How Do Piston Sizes Affect Height Differences in Hydraulic Systems?

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Homework Help Overview

The discussion revolves around a hydraulic system involving two pistons of different diameters and masses, with a focus on determining the height difference between them based on fluid density and pressure principles.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants express uncertainty about the appropriate equations to use, particularly regarding pressure differences and the implications of varying piston sizes. There is mention of using the equation P2=P1+pgh and considerations of pressure equality at a common liquid level.

Discussion Status

Participants are actively engaging with the problem, questioning the assumptions related to pressure and density. Some guidance has been offered regarding the need to consider forces acting on the pistons and the implications of having a single liquid in the system.

Contextual Notes

There is a noted confusion regarding the application of equations typically used in scenarios involving different liquid densities, which may not directly apply to this problem. The discussion highlights the complexity introduced by the differing piston areas and their effects on pressure and force.

map7s
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In a hydraulic system the piston on the left has a diameter of 4.7 cm and a mass of 1.7 kg. The piston on the right has a diameter of 12 cm and a mass of 3.7 kg. If the density of the fluid is 750 kg/m3, what is the height difference h between the two pistons?

I'm not even sure what equation I could use to get started on this problem. I was looking at the equation P2=P1+pgh but the pressure would be the same at both points.
 
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map7s said:
In a hydraulic system the piston on the left has a diameter of 4.7 cm and a mass of 1.7 kg. The piston on the right has a diameter of 12 cm and a mass of 3.7 kg. If the density of the fluid is 750 kg/m3, what is the height difference h between the two pistons?

I'm not even sure what equation I could use to get started on this problem. I was looking at the equation P2=P1+pgh but the pressure would be the same at both points.
The equation you wrote for the pressures is based on the fact that at a common level that is in the liquid on both sides the pressure is equal. P1 and P2 are the pressures at the tops of the liquid, which are at different levels.
 
right, that was one of the reasons as to why i was confused...I also looked at another equation, but it was in regards to a similar problem where the one side that was lower was due to a different density of liquid added and then they used the equation p(water)h1=p(liquid)h2...I was trying to find out some way to tweak that equation so that I would be able to use it for this problem, but it's not really working...
 
map7s said:
right, that was one of the reasons as to why i was confused...I also looked at another equation, but it was in regards to a similar problem where the one side that was lower was due to a different density of liquid added and then they used the equation p(water)h1=p(liquid)h2...I was trying to find out some way to tweak that equation so that I would be able to use it for this problem, but it's not really working...
You only have one liquid, which is easier to deal with. You have different piston areas, so even if the two sides were at the same level (same pressure) you would have different forces on the pistons. You need to find the forces acting on the pistons to find the pressure on each side.
 

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