Transcription of 3 Vorticity, Circulation and Potential Vorticity. 3.1 ...
{{id}} {{{paragraph}}}
Example: dental hygienist
3 Vorticity, Circulation and Potential Vorticity. 3.1 ...
3 vorticity , Circulation and Potential Definitions Vorticityis a measure of the local spin of a fluid element given by~ = ~v(1)So, if the flow is two dimensional the vorticity will be a vectorin the directionperpendicular to the flow. Divergenceis the divergence of the velocity field given byD= .~v(2) Circulationaround a loop is the integral of the tangential velocity around the loop = ~ ~l(3)For example, consider the isolated vortex patch in Fig. 1. The Circulation aroundthe closed curve C is given by = c~ ~l= ( ~v).d~s= ~ .d~s= Aads=aA(4)where we have made use of Stokes theorem. The Circulation around the loop canalso be approximated as the mean tangential velocity times the length of the loopand the length of the loop will be proportional to it s characteristic length the loop were a circleL= 2 r.
3 Vorticity, Circulation and Potential Vorticity. 3.1 Definitions • Vorticity is a measure of the local spin of a fluid element given by ω~ = ∇×~v (1) So, if the flow is two dimensional the vorticity will be a …
Tags:
Information
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document: