for a two dimensional flow u =[Sx,Sy,0]^T, show that the fluid element which was initially circular...

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for a two dimensional flow u =[Sx,Sy,0]^T, show that the fluidelement which was initially circular in shape will be deformed intoan ellipse with major axes aligned pi/4 with positive x-axis andjustify if this prediction is consistent with the streamline.(needto provide asketch off the streamlines)

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The first step is to show that if an ellipse touches all four sides of a square then its axes must lie along the diagonals of the square in other words it is symmetrically placed Let the ellipse have center O semimajor axis a and semiminor axis b Let the line A through O contain the ellipses major axis and the line B through O contain its minor axis Let S be the square in which the ellipse is inscribed Let k be the similarity operation which leaves A invariant and expands by a factor ab perpendicular to A So given a general point P with X be the foot of the perpendicular from P to A P goes to the point P on the See Answer

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for a two dimensional flow u =[Sx,Sy,0]^T, show that the fluid element which was initially circular...

50.1K

Verified Solution

Question

Physics

for a two dimensional flow u =[Sx,Sy,0]^T, show that the fluidelement which was initially circular in shape will be deformed intoan ellipse with major axes aligned pi/4 with positive x-axis andjustify if this prediction is consistent with the streamline.(needto provide asketch off the streamlines)

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