Motion of fluid particles

Motion of fluid particles - Motion of Fluid Particles...

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Motion of Fluid Particles Author: John M. Cimbala, Penn State University Latest revision: 20 September 2007 A fluid particle can undergo four different types of motion, which we express as rates: rate of translation , rate of dilatation , rate of shear strain , and rate of rotation . The diagram below illustrates all four of these simultaneously for motion in the 2-D x 1 - x 2 plane. The concepts can easily be extended to three dimensions. Let point P be the fluid particle, with neighbor particles A and B initially at infinitesimal distances δ x 1 to the right, and x 2 to the top of point P, respectively. The velocity components are shown. The locations of particles P, A, and B are shown both at time t and at some infinitesimal time later, t + dt , where they are denoted by primes. x 1 x 2 P A B u 1 u 2 P A B time t time t + dt u 1 dt x 1 x 2 u 2 + u 2,2 x 2 u 1 + u 1,2 x 2 u 2 + u 2,1 x 1 ( u 2 + u 2,1 x 1 ) dt u 1 + u 1,1 x 1 ( u 1 + u 1,1 x 1 ) dt u 2 dt ( u 2 + u 2,2 x 2 ) dt ( u 1 + u 1,2 x 2 ) dt Rate of translation The rate of translation of point P is simply the change in location divided by the time period. In the
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This note was uploaded on 07/23/2008 for the course ME 521 taught by Professor Cimbala during the Fall '07 term at Penn State.

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