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1-Considerações Básicas

Aula 1. Sandro R. Lautenschlager. Mecânica dos Fluidos. 1-Considerações Básicas. Mecânica dos Fluidos. Definição Estudo dos líquidos e gases no qual não há movimento (estáticos) e naqueles no qual há movimentos (dinâmica). History. Faces of Fluid Mechanics. Archimedes (C. 287-212 BC).

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1-Considerações Básicas

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  1. Aula 1 Sandro R. Lautenschlager Mecânica dos Fluidos 1-Considerações Básicas

  2. Mecânica dos Fluidos • Definição • Estudo dos líquidos e gases no qual não há movimento (estáticos) e naqueles no qual há movimentos (dinâmica)

  3. History Faces of Fluid Mechanics Archimedes (C. 287-212 BC) Newton (1642-1727) Leibniz (1646-1716) Bernoulli (1667-1748) Euler (1707-1783) Navier (1785-1836) Stokes (1819-1903) Prandtl (1875-1953) Reynolds (1842-1912) Taylor (1886-1975)

  4. Weather & Climate Tornadoes Thunderstorm Global Climate Hurricanes

  5. Vehicles Surface ships Aircraft Submarines High-speed rail

  6. Environment River hydraulics Air pollution

  7. Physiology and Medicine Blood pump Ventricular assist device

  8. Sports & Recreation Water sports Cycling Offshore racing Auto racing Surfing

  9. Aplicação em engenharia Computer Simulations Save US $150,000 in Commuter Jet Design by Reducing Wind Tunnel Testing

  10. Aplicação em engenharia

  11. Aplicação em engenharia

  12. Aplicação em engenharia

  13. Propriedades dos Fluidos • Peso específico Onde: g-gravidade local (9,8 m/s2); r-massa especifica (kg/m3); g-peso específico (kg/m2s2) ou N/m3

  14. Propriedades dos Fluidos • Densidade Temperatura de referência 40C

  15. Variação de com a temperatura

  16. Massa Específica

  17. Peso Específico

  18. Nas condições Normais

  19. y Moving plate u=V V Fluid B x Fixed plate u=0 Some Simple Flows • Flow between a fixed and a moving plate Fluid in contact with the plate has the same velocity as the plate u = x-direction component of velocity

  20. r R x V Fluid Some Simple Flows • Flow through a long, straight pipe Fluid in contact with the pipe wall has the same velocity as the wall u = x-direction component of velocity

  21. y Moving plate u=V t0 t1 t2 Fluid x Fixed plate u=0 Fluid Deformation • Flow between a fixed and a moving plate • Force causes plate to move with velocity V and the fluid deforms continuously.

  22. y dL Moving plate u=V+dV da t t+dt dy dx Fluid x Fixed plate u=V Fluid Deformation Shear stress on the plate is proportional to deformation rate of the fluid

  23. Shear in Different Fluids • Shear-stress relations for different typesof fluids • Newtonian fluids: linear relationship • Slope of line (coefficient of proportionality) is “viscosity”

  24. V+dv V Viscosity • Newton’s Law of Viscosity • Viscosity • Units • Water (@ 20oC) • m = 1x10-3N-s/m2 • Air (@ 20oC) • m = 1.8x10-5N-s/m2 • Kinematic viscosity

  25. y Moving plate u=V V Force acting ON the plate Fluid B x Fixed plate u=0 Flow between 2 plates Force is same on topand bottom Thus, slope of velocity profile is constant and velocity profile is a st. line

  26. Shearon fluid Flow between 2 plates Shear stress anywherebetween plates y Moving plate u=V V t B t x Fixed plate u=0

  27. r x y x Flow between 2 plates • 2 different coordinate systems B V

  28. Example: Journal Bearing • Given • Rotation rate, w = 1500 rpm • d = 6 cm • l = 40 cm • D = 6.02 cm • SGoil = 0.88 • noil = 0.003 m2/s • Find: Torque and Power required to turn the bearing at the indicated speed.

  29. Example: cont. • Assume: Linear velocity profile in oil film

  30. Compressibilidade Módulo de elasticidade volumétrica

  31. Módulo de elasticidade para água • B=2100MPa ou 21000x atm Mudança 1% Líquidos podem ser considerados incompressíveis 21Mpa (210atm)

  32. Cálculo velocidade do som Exemplo para água c = 1450m/s (condições normais )

  33. Data da Provas P1 17/08/11 Cap. 1 e 2; P2 05/10/11 Cap. 3 e 4; P3 21/11/11 Cap 4 e 6. Exame 5/12/11 Avaliação final Cap. 1, 2, 3, 4 e 6

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