Lecture 08 Notes - EGN 3353C Fluid Mechanics Lecture 8...

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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida Lecture 8 Fluids in Rigid-Body Motion In a cartesian coordinate system, recall we found that for a fluid with a G = 0 (i.e., at rest), ± (Surface) pressure force per unit volume is given by ˆ ˆˆ Pi j k P xy z ⎛⎞ ∂∂ −∇ = − + + ⎜⎟ ⎝⎠ G ± (Body) gravitational force per unit volume ˆ gk ρ =− ± So governing equation is ˆ 0 m aa Pg k == = G G G When 0 a G but the fluid moves as a rigid body (no shear forces ), we can generalize this equation to ˆ aP g k =−∇ − G G or ( ) ˆ Pa g k ∇= −− G G Æ isobars (constant P) ˆ ag k −− G (vector sum) a G g G a G + G G free surface isobars
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EGN 3353C Fluid Mechanics Lou Cattafesta MAE Dept. University of Florida In component vector form () : : : x y z P x x P y y P z z a a ga ρ = = = + Let’s consider the case of a constant acceleration in x and z directions, : : : 0 x z P x x P y y P a g z a z = = = −+ Æ ( ) ,
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Lecture 08 Notes - EGN 3353C Fluid Mechanics Lecture 8...

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