Consider fully developed two-dimensional Poiseuille

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

Problem 96P 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 96P

Consider fully developed two-dimensional Poiseuille flow—flow between two infinite parallel plates separated by distance h,with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dxdriving the flow as illustrated in Fig. P11–48. (dP/dxis constant and negative.)

FIGURE P11-48

The flow is steady, incompressible, and two-dimensional in the xy-plane. 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 z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise?

Step-by-Step Solution:

Step 1 of 4:

        Consider the steady flow in two-dimensional xy plane. The flow is also considered as Poiseuille flow. It happens between two infinitely long parallel plates. The distance between the two plates is h. And the flow is stationary at the plates. The velocity field components are given by

         = ----(1)

        Where is the fluid’s viscosity

                is the pressure gradient.

        = 0 ------(2)

        To find whether the flow is rotational or irrotational.

Step 2 of 4:

        To find whether the flow is rotational or irrotational.

        This is done by calculating the vorticity vector of z component. Vorticity is the local rotation or the spin of the flow. In the case of two-dimensional flow,

         = -----(3)

        From (2), differentiating with respect to x

= 0 -----(4)

From (1), differentiating with respect to y

=         

= ------(5)

Step 3 of 4

Chapter 4, Problem 96P is Solved
Step 4 of 4

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

Fluid Mechanics was written by and is associated to the ISBN: 9780071284219. This textbook survival guide was created for the textbook: Fluid Mechanics, edition: 2nd. The answer to “Consider fully developed two-dimensional Poiseuille flow—flow between two infinite parallel plates separated by distance h,with both the top plate and bottom plate stationary, and a forced pressure gradient dP/dxdriving the flow as illustrated in Fig. P11–48. (dP/dxis constant and negative.) FIGURE P11-48The flow is steady, incompressible, and two-dimensional in the xy-plane. The velocity components are given by where ? is the fluid’s viscosity. Is this flow rotational or irrotational? If it is rotational, calculate the vorticity component in the z-direction. Do fluid particles in this flow rotate clockwise or counterclockwise?” is broken down into a number of easy to follow steps, and 90 words. This full solution covers the following key subjects: flow, fluid, plate, rotational, counterclockwise. This expansive textbook survival guide covers 15 chapters, and 1547 solutions. The full step-by-step solution to problem: 96P from chapter: 4 was answered by , our top Engineering and Tech solution expert on 07/03/17, 04:51AM. Since the solution to 96P from 4 chapter was answered, more than 291 students have viewed the full step-by-step answer.

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