# In-Depth Pascal's Law Explanation

• Von Neumann
In summary, the conversation discusses the concept of Pascal's Law and its explanation for how pressure is transmitted equally in all directions within a confined incompressible fluid. The question arises as to why this phenomenon occurs and whether it is due to the inherent properties of fluids or can be derived from other principles. The conversation also touches on the idea of pressure being different at different locations within the fluid. Ultimately, the conversation references Wikipedia's definition of Pascal's Law and its role in fluid mechanics.
Von Neumann
Problem:

The general idea makes sense intuitively to me, but most sources I've found cite Pascal's Law merely as scientific fact with not much explanation. What I'm wondering is why pressure applied at one point in a fluid is transmitted undiminished to all other points? Is it a concept due to the inherent properties of fluids that I must simply accept?

Could probably derive it from conservation of energy and incompressibility of the fluid. Consider two pistons located within the fluid. The difference between work done expanding one and allowing the other to shrink by the same volume must be balanced by the net change in PE of the fluid.

If p were not the same in all directions then a particle would be accelerated in some direction, which doesn't happen.

rude man said:
If p were not the same in all directions then a particle would be accelerated in some direction, which doesn't happen.
I don't think that was the question. It's to do with pressures at different locations, not different directions.

haruspex said:
I don't think that was the question. It's to do with pressures at different locations, not different directions.

Oh yes? "Pascal's law or the principle of transmission of fluid-pressure is a principle in fluid mechanics that states that pressure exerted anywhere in a confined incompressible fluid is transmitted equally in all directions throughout the fluid such that the pressure ratio (initial difference) remains the same.[1"
-wikipedia, italics mine.

If I go deeper I go to a different location where the pressure is not the same, is it ...

## What is Pascal's Law?

Pascal's Law, also known as the Principle of Transmission of Fluid-Pressure, states that when a pressure is applied to a confined fluid, that pressure is transmitted equally and undiminished to every part of the fluid and the walls of the container.

## How is Pascal's Law used in real life?

Pascal's Law is used in various applications such as hydraulic systems, brakes, and lifting mechanisms. It is also used in medical devices like blood pressure cuffs and syringes.

## What are some examples of Pascal's Law in action?

A simple example of Pascal's Law in action is using a hydraulic jack to lift a car. When pressure is applied to the small piston, it creates a force that is transmitted to the larger piston, allowing the car to be lifted with ease.

Another example is a scuba diver breathing from a tank. The compressed air in the tank exerts pressure on the water, which is then transmitted equally to the diver's lungs, allowing them to breathe underwater.

## What are the limitations of Pascal's Law?

Pascal's Law only applies to confined fluids at rest. It does not take into account factors such as fluid viscosity, turbulence, and compressibility. In addition, the fluid must be incompressible for the law to hold true.

## How did Pascal's Law come to be discovered?

Pascal's Law was discovered by French mathematician and physicist Blaise Pascal in the 17th century. He conducted experiments with pressure and fluids, and through his observations, he formulated the law that now bears his name.

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