2. Properties of fluids

What is a Fluid?

A fluid is a substance that deforms continuously under shear stress, no matter how small the stress is.
Examples: Water, air, oil, sewage, cement slurry

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1. Density (ρ)

Definition:
Density is the mass per unit volume of a fluid.

Formula:

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

Unit: kg/m³

Physical Meaning:
It tells how heavy a fluid is for a given volume.

Examples:

• Water ≈ 1000 kg/m³

• Air ≈ 1.2 kg/m³

Civil Engineering Applications:

• Calculating pressure in water tanks

• Design of dams and reservoirs

• Flow analysis in pipes and canals

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2. Specific Weight (γ)

Definition:
Specific weight is the weight per unit volume of a fluid.

Formula:

$$\gamma = \rho g$$

Unit: N/m³

Physical Meaning:
It represents the force exerted by gravity on the fluid.

Civil Engineering Applications:

• Determining hydrostatic forces on dams

• Calculating pressure at depth

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3. Specific Gravity (SG)

Definition:
Specific gravity is the ratio of density of a fluid to the density of water at 4°C.

Formula:

$$SG = \frac{\rho_{fluid}}{\rho_{water}}$$

Unit: Dimensionless (no unit)

Physical Meaning:
It compares how heavy a fluid is relative to water.

Examples:

• Oil < 1 (floats on water)

• Mercury = 13.6

Civil Engineering Applications:

• Identifying unknown fluids

• Design of hydraulic systems

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4. Viscosity (μ)

Definition:
Viscosity is the resistance of a fluid to flow due to internal friction.

Newton’s Law of Viscosity:

$$\tau = \mu \frac{du}{dy}$$

Unit: N·s/m² or Pa·s

Physical Meaning:
Higher viscosity → thicker fluid → more resistance to flow.

Examples:

• Water → low viscosity

• Honey → high viscosity

Civil Engineering Applications:

• Design of pipelines

• Flow of bitumen, sludge, and sewage

• Hydraulic machinery

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5. Kinematic Viscosity (ν)

Definition:
Ratio of dynamic viscosity to density.

Formula:

$$\nu = \frac{\mu}{\rho}$$

Unit: m²/s

Physical Meaning:
Represents resistance to flow considering fluid density.

Civil Engineering Applications:

• Used in Reynolds number

• Flow classification (laminar or turbulent)

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6. Compressibility

Definition:
Ability of a fluid to change its volume under pressure.

Formula:

$$\text{Compressibility} = -\frac{1}{V}\frac{dV}{dp}$$

Physical Meaning:
Liquids are slightly compressible, gases are highly compressible.

Civil Engineering Applications:

• Water hammer analysis

• Hydraulic system design

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7. Surface Tension (σ)

Definition:
Surface tension is the force per unit length acting along the surface of a liquid.

Unit: N/m

Physical Meaning:
It causes the liquid surface to behave like a stretched membrane.

Civil Engineering Applications:

• Capillary rise in soils

• Flow in small pipes and pores

• Concrete and soil mechanics

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8. Capillarity

Definition:
Rise or fall of liquid in a narrow tube due to surface tension and adhesion.

Capillary Rise Formula:

$$h = \frac{4\sigma \cos\theta}{\gamma d}$$

Civil Engineering Applications:

• Moisture movement in soils

• Foundation engineering

• Brick masonry dampness

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9. Vapor Pressure

Definition:
Pressure at which a liquid starts to vaporize at a given temperature.

Physical Meaning:
If pressure falls below vapor pressure → cavitation occurs.

Civil Engineering Applications:

• Pump and turbine design

• Prevention of cavitation damage

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10. Bulk Modulus (K)

Definition:
Resistance of a fluid to compression.

Formula:

$$K = \frac{dp}{dV/V}$$

Civil Engineering Applications:

• Water hammer analysis

• Hydraulic system safety

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📌 Summary Table

Property	Symbol	Unit
Density	ρ	kg/m³
Specific Weight	γ	N/m³
Specific Gravity	SG	—
Dynamic Viscosity	μ	Pa·s
Kinematic Viscosity	ν	m²/s
Surface Tension	σ	N/m
Bulk Modulus	K	N/m²