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# Converging duct flow (Fig. P4?17) is modeled by the ISBN: 9780071284219 39

## Solution for problem 33P Chapter 4

Fluid Mechanics | 2nd Edition

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Problem 33P

Converging duct flow (Fig. P4‒17) is modeled by the steady, two-dimensional velocity field of  Prob. 4‒17. Generate an analytical expression for the flow streamlines.

PROBLEM: Consider steady, incompressible, two-dimensional flow through a converging duct (Fig. P11–15). A simple approximate velocity field for this flow is where U0 is the horizontal speed at x= 0. Note that this equation ignores viscous effects along the walls but is a reasonable approximation throughout the majority of the flow field. Calculate the material acceleration for fluid particles passing through this duct. Give your answer in two ways: (1) as acceleration components ax and ay and (2) as acceleration vector . Step-by-Step Solution:

Step 1 of 3</p>

For the given velocity field, we need to derive an analytical expression for the flow streamlines by considering the flow to be steady in the two dimensional in x-y plane.

The steady two dimensional velocity field is given to be, ………...1

Where is the horizontal speed at x=0.

Step 2 of 3</p>

For the two dimensional flow, the streamlines in the x-y plane is given by, From equation 1, and Using in above equation, Rearranging Step 3 of 3

##### ISBN: 9780071284219

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