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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 28: Introduction to hydrodynamics Correction – Euler formulation revisited Euler’s equation for fluid dynamics Bernoulli’s integrals. Newton’s equations for fluids

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PHY 7 11 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103

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  1. PHY 711 Classical Mechanics and Mathematical Methods • 10-10:50 AM MWF Olin 103 • Plan for Lecture 28: • Introduction to hydrodynamics • Correction – Euler formulation revisited • Euler’s equation for fluid dynamics • Bernoulli’s integrals PHY 711 Fall 2012 -- Lecture 28

  2. PHY 711 Fall 2012 -- Lecture 28

  3. Newton’s equations for fluids • Use Euler formulation; properties described in terms of • stationary spatial grid t t’ PHY 711 Fall 2012 -- Lecture 28

  4. Euler analysis -- continued PHY 711 Fall 2012 -- Lecture 28

  5. Continuity equation: PHY 711 Fall 2012 -- Lecture 28

  6. Solution of Euler’s equation for fluids PHY 711 Fall 2012 -- Lecture 28

  7. Bernoulli’s integral of Euler’s equation for constant r PHY 711 Fall 2012 -- Lecture 28

  8. Examples of Bernoulli’s theorem for constant r 1 2 PHY 711 Fall 2012 -- Lecture 28

  9. Examples of Bernoulli’s theorem -- continued Examples of Bernoulli’s theorem -- continued 3 1 2 PHY 711 Fall 2012 -- Lecture 28

  10. Examples of Bernoulli’s theorem -- continued 2 1 PHY 711 Fall 2012 -- Lecture 28

  11. Examples of Bernoulli’s theorem -- continued 2 1 PHY 711 Fall 2012 -- Lecture 28

  12. Examples of Bernoulli’s theorem – continued Approximate explanation of airplane lift Cross section view of airplane wing http://en.wikipedia.org/wiki/Lift_%28force%29 1 2 PHY 711 Fall 2012 -- Lecture 28

  13. Some details on the velocity potential PHY 711 Fall 2012 -- Lecture 28

  14. Example – uniform flow b a z PHY 711 Fall 2012 -- Lecture 28

  15. Example – flow around a cylinder ^ ^ v0Z v0Z to be continued… PHY 711 Fall 2012 -- Lecture 28

  16. Solution of Euler’s equation for fluids -- isentropic PHY 711 Fall 2012 -- Lecture 28

  17. Solution of Euler’s equation for fluids – isentropic (continued) PHY 711 Fall 2012 -- Lecture 28

  18. Solution of Euler’s equation for fluids – isentropic (continued) PHY 711 Fall 2012 -- Lecture 28

  19. Solution of Euler’s equation for fluids – isentropic (continued) PHY 711 Fall 2012 -- Lecture 28

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