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Lecture 17 Fluid Dynamics Handouts

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

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EE C245 Picture credit: Sandia National Lab Fluidic Dynamics Dr. Thara Srinivasan Lecture 17 Picture credit: A. Stroock et al., Microfluidic mixing on a chip 2 U. Srinivasan © EE C245 Lecture Outline Reading From S. Senturia, Microsystem Design , Chapter 13, “Fluids,” p.317-334. 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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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 τ w h U x 4 U. Srinivasan © EE C245 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 © EE C245 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 Conservation of Mass Control volume is region fixed in space through which fluid moves rate of mass efflux outflow of rate ow infl of rate on accumulati of rate = dS Rate of accumulation Rate of mass efflux 8 U. Srinivasan © EE C245 Conservation of Mass 0 = ∫∫ + ∫∫∫ S m V m dS dV t n U ρ ρ dS
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 © EE C245 Continuity Equation Convert surface integral to volume integral using Divergence Theorem ) ( 0 = ∫∫∫ + dV t V U ρ ρ ) ( 0 = + U ρ ρ 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 ρ ρ
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