Chapter 2, Problem 17P

Air flows downward toward an infinitely wide horizontal flat plate. The velocity field is given by $\stackrel{\to }{V}=(ax\hat{i}-ay\hat{j})(2+\cos \omega t),$ where a = 5 s^−l, ω > = 2 π s⁻¹, x and y (measured in meters) are horizontal and vertically upward, respectively, and t is in s. Obtain an algebraic equation for a streamline at t = 0. Plot the streamline that passes through point (x, y) = (3, 3) at this instant. Will the streamline change with time? Explain briefly. Show the velocity vector on your plot at the same point and time. Is the velocity vector tangent to the streamline? Explain.