Fluid Column Height Drop Due to Gravity

[stewartcs]

How far will a column of a fluid with density p1 fall if it is inside of a tube (open to atmosphere at the top), inwhich the tube is inside of a tank of another fluid with density p2 (p1 >> p2)? Assuming that the tube was intially plugged at the bottom while filling it with the higher density fluid and then, once full, suddenly releasing it.

I know that once the hydrostatic pressure of the fluid at the bottom of the tube is balanced with the hydrostatic pressure of the tank (at the same point) the height can be found easily. However, I would like to know how much further, initially, the column would fall do to the fluid being accelerated by gravity, before it rebounds to the balance point.

Any ideas??

Thanks...CS

PS
See attached drawing...

 

[machinest]

how much time?before the case arrives to its balance point?
i don't know really how to calculate the time till u arrive the balance point,i know about the boyancy thing,if u did the boyancy formula would it help?
there is no other givens in this proplem?,like if u have the sizes&the two fluids and u could do it as an experiment,and get the required time till the balance occurred?(if possible).
that was all what i could say:),hope i added any info to u,and waiting others to make things more clear for u and me,interesting to know.
thanks for the forum.

 

[stewartcs]

Thanks for the reply.

Well I imagine the amount of time is dependent on the initial height of the fluid column in the tube and the terminal velocity of the falling fluid, which would probably depend on the frictional forces from the tube walls. I failed to mention the fluid is a non-Newtonian fluid too, so maybe I could use a Power-Law or Bingham-Plastic equation to help determine the friction factors??

I plan on trying model it first then perform an experiment to validate the model. The only problem is getting an accurate measurement of the height change without an enormously long tube or deep tank.

 

[russ_watters]

Consider this: if you take a weight that is sitting on (and attached to) a spring at equilibrium and lift it, then drop it, how far will it fall below it's initial equilibirum position?

The answer is the same for your question (excluding complications such as viscocity). Also, you can test your problem easily enough with a straw and a glass of water...

 

[stewartcs]

Thanks for the reply Russ.

I haven't thought about that. I'm not sure how to fit the concept to the problem though. For example, would the spring constant be the bulk modulus of the fluid in the tube or the fluid in the tank (or an equivalent of the two)? Plus, how would one allow for the viscosity of a non-Newtonian fluid, and the drag, in a spring and mass model?

I don't think testing with a straw and a glass of water would be accurate enough. The problem is with such a small scale experiment, like that of a straw and glass of water, the change in height would be very difficult to measure accurately since it would be very small and happen very fast before rebounding to the equilibrium point.

Any ideas to complete the model? It sounds promising.