# Pressure field of an irrotational vortex

1. Feb 16, 2012

### 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

2. Feb 16, 2012

### 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.

3. Feb 16, 2012

### 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.