Critical radius cont. • Friction force is Newtonian due to flow thinness •  flow height equation: •  η – viscosity ρ – density v0 – initial velocity

  17. Critical radius cont. • Free fall of the liquid causes the existence of initial velocity: g – free fall acceleration d – jet height

  18. Critical radius cont. • Boundary layer thickness is • Inserting: e.g. D. J. Acheson, ˝Boundary Layers˝, in Elementary Fluid Dynamics (Oxford U. P., New York, 1990)

  19. Result comparation • Theoretical scaling confirmed • Comparation of constant in flow rate dependence: Experimental value: 41.0 ± 1.0s/m3

  20. Result comparation cont.

  21. Result comparation cont.

  22. Result comparation cont.

  23. Result comparation cont.

  24. Jump structure • Main jump modes: • Laminar jump • Standing waves – wave jump • Oscillating/weakly turbulent jump • Turbulent jump

  25. Jump structure cont. • Decription of liquid motion – Navier - Stokes equation: Gravitational term (pressure) Inertial term Convection term Viscosity term

  26. Jump structurecont. • laminar jump conditon: •  small velocities • Viscous liquids • Steady rotation in jump region

  27. (slika1)

  28. Jump Structure cont. • Stable turbulent jump: • Large velocities • Weakly viscous liquids • Time – stable mode

  29. (slika3)

  30. Struktura skoka cont. • The remaining time – dependent modes are • Difficult to obtain • Unstable • Mathematical cause: the inertial term in the equation of motion • Observing is problematic

  31. Conclusion • We can now answer the problem: • The jump is pfrmed because of boundary layer separation and vortex formation • Energy is lost in the jump, so the flow height is larger after the jump • The jump in viscous liquids is laminar or wavelike, without turbulence

More Related