Question

Define incompressible flow and incompressible fluid. Must the flow of a compressible fluid necessarily be treated as compressible?

Short answer

Answer: An incompressible flow is a fluid flow in which the density of the fluid remains constant throughout, meaning that any volume of the fluid will maintain its mass and fluctuations in pressure or temperature will not cause significant changes in its density. An incompressible fluid is a fluid whose density does not change significantly under pressure or temperature variations. The flow of a compressible fluid cannot always be treated as compressible. In some cases, when the changes in density resulting from pressure and temperature variations are negligible, the flow can be treated as incompressible. This simplification is valid if the Mach number (ratio of the flow velocity to the speed of sound) is low, which is typically considered to be less than 0.3. When the Mach number is greater than 0.3, the density changes cannot be ignored, and the flow must be treated as compressible.

Step-by-step solution

Define incompressible flow

An incompressible flow is a type of fluid flow in which the density of the fluid remains constant throughout. This means that any volume of this fluid will maintain its mass and the fluctuations in pressure or temperature will not cause any significant changes in its density.

Define incompressible fluid

An incompressible fluid refers to a fluid whose density does not change significantly with the application of pressure or temperature variations. It's important to note that no real fluid is truly incompressible, but some fluids can be considered as incompressible over a certain range of conditions, where the changes in density are negligible. Common examples include water and air at low speeds and low pressure variations.

Address the compressible fluid flow treatment

In some cases, the flow of a compressible fluid can be treated as incompressible when the changes in density resulting from pressure and temperature variations are negligible. This simplification is valid if the Mach number (ratio of the flow velocity to the speed of sound) is low, which is typically considered to be less than 0.3. When the Mach number is greater than 0.3, the density changes cannot be ignored, and the flow must be treated as compressible.