How Do Piston Sizes Affect Height Differences in Hydraulic Systems?

[map7s]

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.

 

[OlderDan]

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.

 

[map7s]

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...

 

[OlderDan]

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.