A fluid is a material that continues to deform when a shear stress is applied. Liquids and gases both behave as fluids, although their density and compressibility can differ greatly.

Density

Mass density is

$$\rho=\frac{m}{V}.$$

It measures how much mass is contained in a given volume. Liquids often change density only modestly under ordinary pressure changes, whereas gases can be much more compressible.

Pressure in a fluid

A fluid can exert normal pressure on boundaries and on imagined internal surfaces. In a fluid at rest, pressure at a point has no preferred spatial direction: the same scalar pressure characterizes every surface orientation through that point.

This isotropy does not mean pressure is spatially uniform. Gravity, acceleration or flow can make pressure vary from place to place.

The continuum approximation

Fluids are made from molecules, but engineering fluid mechanics usually treats density, pressure and velocity as continuously varying fields.

This continuum model is appropriate when the length scales of interest are much larger than molecular scales. It lets us describe a fluid by quantities such as

$$\rho(\mathbf r,t),\qquad p(\mathbf r,t),\qquad \mathbf v(\mathbf r,t).$$

The continuum approximation is the bridge between microscopic matter and the field equations used in ordinary fluid mechanics.