In addition to the customary horizontal velocity components of the air in the atmosphere...

In addition to the customary horizontal velocity components of the air in the atmosphere (the “wind”), there often are vertical air currents (thermals) caused by buoyant effects due to uneven heating of the air as indicated in Fig. P4.8. Assume that the velocity field in a certain region is approximated by u = u₀, y = v₀ (1 - y/h) for 0 < y < h, and u = u₀, v = 0 for y > h. Determine the equation for the streamlines and plot the streamline that passes through the origin for values of u₀/v₀ = 0.5, 1, and 2.