Question

can can liquids not be compressed so easily

Answer 1

I take a rigid cyclindrical container, fill certain level of water, and then put a piston such that it touches the surface of water. after starting compressing the water, the water is compressed.

Liquids are compressible, otherwise shock and sound waves would not exist! In fact, it is a matter of ratio of density change to mean density - or more precise: convective velocity to speed of sound (which is the Mach number) to distinguish between compressible, slightly compressible and incompressible. The terminus incompressible is not a physical state. It is an approximation in the regime (that is the operating conditions) where compressibility effects are negligible. Mach number is a great indicator for this question. A rough estimation is:

a) Ma < 0.2 can be approximated as incompressible (means: it is rather unlikely - though not impossible - that compressibility effects appear and are strong),

b) Ma > 0.7 should/must be considered compressible (also liquids!!!),

c) in between it depends on the type of flow and the attached geometry whether compressibility effects are too strong to be neglected.

Answer 2

it's your anwer

the answer is yes, you can compress water, or almost any material. however, it requires a great deal of pressure to accomplish little compression. for that reason, liquid and solid are sometimes referred to as being incompressible

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