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Consider steady, incompressible, two-dimensional shear

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

Solution for problem 65P 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 65P

Consider steady, incompressible, two-dimensional shear flow for which the velocity field is

where a and b are constants. Sketched in Fig. P4‒69 is a small rectangular fluid particle of dimensions dx and dy at time t. The fluid particle moves and deforms with the flow such that at a later time (t + dt). the particle is no longer rectangular, as also shown in the figure. The initial location of each corner of the fluid particle is labeled in Fig. P4‒69. The lower-left corner is at (x. y) at time t. where the x-component of  velocity is u = a + by. At the later time, this corner moves to (x +u dt. y), or

(a) In similar fashion, calculate the location of each of the other three corners of the fluid particle at time t ‒ dt.

(b) From the fundamental definition of   linear strain rate (the rate of increase in length per unit length). calculate linear strain rates Ɛxx and Ɛyy.

(c) Compare your results with those obtained from the equations for Ɛxx and Ɛyy in Cartesian coordinates, i.e..

FIGURE P4‒69

Step-by-Step Solution:
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PHYS 101 LECTURE NOTES WEEK 4 Spencer Kociba Drexel University Lecture 7 (01/31/2017) ● Apparent weight (normal force that acts on you to counteract other forces) ○ n = m(g + ay) ○ In an elevator, accelerating upwards results in a larger apparent weight (normal force is larger) and accelerating...

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Chapter 4, Problem 65P is Solved
Step 3 of 3

Textbook: Fluid Mechanics
Edition: 2
Author: Yunus A. Cengel, John M. Cimbala
ISBN: 9780071284219

Fluid Mechanics was written by and is associated to the ISBN: 9780071284219. The answer to “Consider steady, incompressible, two-dimensional shear flow for which the velocity field is where a and b are constants. Sketched in Fig. P4?69 is a small rectangular fluid particle of dimensions dx and dy at time t. The fluid particle moves and deforms with the flow such that at a later time (t + dt). the particle is no longer rectangular, as also shown in the figure. The initial location of each corner of the fluid particle is labeled in Fig. P4?69. The lower-left corner is at (x. y) at time t. where the x-component of velocity is u = a + by. At the later time, this corner moves to (x +u dt. y), or (a) In similar fashion, calculate the location of each of the other three corners of the fluid particle at time t ? dt.(b) From the fundamental definition of linear strain rate (the rate of increase in length per unit length). calculate linear strain rates ?xx and ?yy.(c) Compare your results with those obtained from the equations for ?xx and ?yy in Cartesian coordinates, i.e.. FIGURE P4?69” is broken down into a number of easy to follow steps, and 181 words. The full step-by-step solution to problem: 65P from chapter: 4 was answered by , our top Engineering and Tech solution expert on 07/03/17, 04:51AM. Since the solution to 65P from 4 chapter was answered, more than 273 students have viewed the full step-by-step answer. This full solution covers the following key subjects: particle, fluid, corner, Where, rectangular. This expansive textbook survival guide covers 15 chapters, and 1547 solutions. This textbook survival guide was created for the textbook: Fluid Mechanics, edition: 2.

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