Chapter 2, Problem 20P

Consider the flow field given in Eulerian description by the expression $\stackrel{\to }{V}=ax\hat{i}+but\hat{j}$, where a = 0:2 s⁻¹, b = 0:04 s⁻², and the coordinates are measured in meters. Derive the Lagrangian position functions for the fluid particle that was located at the point (x, y) = (1, 1) at the instant t = 0. Obtain an algebraic expression for the pathline followed by this particle. Plot the pathline and compare with the streamlines plotted through the same point at the instants t = 0, 10, and 20 s.