ChapterIII.PartI

# ChapterIII.PartI - Chapter III Part I Rotational vs...

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Chapter III Part I: Rotational vs. Irrotational Flow, Circulation, Stream Function, Potential Flow From now on, we will only deal with steady, incompressible, inviscid flow. We will neglect all body forces, even gravity. In the previous chapter, we derived an expression for vorticity vector: V × = ξ (1) We mentioned that vorticity is a measure of the angular velocity of the fluid elements. A flow in which there is a lot of vorticity is called a rotational flow . In rotational flows, the fluid elements will rotate as they move from upstream to downstream. This is like a snow ball tumbling down a steep hill side. A flow in which there is very little vorticity is called an irrotational flow. The fluid particles may move up and down, laterally etc. However, like boxes placed on an escalator, they will maintain their upright position (whatever it is) as they move from point to point. A B C D A B C D A B C D A B C D In irrotational flow, the fluid elements do not spin about, but maintain their upright orientation What causes fluid particles to rotate? A number of physical phenomena can. Here are a few: 1. Viscous stresses can pull the fluid particles in different direction. Consider a fluid particle right next to a solid surface. The bottom side of the particle may want to stick to the surface due to viscosity. The top side of the particle may be dragged by the particles above in the general direction of the flow. The result is a rotation of the particle. Fluid particle Viscosity causes spin Thus, boundary layers and viscous regions are rotational, and filled with vorticity.

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2. Velocity differences at the edge of a jet can cause the top part of a fluid particle to move faster than the lower part, or vice versa. Result: Rotation.
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ChapterIII.PartI - Chapter III Part I Rotational vs...

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