# Fluid Column Height Drop Due to Gravity

1. Sep 19, 2007

### 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...

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• ###### Falling Mud.jpg
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2. Sep 25, 2007

### 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 occured?(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.

3. Sep 25, 2007

### stewartcs

Well I imagine the amount of time is dependant 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.

4. Sep 25, 2007

### Staff: Mentor

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...

5. Sep 26, 2007