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.
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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)
Transcribed Image Text: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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