Fluid

Definition

A fluid is any substance that can flow. More precisely, a fluid is a substance that deforms continually under the action of an external force. Fluid is a phase of matter that includes liquids, gases and plasmas. A fluid flows under the action of a force or a pressure gradient.

Solid versus fluid

• A solid can be subjected both to shear (tangential) stress and to normal stress. It opposes shear stress either by developing a restoring force, so that the deformation is reversible, or by requiring a certain initial stress before it deforms and begins to flow.
• The shear modulus of a fluid is zero. In simple words, a fluid cannot resist any shear force applied to it when in static equilibrium.
• An ideal fluid can be subjected only to normal, compressive stress, which is what we call pressure.
• Real fluids display viscosity and so are capable of being subjected to low levels of shear stress. Most fluids offer a very weak resistance to deformation.

Properties of fluids

• They do not oppose deformation — they get permanently deformed.
• They have the ability to flow.
• They have the ability to take the shape of the container.

A fluid shows these properties precisely because it cannot oppose a shear stress when in static equilibrium.

The ideal fluid

The behaviour of a real fluid in motion is complicated, so the syllabus works with an ideal fluid, which has four properties:

• It is incompressible: its density is constant.
• Its flow is irrotational: the flow is smooth, with no turbulence.
• It is non-viscous: there is no internal friction in the flow.
• Its flow is steady: its velocity at each point is constant in time.

Diagram to draw

A small flat surface of area $dA$ at rest deep inside a fluid, with two equal and opposite arrows labelled $dF$ pressing normally on its two faces. Because the surface does not accelerate, the surrounding fluid exerts equal normal forces on both sides of it. Two further sketches show a fluid pressing normally on a vertical wall and normally on a horizontal base.

2.2.1 Fluids at rest

The branch of physics that deals with the properties of fluids at rest is called hydrostatics.

Standard results

• A fluid is a substance that deforms continually under an external force; shear modulus of a fluid $= 0$.
• Ideal fluid: incompressible, irrotational, non-viscous, steady flow.