Converging duct flow is modeled by the steady, two dimensional velocity field of Prob. 4‒17. A fluid particle (A) is located on the x-axis at x = xA at time t = 0 (Fig. P4-54). At some later time t, the fluid particle has moved downstream

FIGURE P4‒54

with the flow to some new location. x = xA, as shown in the figure. Since the flow is symmetric about the x-axis, the fluid particle remains on the.x-axis at all times. Generate an analytical expression for the.x-location of the fluid particle at some arbitrary time t in terms of its initial location xA and constants U0 and b. In other words, develop an expression for xA (Hint: We know that u = dxparticle/dt following a fluid particle. Plug in u. separate variables, and integrate.)

ANSWER:

Step 1:-

The velocity field is given as,

Where,

And .

Step 2:-

The acceleration field in this case can be written as,

Where,

and

.