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Consider fully developed axisymmetric Poiseuille flow—flow

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

Solution for problem 104P 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 104P

Consider fully developed axisymmetric Poiseuille flow—flow in a round pipe of radius R(diameter D = 2 R), with a forced pressure gradient dP/dxdriving the flow as illustrated in Fig. P11–53. (dP/dxis constant and negative.) The flow is steady, incompressible, and axisymmetric about the x-axis. The velocity components are given by

where μ is the fluid’s viscosity. Is this flow rotational or irrotational? If it is rotational, calculate the vorticity component in the circumferential (θ) direction and discuss the sign of the rotation.

FIGURE P11-53

Step-by-Step Solution:

Step 1</p>

First determine if the flow is rotational or not, if the flow is rotational then find out the  component of the vorticity.

To determine if the flow is rotational or not calculate the vorticity of the flow, using the formula

        (1)

If the vorticity is nonzero then the flow is rotational and if it is zero then the flow is rotational.

Part (a)

Step 1</p>

The given velocity components are

,

  and

 

Substitute this components in the equation (1), the first component of the equation (1) will be zero because . And the second term si

        (2)

Since the vorticity of the flow is non-zero, the flow is rotational.

Part (b)

Step 2 of 2

Chapter 4, Problem 104P is Solved
Textbook: Fluid Mechanics
Edition: 2
Author: Yunus A. Cengel, John M. Cimbala
ISBN: 9780071284219

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