A fluid is a substance that can flow and take the shape of its container. It includes liquids, gases, and plasmas. Fluids keep flowing as long as a force is applied to them, unlike solids, which keep their shape. Fluids can resist flow a little because of viscosity (internal friction), but they don’t have a fixed shape on their own. Instead, they constantly change shape when a force acts on them.

In simple terms, a fluid is anything that flows when a force is applied.

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Fluid Mechanics

Fluid mechanics is the branch of science that deals with the behaviour of fluids at rest as well as in motion. This field encompasses the static, kinematic, and dynamic aspects of fluids:

• Fluid statics: The study of fluids at rest.
• Fluid kinematics: The study of fluids in motion without considering the forces causing the motion.
• Fluid dynamics: The study of fluids in motion, taking into account the pressure forces and other forces acting on the fluid.

Properties of Fluids

1. Density or Mass Density

The density or mass density of a fluid is defined as the ratio of the mass of the fluid to its volume. Thus, the mass per unit volume of a fluid is called density. It is denoted by the symbol ρ (rho).

$\rho =\frac{\mathrm{Mass}of\mathrm{Fluid}}{\mathrm{Volume}of\mathrm{Fluid}}$

SI Unit of Mass Density: kg/m³

The value of density of water is 1 g/cm³ or 1000 kg/m³.

2. Specific Weight or Weight Density

The specific weight or weight density of a fluid is the ratio of the weight of the fluid to its volume. Thus, the weight per unit volume of a fluid is called weight density. It is denoted by the symbol w.

$w=\frac{\mathrm{Weight}of\mathrm{Fluid}}{\mathrm{Volume}of\mathrm{Fluid}}$

$w=\frac{\mathrm{(Mass\; of\; Fluid)}\times \mathrm{Acceleration\; due\; to\; Gravity}}{\mathrm{Volume}of\mathrm{Fluid}}$

$w=\frac{\mathrm{Mass}of\mathrm{Fluid}\times g}{\mathrm{Volume}of\mathrm{Fluid}}$
$w=\rho \times g$

The specific weight (or weight density) of water is given as:

w = 9.81 × 1000 N/m³ in SI units.

3. Specific Volume

The specific volume of a fluid is defined as the volume occupied by a unit mass of the fluid. In other words, the volume per unit mass of a fluid is called specific volume.

$\frac{1}{\frac{\mathrm{Mass}of\mathrm{Fluid}}{\mathrm{Volume}of\mathrm{Fluid}}}=\frac{1}{\rho }$

Thus, specific volume is the reciprocal of mass density. It is expressed as m³/kg. It is commonly applied to gases.

Specific Gravity

Specific gravity is defined as the ratio of the weight density (or density) of a fluid to the weight density (or density) of a standard fluid.
For liquids, the standard fluid is taken as water, and for gases, the standard fluid is taken as air.
Specific gravity is also called relative density. It is a dimensionless quantity and is denoted by the symbol S.

Mathematical Representation

For liquids:

$S=\frac{\mathrm{Weight}density(\mathrm{or}density)of\mathrm{liquid}}{\mathrm{Weight}density(\mathrm{or}density)of\mathrm{water}}$

For gases:

$S=\frac{\mathrm{Weight}density(\mathrm{or}density)of\mathrm{gas}}{\mathrm{Weight}density(\mathrm{or}density)of\mathrm{air}}$

Calculations

Thus, the weight density of a liquid can be calculated as:

$\mathrm{Weight}densityof\mathrm{liquid}=S\times \mathrm{Weight}densityof\mathrm{water}=S\times 1000\times 9.81 N/m{3}^3$

The density of a liquid is given by:

$\mathrm{Density}of\mathrm{liquid}=S\times \mathrm{Density}of\mathrm{water}=S\times 1000 \mathrm{kg}/m{3}^3$

Example

If the specific gravity of mercury is 13.6, then:

$\mathrm{Density}of\mathrm{mercury}=13.6\times 1000=13600\mathrm{kg}/m{3}^3$

Types of Fluids

Fluids can be categorized based on their viscosity and how they respond to shear stress. Below are the primary types:

1. Ideal Fluid
   • An ideal fluid is an imaginary fluid that is incompressible and has no viscosity or friction.
   • Such fluids do not exist in reality but are used as a conceptual model in fluid mechanics.
2. Real Fluid
   • A real fluid is any fluid that exhibits viscosity or friction.
   • All fluids in the real world are considered real fluids.
3. Newtonian Fluid
   • A Newtonian fluid is a real fluid where the shear stress is directly proportional to the rate of shear strain.
   • These fluids obey Newton’s law of viscosity, and their viscosity (μ) remains constant.
   • Example: Water, air, and most common liquids.
4. Non-Newtonian Fluid
   • A Non-Newtonian fluid is a real fluid where the shear stress is not proportional to the rate of shear strain.
   • In these fluids, the viscosity (μ) changes depending on the applied stress or strain rate.
   • Example: Honey, ketchup, and toothpaste.
5. Ideal Plastic Fluid
   • An ideal plastic fluid is one where the shear stress must exceed a certain yield value before it begins to flow. After this point, shear stress is proportional to the rate of shear strain.
6. Incompressible Fluid
   • A fluid is considered incompressible if its density does not change significantly under the application of external force or pressure.
   • Example: Liquids like water are often approximated as incompressible in practical calculations.
7. Compressible Fluid
   • A compressible fluid is one where the density changes significantly with variations in external pressure or force.
   • Example: Gases like air.