1-Considerações Básicas

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

18. Peso Específico

19. Nas condições Normais

20. 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

21. 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

22. 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.

23. 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

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

25. 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

26. 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

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

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

29. 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.

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

31. Compressibilidade Módulo de elasticidade volumétrica

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

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

34. 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