# Pascal's Law - pressure inside the liquid vs. force needed to lift the liquid

• EnquiringMind
In summary, the conversation discusses the concept of pressure and force in two containers with open tops filled with water. It is explained that the pressure at the bottom of both containers is the same, even though one container has less weight on its piston. This is due to the fact that the force needed to lift the water is the same, as long as the bottom of the containers have the same cross-sectional area. The conversation also addresses the confusion about where the energy goes when lifting the water by a small distance, with the explanation that the difference in mass and center of mass offset each other.
EnquiringMind
I'm going to steal a picture that was used in a different thread in this forum.

[PLAIN]http://img821.imageshack.us/img821/7469/75687957.jpg

(both containers are open at the top, and both contain water)

I watched an MIT video of professor Walter Lewin, who used these very same illustrations and stated that the pressure at point A and point B are the same.
(see minutes 18 through 21 of the video: http://www.youtube.com/watch?v=265icrI3HkM&feature=related")

Although it is not intuitive, I accept that the pressure is the same at the bottom of both containers.

My question is this...

Imagine that the bottom of both containers is actually a piston (of equal area in both containers).

Obviously there is a smaller amount of weight sitting on the piston in the left container, as opposed to the right container.

So intuitively, to begin ejecting water out the top of each container, I have assumed that less upward force would need to be applied to the piston of the left container... than the piston of the right container (more total water weight over the same piston area).

My confusion is how the pressure on the piston inside both containers can be the same... yet the force needed to eject water out the top of both containers is different.

Last edited by a moderator:
Actually, the force needed to lift the water is exactly the same in both containers, assuming the bottom of the containers have the same cross-sectional area. To lift the water, you just need to overcome the water pressure over the entire area of the piston. Both pressure and the area are the same for both containers, so force should also be the same.

This is counterintuitive, but it doesn't violate any laws of physics. The natural question would be to ask where all the energy went in lifting the water by a small distance L, since both containers should have received F*L of energy from the piston. For the right container, the water's center of mass rises by L, so the water gains mgL of potential energy. For the left container, the water is forced into a thin tube, so its center of mass rises by much more than L. Although the water also has less mass, this difference in mass is more than offset by the larger increase in center of mass, so this is where all the work went.

## 1. What is Pascal's Law?

Pascal's Law, also known as the principle of transmission of fluid-pressure, states that pressure applied to an enclosed fluid is transmitted equally in all directions throughout the fluid.

## 2. How does Pascal's Law relate to pressure inside a liquid?

Pascal's Law states that the pressure inside a liquid is the same at all points, regardless of the shape of the container. This means that if pressure is applied to one part of the liquid, it will be transmitted equally throughout the entire liquid.

## 3. How does Pascal's Law affect the force needed to lift a liquid?

According to Pascal's Law, the force needed to lift a liquid is directly proportional to the pressure applied to it. This means that the greater the pressure, the greater the force needed to lift the liquid.

## 4. Can Pascal's Law be applied to gases as well?

Yes, Pascal's Law can also be applied to gases. It states that the pressure applied to an enclosed gas is transmitted equally throughout the gas, just like in liquids.

## 5. What are some real-world applications of Pascal's Law?

Pascal's Law has many practical applications, such as in hydraulic systems, where it is used to create and transmit large forces through the use of small forces. It is also used in hydraulic lifts, car brakes, and other machinery that utilizes the principle of fluid pressure to lift or move heavy objects. Additionally, Pascal's Law is important in understanding how fluids behave in various systems, such as in plumbing and air conditioning systems.

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