Pascal's barrel is an experiment that shows the counterintuitive nature of how pressure increases linearly in depth according to $p=p_0+\rho gz$, where $z$ is the depth. The experiment consists of a barrel and a long hosed attached to it. The hose is raised far above the barrel. By pouring a relatively small amount of fluid inside the hose the depth $z$ inside the barrel increases quickly because the depth is measured from the highest point exposed to air. If setup correctly this can cause the barrel to burst using only a small amount of fluid.
Now I imagined what would happend for the "opposite" of this. Imagine the hose goes down instead of up. The hose starts closed off but at a certain moment the seal is broken and the bottom is exposed to atmospheric pressure. I have the following questions
- What is the pressure distribution before the seal is broken? (left picture)
- What is the pressure after the seal is broken?
- Can the pressure go negative given a long enough hose?
- Will the barrel implode violently?
Best Answer
The culmination of this experiment will be similar to the original Pascal's barrel experiment but the barrel will implode (as opposed to explode as in the original experiment).
It will be as expected, where at any point $z$ pressure is $P=P_0+\rho gz$
Nothing too spectacular at this instant. The fluid is in motion, so the pressure will be governed by Bernoulli's equation $$P_1+\rho gz_1 +\frac 12 \rho v_1^2=P_2+\rho gz_2 +\frac 12 \rho v_2^2$$ where I guess you assume the fluid to be incompressible and the flow is continuous so $A_1v_1=A_2v_2$ ($A_1,v_1$ and $A_2,v_2$ are the areas and speeds in the upper and lower regions respectively).
The differential pressure ($P_{\text{inside}}-P_0)$ will be less than zero since there is a low-pressure region forming in the upper part of the larger container as the fluid is drained from the bottom hose.
This is where things will get interesting. There will be a point where the pressure in the upper part of the container becomes small enough that the atmospheric pressure is enough to cause the barrel to collapse on itself. I would be extremely surprised if the barrel did not suffer this fate (of course you assume the barrel is made from usual materials and not made of some indestructible substance, and the hose is long enough).