Converging duct flow is modeled by the steady, two- dimensional velocity field of Prob. 4‒17. Since the flow is symmetric about the.x-axis. line segment AB along the x-axis remains on the axis, but stretches from length ξ to length ξ+∆ξ as it flows along the channel centerline (Fig. P4‒55). Generate an analytical expression for the change in length of the line segment. ∆ξ .(Hint: Use the result of Prob. 4‒54.)

FIGURE P4‒55

ANSWER:

Step 1:-

The velocity field is given as,

Where,

And .

By certain calculations we found the acceleration field as,

.