Chapter 5, Problem 42P

A steady, two-dimensional velocity field is given by $\stackrel{\to }{V}=Ax\hat{i}-Ay\hat{j},$ where A = 1 s⁻¹. Show that the streamlines for this flow are rectangular hyperbolas, xy = C. Obtain a general expression for the acceleration of a fluid particle in this velocity field. Calculate the acceleration of fluid particles at the points (x, y) = $\left(\frac{1}{2},2\right)$, (1, 1), and $\left(2,\frac{1}{2}\right)$, where x and y are measured in meters. Plot streamlines that correspond to C = 0, 1. and 2 m² and show the acceleration vectors on the streamline plot.