Physical explanation of Pascal’s Law

I have a problem with physical explanation of Pascal’s Law. For example, when I was teaching my sister (a high school student) about force transmitting by a rope, I said her:

“In a very simplified mood, when we pull free end of a rope that is connected to a block, we pull first molecule of the rope, that molecule pulls next one and go on like this and last molecule pull the block. So, our force is transmitted to the block.”

In that case, force is transmitted (and maybe decreases because of loss of energy). In a car hydraulic jack, force not only transmitted but also increases. How can I explain this topic physically (not mathematically)? Additional force comes from where?

• Can you make sense of how gears work (in terms of torque)? Or, equivalently, the balancing of moments? – lemon Apr 28 '16 at 10:16
• @lemon, gears apply forces to each other at their contact surface. – lucas Apr 28 '16 at 10:18
• @lemon, I don't know what means "the balancing of moments". – lucas Apr 28 '16 at 10:20
• Google "lever". – Mike Dunlavey Apr 29 '16 at 1:11

Concerning your wording "force is transmitted (and maybe decreases because of loss of energy)" - no, no, the decrease of force is not easily connected to the loss of energy. Force can be decreased because there is friction, but this does not imply a loss of energy (not if nothing moves). And also energy can be lost (plastic deformation of the rope) without a decrease in force.

To your question... you probably know the famous experiment: take a barrel filled with water and a thin tube connected to it going upward. If you fill the tube with water, the barrel bursts.
The spot below the tube is easy - the whole column of water pushes it. But what with the other spots? Well, they are pushed by the top of the barrel (plus the small column below). So if you cut the barrel in the middle, you have to hold it with the force done by all the water columns, not just the one that actually goes so high.

As to your molecules: it's easier to push someone away when leaning with the back to a wall! :)

• Thank you because of your attention. So, you mean that force increases by getting help from walls. I think so. But I cannot say it simply for a student. Anyway, thanks a lot. Good luck. – lucas Apr 28 '16 at 15:31
• It's like the explanation for the buoyant force, e.g. here: physics.stackexchange.com/a/135577/111915 . If you immerse your whole system in water, so that each part of a wall has the same pressure on both sides, you can remove the walls without changing anything. And on the other hand, if there are walls and no water on the other side, then the walls must do the job which the water on the second side has done before. – Ilja Apr 28 '16 at 15:38

You can use the same explanation :

"The first molecule pushes its nearest neighbours (which also push back), the nearest neighbours push their nearest neighbours, and so on until the force is transmitted throughout the fluid."

The total force transmitted to or by a surface is in proportion to the number of molecules pushing, which is proportional to the area.

• Thank you because of your attention. You right about transmitting of force. But what about increasing of force? – lucas Apr 28 '16 at 14:56
• You are just repeating Pascal's Law statement by the other words. – lucas Apr 28 '16 at 14:59
• Does a molecule push more than 1 molecule with same force? If 1 molecule pushes 2 molecules, then the transmitting force will be divided to 2. – lucas Apr 28 '16 at 15:04
• Isn't it obvious that if a force of 1N is applied equally to 1000 molecules, then each molecule bears a force of 0.001N? – sammy gerbil Apr 28 '16 at 15:07
• I said this in previous comment. – lucas Apr 28 '16 at 15:08

Pascal's law states that when there is an increase in pressure at any point in a confined fluid, there is an equal increase at every other point in the container.

To explain this, the hydraulic jack is a better example. Car jack works on mechanical forces. A mechanical jack employs a screw thread for lifting heavy equipment. But hydraulic jacks use force generated from pressure. It's working can be explained using Pascal's law. A hydraulic jack contains two cylinders (one having larger area and the other smaller) connected each other and inside them an in-compressible liquid. Once a force is applied to the small cylinder, a pressure develops on the surface of the cylinder. According to Pascal's law, the same pressure will be transmitted to the entire parts of the fluid. So at the other cylinder the same pressure appears. At the second cylinder, the surface area is large. Since $\displaystyle{pressure=\frac{force}{area}}$ the force acting in the upward direction on the second surface will be larger. So you apply a small force on the cylinder with smaller surface area and you will get a much larger force on the second surface having larger surface area.

As a quantitative example, suppose I have two cylinders $C_1$ and $C_2$. The surface areas of $C_1$ and $C_2$ are denoted as $S_1$ and $S_2$. Let $S_1=1 m^2$ and $S_2=100 m^2$. An in-compressible liquid is present in the cylinders and both are connected. You apply a force of about $600N$ (an average man's weight; suppose you are standing on the first cylinder's surface) on $S_1$. Then it will generate a pressure of $600N/m^2$. By Pascal's law, the same pressure appears on $S_2$. then the force appearing on $S_2$ will be $60000 N$!!!. Impressive, isn't it? That's the weight of 4 cars. you just lifted 4 cars just with your weight. No sweat.

The additional force came from no where. the pressure just remains the same as the liquid is in-compressible. The effect of force comes different when you apply different surface areas connected by the liquid. If you apply two same surface areas, there is no additional force. Here the surface area has great relevance. You cannot just avoid it and think in terms of force alone.

• Thank you dear Unnikrishnan because of your attention. Forgive me for saying this but you just say to me that $F_1A_2=F_2A_1$.I know Pascal's Law. I want to explain it physically similar to the explanation in the question. – lucas Apr 28 '16 at 14:34
• Suppose you have a spherical ball. When a force is exerted on it, the impact will be so large because the entire force will get concentrated at a single point (a sphere has only one point of contact at a time). Now if the same force is applied to the ground, the effect will not be that much as the force will be carried by a large surface (a large no. of molecules) rather than a single point. The reason is that pressure is some sort of energy. Energy can neither be destroyed nor be created. But it is transferrable. – UKH Apr 29 '16 at 2:57
• Since our liquid is in-compressible, no energy is drawn to do a work. So the entire energy is stored in the liquid and that will appear on the second surface. Remember what is a pressure energy – UKH Apr 29 '16 at 2:59
• The first cylinder where you applied the force is a higher concentration region of energy and so the energy flows from that cylinder to the second cylinder. But at the second cylinder the pressure energy is carried by a large amount of molecules than at the first due to large area. This means these molecules could exert larger force as more no. of molecules could exert their energy on the surface. – UKH Apr 29 '16 at 3:04
• Thank you again dear Unnikrishnan. You say that we transmit energy by devices like hydraulic jack. And transmitted energy doesn't change (not increase not decrease). I agree. So, we can say those devices are able to use our energy better. We have energy, not force. Your comments are useful. Thanks. – lucas Apr 29 '16 at 4:08