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Converging duct flow (Fig. P4?17) is modeled by the

Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala ISBN: 9780071284219 39

Solution for problem 33P Chapter 4

Fluid Mechanics | 2nd Edition

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Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala

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

Chapter 4, Problem 33P is Solved
Textbook: Fluid Mechanics
Edition: 2
Author: Yunus A. Cengel, John M. Cimbala
ISBN: 9780071284219

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