Vorticity_and_rotationality

Vorticity_and_rotationality - 2 A solid-body...

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Vorticity and Rotationality (Section 4-4, Ç engel and Cimbala) The vorticity vector is defined as the curl of the velocity vector , V ζ =∇× G G G It turns out that vorticity is equal to twice the angular velocity of a fluid particle , Greek letter zeta 2 ω = G G Thus, vorticity is a measure of rotation of a fluid particle . if 0, the flow is irrotational if 0, the flow is rotational = G G Examples : 1. Inside a boundary layer , where viscous forces are important, the flow in this region is rotational ( G 0). However, outside the boundary layer, where viscous forces are not important, the flow in this region is irrotational ( G = 0).
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Unformatted text preview: 2. A solid-body rotation (rigid-body rotation) flow is rotational ( ζ G ≠ 0). In fact, since vorticity is equal to twice the angular velocity, 2 ω = G G everywhere in the flow field . Fluid particles rotate as they revolve around the center of the flow. This is analogous to a merry-go-round or a roundabout. G Solid-body rotation 3. A line vortex flow, however, is irrotational ( = 0), and fluid particles do not rotate, even though they revolve around the center of the flow. This is analogous to a Ferris wheel. Line vortex See text for details and calculations....
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This note was uploaded on 07/23/2008 for the course ME 33 taught by Professor Cimbala during the Fall '05 term at Penn State.

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Vorticity_and_rotationality - 2 A solid-body...

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