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This question is based on the content of this video .

The experiment consists of putting a tall, thin column of liquid on top of a barrel filled with water, so that the pressure caused by the large amount of liquid on top of the small area of the base of the column explodes the barrel.

Pascal's barrel experiment

However, one could argue that you could put the same amount of water on a funnnel above the barrel instead of on a column, since you'd have the same weight of water over the same area, thus having the same pressure without needing to install a tall tube.

Pascal's barrel with funnel

The video then explains why this isn't the case, using a column and a funnel filled with water and a scale.

Funnel and column experiment

Despite the funnel having much more water than the column, both containers balance with 50 grams on the scale. The explanation given is that only the water directly above the base counts, since the rest of the water exerts a force on the walls of the funnel, which in turn exerts a force back on the water, cancelling its weight.

Funnel's reaction on the water

So here is my question: wouldn't the force that the water exerts on the walls of the funnel also transfer to the scale, through the rim on the base of the funnel? I think this doesn't happen on the demostration because the arm of the support of the funnel receives this weight instead of the scale.

Support's arm

But if that were the case, wouldn't the funnel work on Pascal's barrel, since there would be no support for the funnel? Maybe the rim of the barrel in contact with the rim of the funnel would play this same role, but I'm not sure. Thanks for your help!

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The point of Pascal's barrel is to show the relationship between height and water pressure in a closed vessel.

What is interesting about Pascal's barrel is that in theory, you can use a very small mass of water (one that the vessel could easily support the weight of), and still have it burst due to the internal pressure being too high.

In their experimental setup, they are measuring fluid pressure at the base of the funnel/cylinder, because that is what Pascal's barrel is an example of. The total weight on the funnel isn't the point. You could externally support all the weight of the water without it weighing on the the barrel, and it would still burst if the fluid in the barrel was in direct contact with the fluid in the water column. What matters is that the pressure of the water in the barrel will depend exclusively on the height of the water column above, not the net weight of that water.

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The force of the water on the funnel would indeed be transferred to the rim of the beaker, but this isn't that much force- as the video says, it's only a couple pounds of water, and so it's only a couple pounds of force. A couple pounds of force isn't enough to break a beaker.

It might be helpful to think of this from an energy standpoint, since it seems much less counter-intuitive that way. It takes a lot of energy to pump that water up 45 feet. So the tall column of water has a lot more potential energy than the funnel of water. Pressure can be considered the capacity that a fluid has to do work, so the more potential energy to column has, the more able to fluid is to do the work required to break the beaker.

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    $\begingroup$ I feel this answer is misdirected. The question was not about the pressure on the beaker, but about why the pressure of water onto scales is the same for vessels of different shapes, the column and the funnel. $\endgroup$
    – Pavlo. B.
    Oct 9, 2021 at 0:50
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    $\begingroup$ @PavloB. The question specifically asks "wouldn't the funnel work on Pascal's barrel, since there would be no support for the funnel?" It's not just about the scale. $\endgroup$
    – Chris
    Oct 9, 2021 at 8:18
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You are right in that if there were no clamp holding the funnel, the weight of the water would all be transferred to the scales through the rim. Because of the clamp, only the piston at the bottom of the funnel can create pressure onto the scales. The force that the piston exerts onto the scales is equal to the 'weight of the piston'+'weight of the water cylinder right above the piston', which is the same for either a vertical tube or the funnel.

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