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)

Answer & Explanation Solved by verified expert

3.9 Ratings (522 Votes)

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

Get Answers to Unlimited Questions

Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!

Membership Benefits:

Unlimited Question Access with detailed Answers
Zin AI - 3 Million Words
10 Dall-E 3 Images
20 Plot Generations
Conversation with Dialogue Memory
No Ads, Ever!
Access to Our Best AI Platform: Flex AI - Your personal assistant for all your inquiries!

Become a Member