Chapter 4, Problem 54P

Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 4—16. A fluid particle (A) is located at x = x_Aand y at time t = 0 (Fig. P4—54). At some later time i. the fluid particle has moved downstream with the flow to some new location $x=x_A,y=y_A$ , as shown in the figure. Generate an analytical expression for the -location of the fluid particle at arbitrary time t in terms of its initial y-location and constant b. In other words, develop an expression for. (Hint: We know that $v=d{y}_{\text{particle}}$ following a fluid particle. Substitute the equation for u, separate variables, and integrate.)