08_potential_f - 2.25 Fluid Mechanics Professors G.H....

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Unformatted text preview: 2.25 Fluid Mechanics Professors G.H. McKinley and A.E. Hosoi Stream Functions for planar ow (satisfy v = 0) Planar ow: Cartesian ( x, y, / z ) v x = y v y = x v z = 0 Planar ow: Cylindrical ( r, , // z ) v r = 1 r v = r v z = 0 Axisymmetric ow: Cylindrical ( r, / , z ) v r = 1 r z v = 0 v z = 1 r r Axisymmetric ow: Spherical ( r, , // ) v r = 1 r 2 sin v = 1 r sin r v = 0 Potential Functions ( v = , requires v = 0 , 2 = 0) Cartesian coordinates ( x, y, z ) v x = x v y = y v z = z Cylindrical coordinates ( r, , z ) v r = r v = 1 r v z = z Spherical coordinates ( r, , ) v r = r v = 1 r v = 1 r sin uniform stream x y U V U,V > 0 shown for W (z) = ( U iV )z = Ux + V y = V x + Uy v x = U v y = V source (Q>0) or sink (Q<0)...
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08_potential_f - 2.25 Fluid Mechanics Professors G.H....

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