A hypothetical pressure question lifting a 10,000kg object

[vaxopy]

Lets say you have a very long (and strong) tube (310m high) filled with water. at the bottom, the tube comes back up, forming a U shape. if the radius at the end of this U shape was 0.1m..

does this mean that (absolutely regardless of the radius of the top at the top, and therefore the volume of water present in the tube) you could lift a 10,000kg object?

This just seems so strange to me. Its not in the books or anything but according the formulas, it should work

P2 = P1 + pgh (P = pressure, p = density, rho, P2 = bottom of the tube)
F/A = 101.3KPa + 1000(9.81)(h)
(10000kg * 9.81) / (pi*0.1*0.1) = 101.3kPa + 9810h
h = 308m

In other words, no matter how big this tube is, no matter how much volume of water it holds (it could be 0.00000000001m wide at the top, and all the way down), if its > 308m, it could lift a 10000kg object placed at the bottom (at the inverted U shape of the tube)...

how odd :). is this right or did i mess something up??

 

[Doc Al]

hydrostatic paradox

I didn't check your math, but your thinking is correct. If it seems strange, you're in good company. This famous phenomenon, which puzzled some of the greatest minds, is called the hydrostatic paradox:

"Hydrostatic paradox, the proposition in hydrostatics that any quantity of water, however small, may be made to counterbalance any weight, however great; or the law of the equality of pressure of fluids in all directions." (from www.dictionary.com)​

Check this out: http://physics.kenyon.edu/EarlyApparatus/Fluids/Hydrostatic_Paradox/Hydrostatic_Paradox.html

Note: You can't make your tube too narrow, else other effects take over (like surface tension).

 

[wais]

Your calculations and reasoning are correct. In theory, with a strong enough tube and enough water, you could lift a 10,000kg object at the bottom of the U shape. This is because of the pressure exerted by the column of water in the tube. As the water gets deeper, the pressure increases, and this pressure can be used to lift the object at the bottom of the U shape. However, in practical terms, there are several factors that could affect this scenario. For example, the strength and stability of the tube, the density and viscosity of the water, and the weight and shape of the object being lifted. It is also important to note that this hypothetical scenario does not take into account the effects of gravity and friction, which could also impact the lifting ability of the tube. So while the calculations may suggest that it is possible, there are other real-world factors that would need to be considered before attempting to lift a 10,000kg object using this method.