why is it counter intuitive for you? It is not to me at all. Gravity pulls down. There is essentially no lateral component to gravity. Height is measured in the verticle dimension, the same as gravity. Now imagine water column as a stack of pennies. The more pennies are added to the stack the more pressure is on the lower pennies. It does not matter how many stacks are in front of or behind or to side of the stack you are looking at.
> There is essentially no lateral component to gravity
Yet you can distribute the weight of a structure on larger bases. If you put two columns on pennies on a steel plate, the pressure under the plate will be higher than if you put only one column.
It is easy to imagine the bottom vessel as similar to such a plate.
I think the key to make this intuitive is to realize a few things:
- pressure in liquids are transmitted differently
- water is actually very slightly compressible
- atmospheric pressure is also an important part of the system
The intuition with the columns of pennies over a plate doesn't translate because in the plate case the surface is fixed (the surface of the plate) so the pressure depends on how much weight you put on it. In the case of multiple columns of water, the pressure you're looking at is the pressure on the combined surface of both columns, which remains constant because both the weight AND the surface are increasing proportionally, keeping the ratio (that gives you the pressure) constant.
> Yet you can distribute the weight of a structure on larger bases.
In the case of solid objects, indeed. This is because in solids atoms are bonded together and so the weight can distribute. An easy and extreme case of this last statement is to imagine standing on a bridge. Your weight is supported not just by the part of the bridge underneath you, but, via transmission, by the two end points attached to land.
In liquids, the atoms are not bonded, so the same distribution cannot happen.
Nobody is saying this fact about liquids isn’t true. We all know it’s true, so proving it doesn’t change anything.
It is counter intuitive though precisely because the pennies analogy doesn’t work.
If I put a 1m stack of quarters on a pressure gauge, then I put one quarter on the gauge and a stack of pennies on top of it up to 1m high, I get two different readings. Conversely if I measure the pressure at the bottom of two bottles the same shape as the stacks of coins, I get the same readings.
If you measure the pressure at the bottom of two bottles containing different density liquids the same shape as the two stacks of different coins you get two different pressure readings.
In case it was not clear in my analogy a "penny" (it can be anything solid and incompressible) is representative of a water molecule. If you want to compare the pressures of stacks of pennies and quarters because for some reason you are fixated in these specific physical coins rather than what they represent then I will make it explicit. Imagine pennies represent water and quarters represent mercury. Two different liquids, two different coins, two different pressures. I don't get what you guys don't get.
Can you explain to me why you think it is intuitive that the downward pressure of a liquid at the bottom of a container should vary for equal depths but different volumes? E.g. you seem to intuitively think that if you have a big pan filled with 1 inch of water the water pressure at the bottom of the pan is greater than the pressure at the bottom of a 50 ml flask also filled with one inch of water. This is false but I am interested as to why you and the others think it is "intuitive?" Where does the additional force come from to increase the pressure in the bigger pan? Gravity pulls straight down.
In my case, the difference in intuitiveness is that I am used to things crushing because of weight/force but not because of pressure.
If you have a bottle of 1 kg of water and put it on a plank between two stools, what matters to know if the plank will break is the total weight (and torque) of the bottle and the surface of contact. The shape of the bottle is irrelevant.
When you have that image in mind and someone suddenly tells you that actually no, 1 kg of water on a 50 meters high column can actually break things 1kg of water in a bucket can't, it is very counterintuitive.
And the stack of pennies is really unhelpful I feel. Make an inverse pyramid with 1000 pennies, all of them resting on one at the bottom tip, or make a column of these, the force exerted on the bottom one will be the same. The force per area as well. Not so with water.
The difference is that the water molecules move until they find an equilibrium in which there is a gradient of pressure and where molecules push back in every direction equally. Pennies do not, they are content exerting "pressure" in a single direction
Water exerts pressure in a single direction too: down. There is no PSI gradient in the lateral direction. This is intuitive because there is no force acting in that direction. I do not believe water molecules ever find a topological equilibrium in a liquid phase. Because then they would be a solid or a crystal. Water as a liquid can flow but it still only exerts pressure in the downward direction. To my analogy, pennies can slide or move from one stack to another (e.g. waves). The only thing affecting the pressure on the bottom penny of a given stack at a given instant is the number of pennies in that same stack resting on top of it. What is going on in the adjacent stacks does not matter, because gravity only pulls down.
Actually, yours is not such a great explanation, since a stack of quarters would manifest greater pressure than a stack of pennies. Whereas, a fluid column would manifest the same pressure no matter the diameter.
No, a stack of pennies would manifest a greater force, but the pressure would be the same. Pressure is force per area, which means that the increased weight from a wider column is exactly cancelled by the increased area that the force is distributed over.
Ok, yes, this holds true if the support surface increases the same. But the parallels still do not hold too well. Imagine sort of a funnel holding water, no matter the thickness of the base or top, the fluid pressure at the base is the same. Whereas with coins it does not work the same.
Hmmm ... reinforces my counter-intuition. The stack of pennies might explain why the bottom of the jar would explode, but not the sides, area not below the stack of pennies.
My intuition (wrong here) is that the extra surface not beneath the stack of pennies (your analogy) would in fact distribute the pressure and therefore represent a lower PSI on all sides of the jar.
I guess I translated "pennies" into "little bags of water". The little bag of water at the bottom only gets pressurized from the little bags of water above it.
And so the bottom bag's "pushing" outward from compression would be affected only by those above it.
