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Unformatted text preview: Chapter 9: Transport phenomena 43 and the defnitions v x = / y , v y =- / x holds: AB = ( B )- ( A ) . In general holds: 2 x 2 + 2 y 2 =- z In polar coordinates holds: v r = 1 r = r , v =- r = 1 r For source ows with power Q in ( x, y ) = (0 , 0) holds: = Q 2 ln( r ) so that v r = Q/ 2 r , v = 0 . For a dipole o strength Q in x = a and strength- Q in x =- a ollows rom superposition: =- Qax/ 2 r 2 where Qa is the dipole strength. For a vortex holds: = / 2 . I an object is surrounded by an uniorm main ow with v = ve x and such a large Re that viscous eects are limited to the boundary layer holds: F x = 0 and F y =- v . The statement that F x = 0 is dAlemberts paradox and originates rom the neglection o viscous eects. The lit F y is also created by because = 0 due to viscous eects. Henxe rotating bodies also create a orce perpendicular to their direction o motion: thedue to viscous eects....
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This note was uploaded on 11/16/2010 for the course ENGR 201 taught by Professor Elder during the Spring '10 term at Blinn College.
- Spring '10