When is Pascal's law about fluid pressure propagation applicable? Is it applicable to a closed circular pipe with a pump rotating the fluid, but not to a tub of water. Most statements require only confinement of the fluid.
Or is the question irrelevant ? This law is no longer used or taught ?
Here is my full story about it.
You do not have to read it all to answer. Your choice.
The question and its context
Being a bit surprised by a dismissal on this site of the applicability of Pascal's Law because the fluid was not confined (well, it was an ocean), I took my favorite browser and asked: Pascal Law, then I took the answers in order, more or less. I do skip youtube.
According to Wikipedia (quoting a book):
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 variations (initial differences) remain the same.
which is confirmed by the Wiktionnary:
The law that states that a confined fluid transmits externally applied pressure uniformly in all directions
Then according to NASA (who seems to equate fluid with liquid):
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.
The Q&A system of the Physics Dept at University of Illinois at Urbana-Champaign agrees (quoting a book):
Pascal's Law (also called Pascal's Principle) says that "changes in pressure at any point in an enclosed fluid at rest are transmitted undiminished to all points in the fluid and act in all directions."
insisting further that it must be "a closed container".
And the sciencefair site confirms for the layman:
Pascal's Law states that when you apply pressure to confined fluids [...], the fluids will then transmit that same pressure in all directions within the container, at the same rate.
While the Hyperphysics site insist for the professional with this statement of Pascal's Principle:
Pressure is transmitted undiminished in an enclosed static fluid.
To be fair, the Free Dictionnary defines Pascal's law as follow:
The principle that external static pressure exerted on a fluid is distributed evenly throughout the fluid. Differences in static pressure within a fluid thus arise only from sources within the fluid (such as the fluid's own weight, as in the case of atmospheric pressure).
Maybe because it is not a science site.
My main question is: Why should the fluid be enclosed ? (for the law to be applicable)
A side question is, why do most statements ignore compressibility ? Well, Pascal did too, afaik, but he was in a much different context. Also we should remember that not all fluids are liquids. Forgetting that fact may lead to death by drowning, or by diving in empty pools.
My own clarification of the issue
Maybe I should not answer myself, so as to better encourage other answers. But then, why pretend I am too stupid to answer it when I can actually prove that I am ?
As I said, I would like some clarification on this, and check my own understanding, which is not quite in agreement with the above definitions.
If this law is considered in a uniform gravity field, the requirement of incompressibility is needed only to preserve a constant density, so that the pressure difference between different heights in the liquid does not change. If correct, this also means that the incompressibility requirement can be lifted regarding the transmission of pressure change between two points at the same height.
Note that if pressure change is small, there is little compression and density variation so that the incompressibility requirement can be lifted as first approximation. That was, I guess, the situation of Pascal as he was analysing atmospheric pressure and its variation under limited height changes.
In free fall, the weight of the fluid no longer matters, and the compressibility should not matter either. However the fluid has to be confined if a non-zero pressure is to be applied. It is actually more complex, as there may be surrounding pressure from the environment, or surface tension in various cases (e.g., a bubble of gas in a liquid). Also, enclosure may be necessary to prevent mixing of the liquid or gaz with surrounding medium, though that does not require a rigid enclosure, and is not related to Pascal's law itself.
However, I do not see the need for the confinement constraint in a gravity field. A container is certainly needed, as is usual for liquids (especially when it is hot coffee), but nothing requires that it be a closed confinement. The top can perfectly well be open to atmospheric pressure in the case of a liquid, or only separated by a very light membrane for gas. This may not be convenient for achieving high pressure in some devices, but that is an engineering issue that has nothing to do with Pascal's law.
This is even true for gas. After all, the law is originally based on a study of Earth atmosphere which can hardly be considered as enclosed.
Of couse, the fluid is considered only in those parts of space where it is present before and after the pressure change.
To conclude, my understanding is that the confinement may be needed to actually achieve a change of pressure somewhere in the fluid, in engineering applications of the law but confinement has nothing to do with Pascal's law itself.
Why then ?
Why this agreement on requiring an irrelevant condition for the applicability of Pascal's law.
The question should possibly be another one. What is meant by requiring that the fluid be confined or enclosed ?
Maybe the answer is given by the sciencefair site which (if I did not miss anything) is the only one to actually define what it means:
contained in a flexible yet leak-proof enclosure so that it can't flow out
I will not dispute this disputable definition, but the intent seem clearly to prevent dynamic flow, to have a static system. Whatever the actual intent, that is the only explanation I found.
Hyperphysics is very professional and to make the point absolutely sure uses both belt and suspenders: "an enclosed static fluid". The University of Illinois has the same worry about decency: "an enclosed fluid at rest".
As I understand the problem, it would be wiser to only use the correct qualifier, and mention "static fluid" or "fluid at rest", rather than inappropriate qualifiers that create much confusion and misunderstanding, particularly in an educational context, as shown by the example that initially motivated this question.
Is this analysis correct or did I miss a point ? If I err, can you tell me where ?
In a widely ignored question (I am very good at that) that only managed to gather one downvote, I was trying get reactions or opinions on the issue of precision in science. I did not mean quantitative but rather qualitative precision, precision in concepts and hypothesis rather than mathematical formulae.
I guess this is just another example, and I did not have to look for it: it found me.
All contributions to understanding this are answers.