The (x) component of velocity in a two-dimensional incompressible flow field is given by (u=-Lambdaleft(x^{2}-y^{2} ight) /left(x^{2}+y^{2}

The \(x\) component of velocity in a two-dimensional incompressible flow field is given by \(u=-\Lambda\left(x^{2}-y^{2}\right) /\left(x^{2}+y^{2}\right)^{2}\), where \(u\) is in \(\mathrm{m} / \mathrm{s}\), the coordinates are measured in meters, and \(\Lambda=2 \mathrm{~m}^{3} \cdot \mathrm{s}^{-1}\). Show that the simplest form of the \(y\) component of velocity is given by \(v=-2 \Lambda x y /\left(x^{2}+y^{2}\right)^{2}\). There is no velocity component or variation in the \(z\) direction. Calculate the acceleration of fluid particles at points \((x, y)=(0,1),(0,2)\), 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.