Pressure field of an irrotational vortex

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SUMMARY

The pressure field of an irrotational vortex can be analyzed using Bernoulli's equation, which states that total pressure remains constant in inviscid flow. In this scenario, the tangential velocity is defined as v_theta = 1/r and radial velocity as v_r = 0. A pressure difference exists between adjacent streamlines, resulting in a suction force that draws objects toward the axis of rotation. Additionally, a force balance can be employed to determine pressure changes by equating centrifugal force with pressure force.

PREREQUISITES
  • Understanding of Bernoulli's equation in fluid dynamics
  • Familiarity with irrotational vortex flow concepts
  • Knowledge of inviscid flow characteristics
  • Basic principles of force balance in fluid mechanics
NEXT STEPS
  • Study the application of Bernoulli's equation in vortex dynamics
  • Explore the characteristics of inviscid flow and its implications
  • Learn about force balance techniques in fluid mechanics
  • Investigate the effects of pressure differences in vortex-induced suction
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This discussion is beneficial for fluid dynamics students, mechanical engineers, and researchers focusing on vortex behavior and pressure field analysis in inviscid flows.

mikeph
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time for some revision... I can't find any definitive verification for this

I'm trying to find the pressure field of an irrotational vortex, v_theta = 1/r, v_r = 0; I guess the pressure falls but I'm not sure how since the Bernoulli equation constant only holds over streamlines, and over streamlines of the vortex, velocity is constant!

Thanks for any help
 
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There will be a pressure difference between adjacent streamlines. On any finite sized object there will be a suction force drawing the object toward the axis of rotation.
 
If the flow is inviscid then the total pressure is the same everywhere so you can use Bernoulli to find the change in pressure across streamlines.

You could also determine this change in pressure by doing a force balance in the direction perpendicular to the motion. Balance the centrifugal force on the fluid element with the pressure force.
 

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