Fundamentals (Fluids)

Fluid properties: density, compressibility, static pressure, and surface tension.

General idea of the topic

A fluid is a substance that deforms continuously under a shear stress, however small. That property distinguishes liquids and gases from solids and forces them to be described with local quantities: density, pressure, compressibility and, at the surface of a liquid, surface tension.

The topic defines each of those properties, their units and orders of magnitude, and establishes when a fluid can be treated as incompressible, an assumption that simplifies almost everything that follows.

What the student is expected to understand

By the end, the student should be able to compute the density of a substance and the pressure produced by a force on a surface, estimate how much a fluid compresses under pressure and explain surface tension phenomena such as the shape of drops.

The student should also know why a liquid is considered incompressible and a gas is not.

Recommended learning route

1. Concept of a Fluid: what distinguishes a fluid from a solid and what is meant by a continuum.
2. Density: mass per unit volume and its dependence on temperature and pressure.
3. Pressure: normal force per unit area, its units and its scalar character at a point.
4. Compressibility: bulk modulus and the conditions for incompressibility.
5. Surface Tension: force per unit length at the surface of a liquid and capillarity.

Physical criterion to acquire

The essential criterion is to distinguish pressure from force: pressure acts at a point and in all directions, while the force on a wall is obtained by multiplying by the area. For a liquid, the density is practically constant; for a gas, it depends on pressure and temperature.

Connection with real problems

• laboratory density measurement.
• tires, balloons and pressure vessels.
• insects walking on water.
• capillary tubes and plants.

Final goal of the topic

The final goal is to master the basic quantities of fluids and know when they can be simplified in a model.