3.1 Two-dimensional incompressible flow can also be simulated using the vorticity w and streamfunction , instead of using the velocity and pressure variables. The vorticity field can be related to the velocity variables through the curl operation du Əy and the velocity field (u, v) can be related to the streamfunction with მს 11== ду Əv Əx v== Using the continuity equation, show that 2² 2² 8x² dy2 . + მს Ox =11. (3.252) (3.253)

3.1 Two-dimensional incompressible flow can also be simulated using the vorticity w and streamfunction , instead of using the velocity and pressure variables. The vorticity field can be related to the velocity variables through the curl operation du Əy and the velocity field (u, v) can be related to the streamfunction with მს 11== ду Əv Əx v== Using the continuity equation, show that 2² 2² 8x² dy2 . + მს Ox =11. (3.252) (3.253)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

3.1 Two-dimensional incompressible flow can also be simulated using the vorticity
w and streamfunction , instead of using the velocity and pressure variables. The
vorticity field can be related to the velocity variables through the curl operation
Əv
ди
Əx ду
and the velocity field (u, v) can be related to the streamfunction with
მს
ду
11==
v==
Using the continuity equation, show that
2² 2²
+
əx² Əy²
მს
əx
=-w.
(3.252)
(3.253)

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