B Question about pressure of a liquid

[Reuben_Leib]

I am looking at pressure in liquids and I am testing my idea.

The vertical tube is 100m, the contraption is filled with water. The vertical tube is very thin(maybe 1mm^2 cross section). The area of the base is ~100m^2. Will he top half be launched in the air if suddenly it cracked?- assuming its light enough.

I want to test my idea that if I had a thin long ruber tube that I lifted up, then the pressure at "red lines" will be high and that the $force = pressure * area$ would be massive, that if the contraption were to break at the "cracked" lines then there will be a net upwards force on the top half, lauching the top half into the air.

According to the pressure of a liquid, pressure depends on the hight and not shape, so

pressure$$ = pgh=1000*9.81*100 = 981$$KPa

The force then is $$981*10=9.81MN$$

This is a massive amount of force, which I believe will launch the top half upwards, but its just seems a bit strange that something so little can cause this, so maybe I missed something?

**Question**: will the top half be launched as I described or am I missing something?

 

[Baluncore]

Will he top half be launched in the air if suddenly it cracked?- assuming its light enough.

There is a high upward force on the red surface, but there is no immediate volume of liquid available to accelerate that surface upwards. The rate of rise will be limited by the flow of water down the 1mm vertical tube.

It would be different if there were gas bubbles in the lower space, or the water there was about to boil at about 10 bar pressure, as that would result in energy release from the compressed gas, or a steam explosion.

 

[Dale]

The force is high and if there is a crack then it will accelerate upwards. However, it will not go very far or get very fast.

Remember, to get a lot of velocity you have to apply a force for a decent amount of time. The shorter time the less the change in velocity.

Since your volume of water is so small, the force can only be exerted for a small time. It can break things, but won’t move them very far.

 

[Baluncore]

The immediate pressure release, as the crack propagates, will be sideways through the crack. The red surface will be stuck to the water below, by surface tension.

It will take time to build up pressure while setting up the experiment. The red surface of the lower chamber will bend upwards, like a balloon, as the pressure increases. To prevent that bending, the red surface will need much structural reinforcing, so it will have a very great mass, breaking your assumption.

... ?- assuming its light enough.

The principle you are examining here is the basis for hydraulic fracking, where a low volume of high pressure fluid, is used to crack, extend and widen, large-area sheet-cracks in rocks underground.

 

[Frabjous]

Fluids are used instead of gases in hydrostatic testing to prevent this very behavior.
https://en.wikipedia.org/wiki/Hydrostatic_test

 

[Gavran]

This is a massive amount of force, which I believe will launch the top half upwards, but its just seems a bit strange that something so little can cause this, so maybe I missed something?

A small amount of water in a tube means a small amount of potential energy of water, which means a small amount of work that can be done.

 

[Baluncore]

When the tube is filled with water and the contraption cracks at the "red lines," the rapid loss of pressure would likely cause a force to act on the remaining water, potentially pushing the top half upwards.

The red lines are the solid upper surface of the cylindrical cell, made from infinite strength unobtainium. The crack location is shown as a black zigzag.

However, the magnitude of the upward force depends on how quickly the water is displaced and how the surrounding air or structures interact with it.

The water is under pressure and an upward force is applied to the red surface, before the crack even begins to propagate. The vertical side of the cell is under tension, stretched due to the internal pressure.

The shape and size of the crack play a critical role in determining whether enough force is generated to "launch" the top half.

The side wall is under tension, so once a crack begins, it will propagate around the cell in both directions. The crack in the wall under tension will open slightly as the material yields, fluid will escape outwards, radially. The internal pressure will be rapidly lost as a depression wave propagates from the crack, through the liquid towards the centre of the cell. As the depression wave is focussed on the centre, the depression will increase to where the 1 mm tube is connected, a single drop of fluid will be pulled in by the concentrated depression wave as it passes the centre. The wave will continue on, being attenuated, until it reaches the crack on the other side of the cell.

External pressure will hold the red surface in place, stuck to the fluid by surface tension. Fluid top launch the red disc is not available. Cavitation under the red disc will not allow the red disc to rise.

 

[Frabjous]

For a gas in these situations ρ>>ρ₀
For a liquid ρ≈ρ₀
So it will take very little expansion for the liquid to return to ambient density
Since the fluid and gas start at the same pressure, the energy desposited in the fragment (force x distance) will be much less for the fluid

 

[sophiecentaur]

Fluids are used instead of gases in hydrostatic testing to prevent this very behavior.
https://en.wikipedia.org/wiki/Hydrostatic_test

A failure can be disastrous in a pneumatic system because of the stored energy in the gas. There are tales of charged diving bottles exploding in a car accident. Drive carefully to a dive site!