Is there really any such thing as an incompressible liquid?

Abu Rehan

1. The problem statement, all variables and given/known data
Given- Pressure increases with depth.


2. Relevant equations
We know that pressure under a depth h is given by pgh. Where p=density of liquid, g= acceleration due to gravity.


3. The attempt at a solution
Let us take an example.
There is an ocean of a liquid which is 100% incompressible. At a depth h there is a lobster experiencing a pressure of pgh. Suppose we go deep inside the ocean and seal the lobster and the liquid in a box. Clearly, the lobster is still experiencing the same amount of pressure. We bring the sealed box above with us. We take another box, pour some water in that, put a lobster in that and seal the box.
Now observe the two boxes. If the liquid is incompressible then the two boxes are identical(apart from the compression in lobster's body). But we earlier saw that the first lobster is experiencing much more pressure than the second one. So we arrive at a contradiction. Therefore there must be something different in case of the first box i.e., it must have a little compressed liquid. The decrease in volume may be very very little but compression must be there. What is relevant is the pressure. Some liquid may apply huge amount of force by getting compressed very little while others may apply that amount of force by getting compressed a lot.
Therefore however incompressible a liquid may be, it cannot be 100% incompressible.

gneill

This doesn't appear to be a homework problem, it's more of a philosophy of science issue like light flexible strings and massless pulleys. Possibly it would be better served up in one of the general physics forums for discussion.

Also, you forgot about the compressibility/flexibility of the box material