Last reviewed 16 Sept 2026 · 5 min read
What a fluid is
A fluid is a substance that deforms continuously under the action of a shear stress, however small. Liquids and gases are fluids. A solid resists shear by a finite deformation; a fluid at rest cannot sustain any shear stress.
- Liquids have a definite volume and a free surface; nearly incompressible.
- Gases fill their container; highly compressible.
Continuum assumption: fluid properties are treated as continuous functions of position, ignoring molecular structure — valid when the dimensions of interest are much larger than the mean free path of molecules.
Mass and weight properties
| Property | Definition | Water at 4 °C (standard) |
|---|---|---|
| Mass density | Mass per unit volume (kg/m³) | 1000 kg/m³ |
| Specific weight or | Weight per unit volume (N/m³) | 9810 N/m³ |
| Specific volume | Volume per unit mass (m³/kg) | 0.001 m³/kg |
| Specific gravity (relative density) | (liquids) | 1.0 (mercury 13.6) |
Viscosity
Viscosity is the property by which a fluid resists relative motion (shear) between adjacent layers.
= shear stress; = velocity gradient (rate of shear strain); = dynamic (absolute) viscosity.
Kinematic viscosity:
| Quantity | SI unit | CGS unit |
|---|---|---|
| Dynamic viscosity | N·s/m² = Pa·s | poise (1 poise = 0.1 N·s/m²; 1 centipoise = 0.001 N·s/m²) |
| Kinematic viscosity | m²/s | stoke (1 stoke = 1 cm²/s = m²/s) |
Water at 20 °C: ≈ 1.0 × 10⁻³ N·s/m² (1 centipoise), ≈ 1.0 × 10⁻⁶ m²/s.
Effect of temperature
- Liquids: viscosity decreases with temperature (cohesive forces between molecules weaken).
- Gases: viscosity increases with temperature (molecular momentum exchange increases).
Newtonian and non-Newtonian fluids
| Fluid | Shear stress–rate relation | Examples |
|---|---|---|
| Newtonian | Linear through the origin (constant ) | Water, air, most oils |
| Non-Newtonian — shear thinning (pseudoplastic) | Apparent viscosity decreases with shear rate | Paints, blood, polymer solutions |
| Shear thickening (dilatant) | Apparent viscosity increases | Starch–water, some suspensions |
| Bingham plastic | Needs a yield stress before flowing, then linear | Toothpaste, sewage sludge, drilling mud |
| Thixotropic / rheopectic | Viscosity changes with time of shearing | Some gels, printer ink |
| Ideal fluid | No viscosity, incompressible (theoretical) | — |
Compressibility and bulk modulus
Water: ≈ 2.1–2.2 × 10⁹ N/m² — liquids are treated as incompressible except in problems such as water hammer. Gases: for isothermal compression ; for adiabatic compression ( = ratio of specific heats).
Surface tension
At the free surface of a liquid, molecules are pulled inward, so the surface behaves like a stretched membrane. Surface tension is the tensile force per unit length of a line on the surface (N/m). Water–air at 20 °C: about 0.073 N/m; mercury about 0.48 N/m.
- Liquid droplet (diameter ):
- Soap bubble (two surfaces):
- Liquid jet (cylinder):
Capillarity
Rise or fall of a liquid in a small tube due to adhesion and cohesion:
- Water in glass (): adhesion > cohesion → liquid rises, concave meniscus.
- Mercury in glass (–140°): cohesion > adhesion → liquid is depressed, convex meniscus.
Capillary errors are significant in small piezometer tubes; tubes should be at least about 6 mm in diameter to limit error.
Vapour pressure and cavitation
- Vapour pressure — partial pressure of vapour in equilibrium with its liquid; rises with temperature (water ≈ 2.34 kPa at 20 °C; equals atmospheric pressure at 100 °C).
- When local absolute pressure falls to the vapour pressure, the liquid boils at that temperature, forming vapour bubbles. When these bubbles move into higher-pressure regions they collapse violently — cavitation — causing noise, vibration, loss of efficiency and pitting erosion of pump impellers, turbine runners, spillway surfaces and siphons.
Worked examples
A plate 0.025 mm from a fixed plate moves at 60 cm/s and needs a force of 2 N per m² to maintain the speed. Find the dynamic viscosity of the fluid between them.
Solution. s⁻¹ N·s/m²
An oil has = 0.05 poise and specific gravity 0.9. Find in stokes and m²/s.
Solution. N·s/m²; kg/m³. m²/s
Find the excess pressure inside a water droplet of 0.04 mm diameter ( = 0.0725 N/m).
Solution.
Find the capillary rise of water in a 3 mm glass tube ( = 0.0735 N/m, = 0).
Solution. m
Water's volume decreases by 0.15% when pressure rises from 70 N/cm² to 130 N/cm². Find .
Solution. N/cm² N/m²; .
Frequently tested points
- A fluid deforms continuously under any shear stress.
- ; ; 1 poise = 0.1 N·s/m²; 1 stoke = 10⁻⁴ m²/s.
- Liquid viscosity falls with temperature; gas viscosity rises.
- Bingham plastic needs a yield stress; ideal fluid has zero viscosity.
- Droplet ; bubble ; jet .
- Capillary rise ; mercury depressed.
- Cavitation when pressure drops to vapour pressure.
- Using for a liquid droplet (that is a soap bubble with two surfaces).
- Mixing poise with N·s/m² (factor of 10).
- Stating that gas viscosity decreases with temperature.
- Fluids cannot resist shear at rest; the continuum model describes them.
- Density, specific weight and specific gravity describe mass properties.
- Viscosity follows Newton's law for Newtonian fluids and varies oppositely with temperature for liquids and gases.
- Compressibility, surface tension, capillarity and vapour pressure explain water hammer, droplets, capillary rise and cavitation.