Aula 1 Sandro R Lautenschlager Mecnica dos Fluidos

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) Navier (1785 -1836) Newton (1642 -1727) Stokes (1819 -1903) Leibniz (1646 -1716) Reynolds (1842 -1912) Bernoulli Euler (1667 -1748) (1707 -1783) Prandtl Taylor (1875 -1953) (1886 -1975)

Weather & Climate Tornadoes Thunderstorm Global Climate Hurricanes

Vehicles Aircraft High-speed rail Surface ships Submarines

Environment Air pollution River hydraulics

Physiology and Medicine Blood pump Ventricular assist device

Sports & Recreation Water sports Auto racing Cycling Offshore racing Surfing

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

Aplicação em engenharia

Aplicação em engenharia

Aplicação em engenharia

Propriedades dos Fluidos • Peso específico Onde: g-gravidade local (9, 8 m/s 2); r-massa especifica (kg/m 3); g-peso específico (kg/m 2 s 2) ou N/m 3

Propriedades dos Fluidos • Densidade Temperatura de referência 40 C

Variação de temperatura com a

Massa Específica

Peso Específico

Nas condições Normais Massa Especifica (kg/m 3) Peso Especifico (N/m 3) Densidade Ar 1, 23 12, 1 0, 00123 Água 1000 9810 1

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 y Moving plate u=V V B Fluid Fixed plate x u=0

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 R r x V Fluid

Fluid Deformation • Flow between a fixed and a moving plate • Force causes plate to move with velocity V and the fluid deforms continuously. y Moving plate t 0 u=V t 1 t 2 Fluid Fixed plate x u=0

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

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

Viscosity • Newton’s Law of Viscosity • Units • Water (@ 20 o. C) – • V+dv Air (@ 20 o. C) – • m = 1 x 10 -3 N-s/m 2 m = 1. 8 x 10 -5 N-s/m 2 Kinematic viscosity V

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

Flow between 2 plates Shear stress anywhere between plates y Moving plate V u=V t B t Fixed plate Shear on fluid x u=0

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

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 m 2/s • Find: Torque and Power required to turn the bearing at the indicated speed.

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

Compressibilidade Módulo de elasticidade volumétrica

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

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

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