The x component of velocity in a two-dimensional
incompressible flow field is given by u 5 2Λðx2 2 y2Þ=
ðx2 1 y2Þ
2
, where u is in m/s, the coordinates are measured in
meters, and Λ 5 2 m3 s
21
. Show that the simplest form of the
y component of velocity is given by v 5 22Λxy=ðx2 1 y2Þ
2
.
There is no velocity component or variation in the z direction. Calculate the acceleration of fluid particles at points
(x, y) 5 (0, 1), (0, 2), and (0, 3). Estimate the radius of curvature of the streamlines passing through these points. What
does the relation among the three points and their radii of
curvature suggest to you about the flow field? Verify this by
plotting these streamlines. [Hint: You will need to use an
integrating factor.]