Lecture 17 Fluid Dynamics Handouts

# Lecture 17 Fluid Dynamics Handouts - Fluidic Dynamics EE...

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EE C245 Picture credit: Sandia National Lab

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3 U. Srinivasan © EE C245 Viscosity Fluids deform continuously in presence of shear forces For a Newtonian fluid, Shear stress = Viscosity × Shear strain N/m 2 [=] (N s/m 2 ) × (m/s)(1/m) Centipoise = dyne s/cm 2 No-slip at boundaries η air = 1.8 × 10 -5 N s/m 2 η water = 8.91 × 10 -4 η lager = 1.45 × 10 -3 η honey = 11.5 U τ w w h U x 4 U. Srinivasan © Density Density of fluid depends on pressure and temperature… For water, bulk modulus = Thermal coefficient of expansion = …but we can treat liquids as incompressible Gases are compressible, as in Ideal Gas Law T M R P nRT PV W m = = ρ
5 U. Srinivasan © EE C245 Surface Tension Droplet on a surface gr h ρ θ γ cos 2 = P 2r γ γ Capillary wetting 6 U. Srinivasan © Lecture Outline Today’s Lecture Basic Fluidic Concepts Conservation of Mass Continuity Equation Newton’s Second Law Navier-Stokes Equation Incompressible Laminar Flow in Two Cases Squeeze-Film Damping in MEMS

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7 U. Srinivasan © EE C245
9 U. Srinivasan © EE C245 Operators Gradient and divergence z U y U x U z y x z U y U x U z y x z y x z y x + + = = + + = + + = U div U e e e k j i U 10 U. Srinivasan © Continuity Equation Convert surface integral to volume integral using Divergence Theorem ) ( 0 = ∫∫∫ + dV t V U ρ ) ( 0 = + U t For differential control volume Continuity Equation

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11 U. Srinivasan © EE C245 Continuity Equation Material derivative measures time rate of change of a property for observer moving with fluid ) ( 0 = + + U U ρ t ) ( + = U t Dt D + = U t Dt D 0 = + U Dt D 0 = + U Dt D For incompressible fluid z U y U x U t z y x + + + = 12 U. Srinivasan © Lecture Outline Today’s Lecture Basic Fluidic Concepts Conservation of Mass Continuity Equation Newton’s Second Law Navier-Stokes Equation Incompressible Laminar Flow in Two Cases Squeeze-Film Damping in MEMS
13 U. Srinivasan © EE C245 Newton’s Second Law for Fluidics Newton’s 2 nd Law: Time rate of change of momentum of a system equal to net force acting on system Sum of forces

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Lecture 17 Fluid Dynamics Handouts - Fluidic Dynamics EE...

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