Question

Pascal's law states that a change in pressure in an enclosed body of a fluid gets equally disturbed throughout the entirety of the fluid without getting diminished.My question is.. is the Without getting diminished part always true?. Like it is true here on earth for a small container where density and g are almost constant. Imagine a fluid enclosed in a container that is a million kilometer³ in volume in vast empty space, without any nearby stars or anything so it is devoid of Gravitational effects. Let's say the fluid is filled to the brim. If we apply 1Pa pressure on one end, will the atoms in the other end a million km away feel the same pressure? Shouldnt the pressure diminish atleast by a tiny bit cause pushing all the way, some atoms absorb some of the force, as if heat or something. Will the pressure not get diminished, atleast by small amount?I was just curious if Pascal's law is a universal law or if it just works very good enough in real life purposes here on earth so we call it a law.

Answer 1

Pascal's Principle states that pressure in an enclosed fluid is transmitted undiminished, but on an extremely large scale and in deep space, factors such as heat conversion or compressibility could potentially lead to diminishment. However, for practical, terrestrial applications, Pascal's Law remains effectively accurate.

Step-by-step explanation:

Pascal's Law, or Pascal's Principle, states that when a change in pressure is applied to an enclosed fluid, it is transmitted undiminished to every part of the fluid and to the walls of the container. The key here is that the law applies to the ideal scenario where the fluid is incompressible and there are no energy losses due to factors like friction or viscosity. In the hypothetical situation of a fluid enclosed in a container in deep space, and assuming the fluid does not compress or transfer energy to another form (like heat), Pascal's Law suggests the pressure change would indeed be transmitted undiminished. However, if on such a colossal scale some energy is converted to heat or if the fluid behaves in a compressible manner, the pressure transmission could potentially be less efficient, and the pressure might diminish slightly over vast distances. Nonetheless, for most practical applications, especially those with much smaller scales and controlled conditions, Pascal's Law holds true and is foundational for understanding fluid mechanics and the design of hydraulic systems.