Properties of a fluid

In this section we are going to define the most important characteristics of a fluid from the viewpoint of fluid mechanics.

Density (ρ)

The density of a homogeneous fluid is a scalar quantity defined as the mass of a unit volume of the fluid:

If the fluid is not homogeneous, then its density varies from point to point, and therefore it has to be defined at each point:

Generally speaking, the density of a substance is a function of pressure. However, the density of a liquid may be considered constant unless it is subjected to very high pressure changes.

In these pages we will deal with homogeneous fluids.

Units: The SI unit of density is kg/m3.

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Pressure is a scalar quantity defined as the magnitude of the force applied perpendicular to the surface of an object per unit area over which that force is distributed:

When dealing with fluids at rest, the force must be applied perpendicular to the force because, if the force had tangent projection, the fluid would flow (see figure below).

Units: The SI unit of density is Pascal (Pa). 1Pa = 1 N/m2.


Viscosity is the quantity that describes the fluid’s resistance to deformation (or flow). It is analogous to the friction acting on a body when it slides on a surface.

Viscosity corresponds to the informal perception of “thickness” as opposed to “thinness”. It is often mistaken for density, but both are different properties of a fluid. Oil for instance is more viscous than water, but its density is smaller. That’s why it floats on water.

In these pages we will deal with non-viscous or perfect fluids.

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