The main difference between a compressible and an incompressible fluid lies in their response to changes in pressure and density.
1. Incompressible Fluid:
An incompressible fluid is one in which the density remains nearly constant regardless of changes in pressure. In practical terms, the density change in an incompressible fluid under normal operating conditions is negligible. Liquids, such as water and oil, are often treated as incompressible fluids for most engineering applications. Incompressible fluids are characterized by their relatively low compressibility and are assumed to have a constant density in most analyses.
Mathematically, the incompressible fluid assumption is expressed as:
∂ρ/∂p ≈ 0
2. Compressible Fluid:
A compressible fluid is one in which changes in pressure significantly affect its density. Compressible fluids, such as gases (e.g., air and steam), exhibit a considerable change in density when subjected to changes in pressure and temperature. These fluids can be compressed or expanded, resulting in variations in their density, volume, and other thermodynamic properties. The compressibility of a fluid is a measure of its ability to change in density in response to pressure changes.
Mathematically, the compressibility of a fluid is represented by the coefficient of compressibility (β) and is defined as:
β = -1/ρ (∂ρ/∂p) [where ρ is the density of the fluid]
In compressible fluid flow, changes in pressure and density become significant factors, requiring the inclusion of compressibility effects in the analysis. Compressible fluid flows are encountered in applications such as aerodynamics, gas dynamics, combustion processes, and high-speed flow phenomena.
It is important to note that while all gases are compressible fluids, the compressibility of liquids is typically considered negligible for most engineering applications, and they are treated as incompressible fluids. However, there are cases where the compressibility of liquids, such as in high-pressure hydraulic systems or certain chemical processes, needs to be accounted for in the analysis.
In summary, the distinction between compressible and incompressible fluids lies in the response of density to changes in pressure. Incompressible fluids exhibit negligible density changes with variations in pressure, while compressible fluids undergo significant density changes under the influence of pressure fluctuations.