1. 11/24/2014PHY 711 Fall 2014 -- Lecture 381 PHY 711 Classical Mechanics and Mathematical Methods 10-10:50 AM MWF Olin 103 Plan for Lecture 38 1.Chapter 12: Example of solution to Navier-Stokes equation 2.Chapter 13: Physics of elastic continua

2. 11/24/2014PHY 711 Fall 2014 -- Lecture 38211/22/2013PHY 711 Fall 2013 -- Lecture 342 Final grades due 12/17/2014

3. 11/24/2014PHY 711 Fall 2014 -- Lecture 383

4. 11/24/2014PHY 711 Fall 2014 -- Lecture 384 Newton-Euler equations for viscous fluids

5. 11/24/2014PHY 711 Fall 2014 -- Lecture 385 Example – steady flow of an incompressible fluid in a long pipe with a circular cross section of radius R

6. 11/24/2014PHY 711 Fall 2014 -- Lecture 386 Example – steady flow of an incompressible fluid in a long pipe with a circular cross section of radius R -- continued R v(r)v(r) L

7. 11/24/2014PHY 711 Fall 2014 -- Lecture 387 Example – steady flow of an incompressible fluid in a long pipe with a circular cross section of radius R -- continued R v(r)v(r) L

8. 11/24/2014PHY 711 Fall 2014 -- Lecture 388 Example – steady flow of an incompressible fluid in a long pipe with a circular cross section of radius R -- continued R v(r)v(r) L Poiseuille formula;  Method for measuring 

9. 11/24/2014PHY 711 Fall 2014 -- Lecture 389 Newton-Euler equations for viscous fluids – effects on sound Recall full equations:

10. 11/24/2014PHY 711 Fall 2014 -- Lecture 3810 Newton-Euler equations for viscous fluids – effects on sound Without viscosity terms:  Pure longitudinal harmonic wave solutions

11. 11/24/2014PHY 711 Fall 2014 -- Lecture 3811 Newton-Euler equations for viscous fluids – effects on sound Recall full equations:

12. 11/24/2014PHY 711 Fall 2014 -- Lecture 3812 Newton-Euler equations for viscous fluids – effects on sound Note that pressure now depends both on density and entropy so that entropy must be coupled into the equations

13. 11/24/2014PHY 711 Fall 2014 -- Lecture 3813 Newton-Euler equations for viscous fluids – effects on sound Linearized equations (with the help of various thermodynamic relationships):

14. 11/24/2014PHY 711 Fall 2014 -- Lecture 3814 Newton-Euler equations for viscous fluids – effects on sound Linearized plane wave solutions:

15. 11/24/2014PHY 711 Fall 2014 -- Lecture 3815 Newton-Euler equations for viscous fluids – effects on sound Linearized plane wave longitudinal solutions:

16. 11/24/2014PHY 711 Fall 2014 -- Lecture 3816 Brief introduction to elastic continua reference deformation r1r1 r1’r1’

17. 11/24/2014PHY 711 Fall 2014 -- Lecture 3817 Brief introduction to elastic continua

18. 11/24/2014PHY 711 Fall 2014 -- Lecture 3818 To be continued …. Have a great Thanksgiving Holiday.