Lecture 11 Notes - EGN 3353C Fluid Mechanics Lecture 11...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Lecture 11 Types of Motion (Deformation) of Fluid Elements ± 4 types a) translation (already covered) () dV V aV V dt t ==+ GG GG G G i b) rotation rate c) dilatation or linear deformation rate d) shear strain rate
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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida ± Let’s look at a fluid element (abcd) of unit thickness (dz = 1) in the xy plane at time t and later time t + dt t x y t+dt a a b b c c d d , uv u ud x x v vd x x + + u y y v y y + + uu xd y xy vv y ∂∂ ++ d β d α udt u y d t y ⎛⎞ + ⎜⎟ ⎝⎠ dx u dy dt + u u dx dt x vdt v x d t x + v dy v y v + 1 5 2 4 3 6
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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida R ate of change in volume Æ called dilatation or linear deformation that is related to compressibility t dxdy ∀= 1 2 6 1 of large rectangle - 1 2 1 2 t i d i t uu vv dx dxdt dydt dy dxdt dydt xy uv u dx dxdt dxdt dydt dxdt dydt xx yx y + = ⎛⎞ ∂∂ = + + + + ⎜⎟ ⎝⎠ −+ ∀∀ ⎠⎝ ±²²²²³²²²²´ ±²²²³²²²´ 3 4 56 2 11 22 v dy dydt y u v dx dxdt dxdt dydt dxdt dydt dy dydt y y u dxdy dx dt dxdydt dxdyd x + + =+ + + ( ) 22 2 4 discard terms of O uvu t dyd t dxd t t yxy dxdy dxdydt dxdydt ∂∂∂ +
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This note was uploaded on 08/17/2011 for the course EGN 3353C taught by Professor Lear during the Spring '07 term at University of Florida.

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Lecture 11 Notes - EGN 3353C Fluid Mechanics Lecture 11...

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