p09fl33 - Lecture 33: Hydrodynamics (18 Nov 09) A....

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Lecture 33: Hydrodynamics (18 Nov 09) A. Beginnings 1. FW Sec. 48 2. This is an ad hoc approach to the dynamics of a continuous fluid. More systematic (statistical physics) approach starts from the N -particle dis- tribution with particle-particle interactions and works to get an equa- tion of motion for the 1-body averages. There are a few conservation laws: mass, energy, total momentum. Force terms reflect both the external forces and the interparticle forces. 3. Text introduces the subject using isotropic simple fluid. Then for a small volume boundary by a surface, (1) there is a force/area P , the pressure, (2) P is normal, the bounding surfaces [i.e., no shear], and (3) P is independent of the orientation of the surface element. However, P may depend on position r and then there are gradients of P and hence net forces on a volume element. 4. Calculate forces on face x of dV = dx × dy × dz : F x = [ P ( x,y,z ) - P ( x + dz,y,z )] dydz ’ - ∂P ∂x dV 5. The acceleration term of a volume element is d v dt = v ∂t
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This note was uploaded on 12/14/2009 for the course PHYS 711 taught by Professor Bruch during the Fall '09 term at Wisconsin.

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p09fl33 - Lecture 33: Hydrodynamics (18 Nov 09) A....

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