Chapter 2, Problem 26P

A flow is described by velocity field $\stackrel{\to }{V}=a{y}^2\hat{i}+b\hat{j}$, where a = 1 m⁻¹ s⁻¹ and b = 2 m/s. Coordinates are measured in meters. Obtain the equation for the streamline passing through point (6, 6). At t = 1 s, what are the coordinates of the particle that passed through point (1, 4) at t = 0? At t = 3 s, what are the coordinates of the particle that passed through point (−3, 0) 2 s earlier? Show that pathlines, streamlines, and streaklines for this flow coincide.