Rotating water forms a parabola - why?

[JTressy]

Rotating water forms a parabola - why??

I've done some experiments involving rotating a beaker of water, and then measuring the height of the parabola that forms. I am now trying to explain this in my write up, but there are some things that I am simply not understanding, and any help would be greatly appreciated.

- Firstly, one diagram I found shows that the centripetal force making the water go in a circle comes from the horizontal component of the buoyancy of the water - but where does this buoyancy come from? I could understand it if there was a ball that needed supporting!

- Is there a name for this behaviour that will yield decent results when googled? I have tired various combinations of parabola, circular motion, centripetal force, rotating water etc etc and have not yet found a decent page explaining this, I have instead found little bits of information across several different sites.

- Is there a 'correct' way of looking at the system? I am explaining it by using centripetal force, and as this increases further away from the centre then the resultant force on the water is more horizontal, so it is consequently steeper (perperndicular to resultant). However I have also seen that it can be explained with centrifugal force pushing the water to the outside, but from what I can tell this is in a rotating reference frame, does it matter?

If anyone can answer any of these questions, or point me to somewhere that can I would be eternally grateful :)

 

[J Hann]

There are 2 forces acting on a mass m at the surface of the liquid at coordinates x,y taken from a point at the surface along a tangent drawn from that point to the center of rotation (the origin). The forces are
the centripetal force m * omega^2 * x and the gravitational force mg. Therefore

tan(theta) = dy/dx = x * omega^2 / g

Integrating this equation gives y = x^2 * omega^2 / (2 * g) + C
which is the equation of a parabola.
Note that tangent is taken at the surface and the origin does not
change with integration. Actually C disappears if the origin is taken
at the surface of the liquid at the center of rotation.

Hope this helps.

 

[civil_dude]

The phenomena is that a pressure gradient is required in fluids under acceleration.

 

[andrevdh]

https://www.physicsforums.com/showthread.php?t=95680&highlight=water"

and the link in it

https://www.physicsforums.com/showthread.php?p=769852"

 

[JTressy]

Thanks very much for the help guys, I just want to clarify what I'm now thinking.

Is the centripetal force that makes the water go in a circle caused by the pressure gradient? Water tries to go in a straight line but can't because of the glass, so builds up around the edge and the pressure gradients means there is a force acting into the centre of the circle, where there is less water.

I'm happy with the rotating/non rotating frames of reference now, back to school so I was able to talk to my physics teacher about it!

 

[arildno]

The (ultimate) source of the centripetal force is the container wall (denying the fluid to disperse outward).