11/16/2015PHY 711 Fall 2015 -- Lecture 331 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 33: Effects of.

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11/16/2015PHY 711 Fall Lecture 331 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 33: Effects of viscosity in fluid motion – Chap.12 in Fetter & Walecka 1.Navier-Stokes equation 2.Terminal velocity of a sphere moving with constant applied force in a viscous medium 3.Stokes’ viscosity relation

11/16/2015PHY 711 Fall Lecture 33211/22/2013PHY 711 Fall Lecture 342

11/16/2015PHY 711 Fall Lecture 333 Brief introduction to viscous effects in incompressible fluids Plan: 1.Consider the general effects of viscosity on fluid equations 2.Consider the solution to the linearized equations for the case of steady-state flow of a sphere of radius R 3.Infer the drag force needed to maintain the steady-state flow u FDFD

11/16/2015PHY 711 Fall Lecture 334 Fluid (m 2 /s) Water 1.00 x Air14.9 x Ethyl alcohol 1.52 x Glycerine1183 x Typical kinematic viscosities at 20 o C and 1 atm:

11/16/2015PHY 711 Fall Lecture 335 u FDFD F

11/16/2015PHY 711 Fall Lecture 336 t u u FDFD F

11/16/2015PHY 711 Fall Lecture 337 u u FDFD t

11/16/2015PHY 711 Fall Lecture 338 Recall: PHY Assignment #24 Oct. 28, 2015 Determine the form of the velocity potential for an incompressible fluid representing uniform velocity in the z direction at large distances from a spherical obstruction of radius a. Find the form of the velocity potential and the velocity field for all r > a. Assume that the velocity in the radial direction is 0 for r = a and assume that the velocity is uniform in the azimuthal direction.

11/16/2015PHY 711 Fall Lecture 339

11/16/2015PHY 711 Fall Lecture 3310

11/16/2015PHY 711 Fall Lecture 3311 Digression

11/16/2015PHY 711 Fall Lecture 3312

11/16/2015PHY 711 Fall Lecture 3313

11/16/2015PHY 711 Fall Lecture 3314

11/16/2015PHY 711 Fall Lecture 3315 u FDFD

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