Buoyancy gedanken

spamTHISbrp · 2007-06-05T18:48:43+00:00

Not really OT givien the recent thread.Buoyancy gedankenTake a 3 inch inside-diameter tube, one end is open, the other end isclosed with a cap with a rod going through it, and this terminates ina piston that seals watertight to the walls of the cylinder.The purpose of the piston/rod is to form a moveable bottom for thecylinder.Think of it as a hydraulic cylinder with the piston and shaft still inplace, but the other end is cut off.Let the piston have a valve in it so that water can be drained throughto the bottom of the cylinder, and the bottom of the cylinder also hasa drain valve.The system starts with the piston at the bottom of the cylinder, thepiston valve is open, the cylinder valve is closed.Whatever cylinder volume exists below the piston is filled with water,and the rod seals watertight to the cap.Further assume the rod is infinitely thin, so the volume of the rodinside the cylinder does not increase as the piston is pushed up intothe cylinder.(Or, just forget the rod, and assume the piston moves up and down thebore via magic, magnetism, etc.)Water fills the cylinder (held open end up) to within say 1 inch ofthe top.An item floats on top of the water, not fully submerged. The moveablebottom is, say, one foot from the bottom of the floating object.Lets make it easy and say the object is cylindrical and is onlyslighty smaller than the bore of the cylinder.Keep the piston valve open, keep the cylinder valve closed. Pistonmoves up, water level does not change since the water above the pistonmoves to below the piston via the valve.Bring the piston up to, say, 0.125 inches below the object.Is the object still flaoting?Has its position in the cylinder changed?Assume the object fits close enough in the bore, and that the pistonis close enough to the object, that the weight of the water above thepiston is less than that of the floating object.Is this even possible?Close the valve in the piston.Does the object move?Drain the water below the piston.Does the object...

Jun 05, 2007 27 Replies

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Leo Lichtman 19 years ago

"Don Foreman" wrote: Two experiments have shown cases where this is not true, and the results are consistent with theory -- though perhaps not with your theory. ^^^^^^^^^^^^^^^^^ Your experiments were neatly designed. My compliments. I think the distance between us is in the definition of "displaced liquid." I define the displaced liquid as the volume of the floating object that is beneath the surface. With that definition, I believe your experiments are in agreement with my theory.

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engineman1 19 years ago

I wonder if this could be considered as a variation of the "hydrostatic paradox" problem? If you have a 1' diameter pipe and a 1" dia. pipe and they are both vertical and 10' long full of water, a pressure gauge placed at the bottom of either will read the same. In the floating object experiment the pressure on the bottom of the object in PSI is a function of the height of the water from the surface to the bottom of the object rather than the quantity of water. That's how I analyzed the problem anyway. Engineman

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spamTHISbrp 19 years ago

Define the system from the reference frame of the floating object.

"Fluid will rise around the object until the pressure due to the column of fluid (column as measured from the bottom of the object to the top of the fluid), times the area of the bottom of the object, equals the weight of the object", assuming the object will float.

Very clean conceptually for flat-bottomed objects, just a little calculus for irregular objects.

Dave

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Don Foreman 19 years ago

With that definition, yes. I'll defer to you to explain how an object displaced 150 grams of liquid when there were less than 20 grams of liquid to begin with ...

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Don Foreman 19 years ago

Exactly. That's true both in the constrained case and in a lake or pool.

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engineman1 19 years ago

Well, this has been an interesting thread, I learned a few things about buoyancy and saw an example of military intelligence.

Engineman

On Thu, 07 Jun 2007 12:30:49 -0700, " snipped-for-privacy@aol.com"

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Don Foreman 19 years ago

Military intel in this thread?

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Pete Snell 19 years ago

I think that was a poke at me Don...;-)

Pete

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