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Because there are smaller spaces between their molecules, liquids and solids are considered incompressible under practical conditions. (This is one reason that hydraulic systems can work.) Gases that are very highly compressed may change phase to liquid or solid when compressed.

Air Flow and Compressibility

It depends on the Mach number and the changes in density occurring for that physical process. Eg. Airflow from a fan in a room is considered incompressible flow although air is a gas; even airflow over gliders and low speed aircraft is reasonably incompressible. However, flow over high speed aircraft (above Mach 0.3) can be safely assumed to be compressible, as density changes of gas cannot be neglected.

The same applies to liquids and solids. However since the speed of sound in solids and liquids is very high, it is difficult to acheive mach 0.3 without causing a very large pressure difference. Hence these flows are assumed to be incompressible flows.

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What is the only matter is rigid and incompressible?

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