Vorticity_Irrotationality_web

Vorticity_Irrotationality_web - ENU 4133 Vorticity and...

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Unformatted text preview: ENU 4133 Vorticity and Irrotationality March 7, 2011 Stream Function When only two terms of the continuity equation are non-zero, it is possible to develop an equation for a single variable (the stream function, ). Ignore cases where one of the non-zero terms is / t . Incompressible, Cartesian: u x + v y = 0 (1) u = y (2) v =- x (3) x y + y- x = 0 (4) Steam Function (2) ~ V = ~ i y- ~ j x (5) ~ V =- ~ k 2 (6) ~ V =- ~ k 2 x 2 + 2 y 2 (7) Stream Function along Streamline Along streamline in 2-D flow: dx u = dy v (8) udy- vdx = 0 (9) x dx + y dy = 0 (10) d = 0 (11) Therefore, is constant along a streamline. Other Cases Compressible, Cartesian: u = y (12) v =- x (13) 0 = x ( u ) + y ( v ) (14) Incompressible flow in r- plane: v r = 1 r (15) v =-...
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This note was uploaded on 07/14/2011 for the course ENU 4133 taught by Professor Schubring during the Spring '11 term at University of Florida.

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Vorticity_Irrotationality_web - ENU 4133 Vorticity and...

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