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1. Write down the ODEs defining the streamlines of the time-independent (steady- state) flow u(x, t) = (–y, x, 0). a) Integrate these equations and, if possible, write the solution in parameterless form. Sketch few streamlines, indicating the direction of fluid motion. b) In addition, find the stationary point of these equations and analyse it using the standard matrix calculations. Hence verify that the results are consistent with the streamlines found in part a).

1. Write down the ODEs defining the streamlines of the time-independent (steady- state) flow u(x, t) = (–y, x, 0). a) Integrate these equations and, if possible, write the solution in parameterless form. Sketch few streamlines, indicating the direction of fluid motion. b) In addition, find the stationary point of these equations and analyse it using the standard matrix calculations. Hence verify that the results are consistent with the streamlines found in part a).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. Write down the ODEs defining the streamlines of the time-independent (steady- state) flow u(x, t) = (-y, x, 0). a) Integrate these equations and, if possible, write the solution in parameterless form. Sketch few streamlines, indicating the direction of fluid motion. b) In addition, find the stationary point of these equations and analyse it using the standard matrix calculations. Hence verify that the results are consistent with the streamlines found in part a).
Transcribed Image Text:1. Write down the ODEs defining the streamlines of the time-independent (steady- state) flow u(x, t) = (-y, x, 0). a) Integrate these equations and, if possible, write the solution in parameterless form. Sketch few streamlines, indicating the direction of fluid motion. b) In addition, find the stationary point of these equations and analyse it using the standard matrix calculations. Hence verify that the results are consistent with the streamlines found in part a).
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