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Answer: Converging duct flow is modeled by the steady,

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

Solution for problem 56P 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 56P

Converging duct flow is modeled by the steady, two- dimensional velocity field of Prob. 4‒17. As vertical line segment AB moves downstream it shrinks from length η to length η+ ∆η  as sketched in Fig. P4‒58. Generate an analytical expression for the change in length of the line segment, ∆η. Note that  the  change in length, ∆η, is negative. (Hint: Use the result of Prob. 4‒57.)

FIGURE P4‒58

Step-by-Step Solution:

Solution

Introduction

The vertical line segment AB moves downstream it shrinks its length from η to  η+is shown in the figure below

Step 1

For the particle A at time t , its location is yA1 = yA. E-bt

Similarly the location for the particle B at a time is yB1 =yB. E-bt

Initial length η is nothing but the separation between the two particles initial  position

η= yB - yA

The length η+ is the separation between the two particles at the secondary position

η+ = yB1 - yA1

Step 2 of 2

Chapter 4, Problem 56P is Solved
Textbook: Fluid Mechanics
Edition: 2
Author: Yunus A. Cengel, John M. Cimbala
ISBN: 9780071284219

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Answer: Converging duct flow is modeled by the steady,