What is the pressure in the middle of a vortex?

[PhyIsOhSoHard]

Homework Statement

The expression below describes a potential vortex in polar coordinates. What is the pressure p in the middle of the vortex, i.e. at radius r=0, relative to the surroundings?
$V_{\theta}=\frac{a}{r}$

Answer:
$p=-∞$


Does anyone have any explanation to this answer? Why is the pressure infinite? And why is it a negative? I've been thinking about this for so long and can't come up with any explanation...

 

[PhyIsOhSoHard]

Anyone?

 

[Andrew Mason]

Homework Statement

The expression below describes a potential vortex in polar coordinates. What is the pressure p in the middle of the vortex, i.e. at radius r=0, relative to the surroundings?
$V_{\theta}=\frac{a}{r}$

Answer:
$p=-∞$Does anyone have any explanation to this answer? Why is the pressure infinite? And why is it a negative? I've been thinking about this for so long and can't come up with any explanation...

The minimum force per unit area is 0. The - or + sign simply denotes the direction in which the force acts on a unit of area which depends on which direction you choose to be +.

In a vortex, the swirling mass of air is kept from flying outward by the external pressure. So the difference between the vortex pressure and the external pressure supplies the centripetal force that the swirling molecules need in order to keep from flying outward. If the molecules swirl fast enough for a given radius of curvature, the centripetal force can be equal to the external pressure (atmospheric pressure) and the vortex pressure is then 0. It cannot go any lower than that.

AM