# Static equilibrium in fluids

• map7s
In summary, the conversation discusses the use of equations to determine the height difference between two pistons in a hydraulic system. The equation P2=P1+pgh is mentioned, but it is noted that the pressure would be the same at both points. Another equation involving different densities of liquid is also considered, but it is determined that it cannot be applied to this specific problem. The expert suggests finding the forces acting on the pistons to determine the pressure on each side.
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.

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.

## 1. What is static equilibrium in fluids?

Static equilibrium in fluids refers to the state in which the forces acting on a fluid are balanced, resulting in no net movement or change in shape of the fluid.

## 2. How is static equilibrium achieved in fluids?

Static equilibrium in fluids is achieved when the forces acting on the fluid, such as gravity and pressure, are equal and opposite. This can also be achieved when the fluid is at rest and not affected by any external forces.

## 3. What is the importance of static equilibrium in fluids?

Static equilibrium in fluids is important in understanding the behavior of fluids, such as water, oil, and air, in various situations. It allows us to predict the movement and stability of fluids in a given environment.

## 4. How does the shape of a container affect static equilibrium in fluids?

The shape of a container can affect the distribution of forces on a fluid and therefore, influence its static equilibrium. For example, a tall and narrow container may have a higher pressure at the bottom due to the weight of the fluid, while a wide and shallow container may have a more even distribution of pressure.

## 5. What factors can disrupt static equilibrium in fluids?

Any external force, such as wind or a change in temperature, can disrupt static equilibrium in fluids. Additionally, changes in the shape or density of the fluid can also affect the balance of forces and disrupt the equilibrium.

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