Chapter 2, Problem 22P

Consider the garden hose of Fig. 2.5. Suppose the velocity field is given by $\stackrel{\to }{V}=u_0\hat{i}+v_0\sin \left[\omega \left(t-x/u_0\right)\right]\hat{j}$, where the x direction is horizontal and the origin is at the mean position of the hose, u₀ = 10 m/s, υ₀ = 2 m/s, and ω = 5 cycle/s. Find and plot on one graph the instantaneous streamlines that pass through the origin at t = 0 s, 0.05 s, 0.1 s, and 0.15 s. Also find and plot on one graph the pathlines of particles that left the origin at the same four times.

Fig. 2.5 Pathlines and streaklines for flow from the exit of an oscillating garden hose.