Problem 5.59 - 2 4 x a px U 2 4 x y 2 a py u x v v y v U y...

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Problem 5.59 [Difficulty: 3] Given: Linear approximate profile for two-dimensional boundary layer Find: ratio 100 Solution: We will apply the acceleration definition. t V z V w y V v x V u Dt V D a p Governing Equation: (Particle acceleration) Assumptions: (1) Two-dimensional flow (velocity is not a function of z) (2) Incompressible flow (3) Steady flow y V v x V u a p Based on the above assumptions the particle acceleration reduces to: The velocities and derivatives are: u Uy δ v uy 4x Uy 2 4 δ x δ cx 1 2 x u δ Uy δ x δ d d Uy δ 2 δ 2x Uy 2 δ x y u U δ x v x Uy 2 4 δ x δ Uy 2 4 δ x x δ d d Uy 2 4 δ x 2 Uy 2 4 δ 2 x δ 2x 3U y 2 8 δ x 2 y v Uy 2 δ x So the accelerations are: a px u x u v y u Uy δ Uy 2 δ x Uy 2 4 δ x U δ U 2 y
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Unformatted text preview: 2 4 x a px U 2 4 x y 2 a py u x v v y v U y 3 U y 2 8 x 2 U y 2 4 x U y 2 x U y 3 4 2 x 2 a py U 2 4 x y 2 y x The maximum values are when y = : a pxmax U 2 4 x a pymax U 2 4 x x The ratio of the accelerations is: a pymax a pxmax U 2 4 x 4 x U 2 x x When x = 0.5 m and = 5 mm: ratio 0.5 m 0.005 m (a) x- and y-components of acceleration of a fluid particle (b) locate the maximum values of acceleration (c) compute ratio of maximum acceleration components...
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This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.

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