Consider the 2D planar potential flow which is the sum of a uniform flow with the speed U0>0 at infinity and a line source of strength m>0. Since the speed of the point-source flow grows from zero at infinity to infinity at its origin, we expect the speed of the combined flow to vanish at some point in space. Hence the combined flow can be a flow past some stationary solid body. Find the velocity field of the combined flow and its stagnation point. Use the complex potential of this flow to determine its streamfunction. Use the streamfunction to determine the shape of this body. Make a plot showing the shape and few streamlines past the body.
Consider the 2D planar potential flow which is the sum of a uniform flow with the speed U0>0 at infinity and a line source of strength m>0. Since the speed of the point-source flow grows from zero at infinity to infinity at its origin, we expect the speed of the combined flow to vanish at some point in space. Hence the combined flow can be a flow past some stationary solid body. Find the velocity field of the combined flow and its stagnation point. Use the complex potential of this flow to determine its streamfunction. Use the streamfunction to determine the shape of this body. Make a plot showing the shape and few streamlines past the body.
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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Consider the 2D planar potential flow which is the sum of a uniform flow with the speed U0>0 at infinity and a line source of strength m>0. Since the speed of the point-source flow grows from zero at infinity to infinity at its origin, we expect the speed of the combined flow to vanish at some point in space. Hence the combined flow can be a flow past some stationary solid body. Find the velocity field of the combined flow and its stagnation point. Use the complex potential of this flow to determine its streamfunction. Use the streamfunction to determine the shape of this body. Make a plot showing the shape and few streamlines past the body.
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