When is a fluid incompressible?

Definition of compressibility

Next:Equations of the frictionless compressible Up:Compressible currents Previous:Second law of thermodynamics

All real fabrics are more or less compressible. When they are subjected to compressive stress, their density changes. This is particularly the case with gases, less so with liquids and hardly with solids. The amount by which a medium can be compressed at a given pressure is called Compressibility designated.

Let us consider a small volume element, Figure 6.1. Mathematically, compressibility is defined as the relative change in volume with a change in pressure dp .

Figure 6.1: Definition of compressibility

Eq. (6.52) is not precise enough. If we change the volume of the volume element, we also need to know what kind of process we are using to achieve this. If the temperature is kept constant, we speak of a isotherms Process and receive

and with the entropy fixed we get that isentropic Compressibility

The role of compressibility in determining the properties of a flow can be described as follows. If we in Eq. Inserting (6.52) gives that

I.e. when the pressure changes dp the fluid experiences a corresponding change in density . From the last equation it follows

For interpretation we consider the flow around a profile. If the fluid is a liquid, the compressibility is very small, then the density change as a result of a change in pressure dp very little from one point to another. This means that we can assume with sufficient accuracy that the density is constant and that the liquid is therefore incompressible. When a gas flows around it, the compressibility is on the other hand very large and already small dp cause not negligible changes in density, so that a gas flow i. general compressible is. Form an exception to this Low velocity currents. In this case the pressure change is dp small, so even with large only a very small change in density takes place.

We will see later that the Mach number, i.e. the ratio between flow velocity and speed of sound,

is particularly suitable to describe the importance of compressibility.

Next:Equations of the frictionless compressible Up:Compressible currents Previous:Second law of thermodynamicsroot
Sun Dec 15 23:00:07 CET 1996