Predicting balls's movement in well due to fluid flow I am a total newbie in fluid dynamics. In one of my experiments/open project, my experiment setup is as below: a small ball sits in a circular well (has mass density a bit heavier than water), with closed, half-moon channel on top of the well. A flow going in the channel from left to right. 


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*If this problem is solvable by theorem, how to/what fluid theories should be applied to predict the flow velocity needed to start lifting the ball?

*What fluid theories should be applied (and how) to predict the ball's angular velocity and its movements, with regards to fluid flow velocity?


It will be nice if at least I can find some clue on what part of fluid dynamic theorie can be applied to figure out this problem.
 A: This is a very interesting problem.  Probably the first thing that is going to happen is that the ball will roll to the right, so that it will be in contact with both the 'floor' and the right-hand wall.  Presumably, what will cause the ball to start lifting will be a combination of two things:


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*The ball may start spinning and try to lift on the right-hand wall, due to friction.

*Lift may be generated by the venturi effect, due to the fluid flowing past the ball.


As for case 1, the steady-state angular velocity of the ball will probably depend on a balance between the friction on the walls and the viscous shear stress acting on the ball due to the fluid flow.  So, I would think the coefficient of friction between ball and wall would be important, as well as the viscosity of the fluid and the velocity profile, as the velocity gradient at the fluid/ball contact surface will determine the amount of fluid friction.  You might be able to model the velocity profile somehow by using a modified version of poiseuille flow through a pipe, although you would probably have to make some fairly big simplifications.  Regarding the friction with the walls, we should also consider that the motion is in a fluid, so you may have to take into account some sort of lubrication factor, so modelling the friction there will not be too easy.
Case 2 may be simpler to model/analyze, as it doesn't depend on viscous effects.  The pressure on top of the ball will be lower than at the bottom, due to Bernoulli's principle (at the bottom the static pressure will be equal to the stagnation pressure, whilst at the top it is reduced due to the flow velocity).  If this is water then this should be fairly easy to model just using Bernoulli and the conservation of mass.  This way you should be able to link the lift on the ball with the flow velocity - at some point the ball will start to lift.  I'm not entirely sure what will happen once the ball starts lifting.  The flow area will decrease, so for the same inlet velocity the lift should increase, although you will also get increased resistance to the flow and so the overall flow may reduce.  I don't know whether you will end up with the ball sitting at some equilibrium, or whether you will get some kind of unsteady behaviour where the ball rises and then falls cyclically.  That's an interesting question and I'll give that some more thought ...
So, I'd probably start with the venturi effect (case 2), as I think it will simpler to analyze and you could probably argue that the spinning won't have too much of an effect on the lift anyway, since the ball/wall interface is lubricated, so the friction coefficient will probably be low.
