Pressure field of an irrotational vortex

[mikeph]

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

 

[Antiphon]

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.

 

[RandomGuy88]

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.