How Does Pascal's Principle Affect Fluid Dynamics and Comfort in Bedding?

[Aristotelian]

Hey all, I apologize if this question has a really obvious, basic answer, but I've done a lot of searching and haven't come across anything that explains it satisfactorily for me.

So, I know that Pascal's principle underlies the workings of the hydraulic lift, and I know that while force is multiplied on the piston/platform with larger area, the distance moved relative to the smaller piston/platform is inversely proportional to the increase in force. What I'm not quite understanding is why in this case the ratio of the areas affects the distance the fluid is raised, while in the case of, say, a mercury barometer the ratio of the area of the reservoir to the area of the tube is not relevant to the distance the fluid in the tube is raised, and only the pressure difference is. I've found a lot of resources that say THAT this is the case, just not any that explain why.

Tangentially, to the degree that comfort in bedding is related to pressure on the body (not the only factor, obviously, but a significant one), wouldn't Pascal's principle indicate that air/water beds would be among the least comfortable sleeping surfaces, since the pressure applied by the densest areas of the anatomy would be transmitted largely undiminished across the surface of the container? I often hear it said by people who market air/water beds that they "redistribute" pressure, but as I understand Pascal's principle, they definitely don't redistribute pressure (in the sense in which if you had 2 equal areas of the body that would otherwise have, say, 40 mmHg and 20 mmHg of pressure applied to them, they instead have 30 mmHg applied across the combined surface). Instead, it seems they would take the worst pressure point and apply that pressure across the entire surface. Is there something I'm completely misunderstanding here (I imagine there is, but I'm not sure what it is)?

I realize the first question is probably really basic, and that the second is probably really basic and a little odd, but I couldn't think of a better place to ask these questions. I apologize if there's a better place I should be asking these questions, and I thank you in advance for any attempts to help!

 

[Studiot]

Hello Aristotelian and welcome to Physics Forums.

Yes that is a good question. Both the hydraulic press and the manometer work on fluid pressure, but under very different circumstances.

In the hydraulic press we assume that the forces transmitted by the load and the effort are so great that we can ignore the self weight of the liquid displaced.
This means that we ccan make the assumption that the pressure (due to the effort) is the same throughout the liquid.

In a manometer we are applying no such forces and we cannot make this assumption. Indeed if you look at the derivation for the manometer formula you see we assume exactly the opposite - we take the weight of the displaced fluid as balancing the difference in pressure between the ends of the manometer. By acknowledging the difference in pressure we are stating that the pressure is not the same throughout the fluid.