Re: Centrifugal Forces in a Vortex/Whirlpool

Hi Graham,

It's hard to answer your questions without knowing more about what you want your vortex to look like. A vortex is any spinning flow with closed streamlines (meaning the water comes back to the same place). See the Wikipedia article for a more complete description. Different applied forces will result in different circulation strengths or, equivalently, different angular velocities. A spinning flow with weak angular velocity is still a vortex, but will have very little surface expression.

If you aren't interested in refilling your vortex tank all the time, the best way to create a vortex is to set the water into solid body rotation by spinning the tank on a rotating table. (I'm not sure if this is what you had in mind when you mentioned a centrifuge.) For such a huge tank, you'll need a very sturdy rotating table because as you correctly calculated, just the water in your tank will weigh 2,356 kg. With a rotating table, it's probably best to think about what angular velocity (rather than force) is needed to achieve the desired vortex. Angular velocity (let's call it w) is related to the rotation rate (T) of the tank (in Hertz, or rotations per second) by

w=2 pi / T.

The surface of the water will form a parabola, with the height of the water at a distance r from the centre of the tank being

w^2 (r^2)/2g

higher than the height of the water in the centre of the tank. If you were to create the vortex using a water pump, your vortex will be asymmetric because of the necessity of introducing an obstruction (the outflow and inflow nozzles). Nevertheless, in this case you might want to express the problem in terms of the required tangential flow velocity. In this case the angular velocity is given by

w = v_theta / r,

where v_theta is the tangential flow velocity (the output of your pump, oriented tangentially to the diameter of the tank) and r is the distance from the pump to the centre of the tank. The surface parabola should be (approximately) given by the same equation as for the rotating table.

As for the question of how strong the tank will need to be, it needs to be strong enough to hold the water. The added force due to the rotation will likely be small compared with the sheer weight of the water. Here's a nice article aimed at aquarium enthusiasts that discusses tank strengths and wall thicknesses.

I hope this helps.
Cheers,
Tetjana