310105f Fluid Principles 2025 TF

Objectives

• Describe the following concepts:

  • Atom

  • Molecule

  • Element

  • Molecular attraction

  • Cohesion and adhesion

  • Capillary action

  • Compressibility

  • Thermal expansion

  • Density

  • Relative density and specific volume

• Solve problems related to:

  • Mass, density, and relative density of liquids

  • Pascal’s Law and pressure head

  • Pressure, density, and height of a liquid column

  • Archimedes’ principle and buoyancy in submerged objects

  • Turbulent flow, laminar flow, and the continuity equation

  • Bernoulli’s equation, resistance to flow, and flow turbulence

Definitions

Matter

• Anything that has mass and occupies space.

Atom

• The smallest unit of matter, composing all substances.

Molecule

• Composed of 2 or more atoms, which can be the same or different.

Element

• A pure substance made of one type of atom, all with identical numbers of protons in their nuclei.

Molecular Attraction

• Cohesion: Attraction between molecules of the same substance.

• Adhesion: Attraction between different substances.

Capillary Action

• Determined by adhesive forces of water in a glass tube.

• The weight of the water limits the capillary action; thinner tubes display greater capillary action.

• Important in soldering, allowing solder to rise between copper tubing and fittings through adhesive forces.

Pressure & Fluids

Fluid Properties

• Fluids (liquids and gases) conform to the shape of their containers.

• Under pressure, gases are compressible while liquids and solids exhibit limited compressibility.

Density of Matter

• Density formula:

  • ρ = Mass (kg) / Volume (m³)

  • Measured in kg/m³.

• Specific volume formula:

  • Vg = Volume (m³) / Mass (kg)

• Relative Density (RD):

  • RD = ρ (liquid) / ρ (water)

  • Density of water peaks at 4°C, equals 999.97 kg/m³.

Buoyancy

Buoyant Force

• Force of a fluid pushing upwards on an object:

  • Fb = ρgV

  • where Fb = buoyant force, ρ = density of fluid, g = gravitational pull (9.81 N/kg), V = volume in m³.

• Archimedes’ Principle: The buoyant force on an object submerged in fluid equals the weight of the fluid displaced.

Height of Floating Bodies

• If the buoyant force exceeds the weight of the object, it will float. Related formulae involve height submerged and densities. On the example:

  • A 10" pine board floats with a submerged height (h') of 5.6".

Example Calculations

1. For an iceberg with a volume of 100,000 m³:

   • RD of seawater = 1.027

   • Buoyant force (Fb) = ρgV = 1.01 x 10^9 N or 1.01 GN.

Types of Flow

Fluid Flow Types

• Laminar Flow: Smooth and orderly flow parallel to pipe walls.

• Turbulent Flow: Highly irregular flow characterized by eddies and swirls.

• Transitional Flow: Between laminar and turbulent, determined by Reynolds number.

  • Reynolds < 2000 = Laminar

  • Reynolds 2000-4000 = Transitional

  • Reynolds > 4000 = Turbulent

Flow Rate and Velocity

• For a fluid flowing through pipes:

  • Qv = A * V where A is cross-sectional area (cm² or m²) and V is linear speed (m/s).

  • Continuity equation: A₁V₁ = A₂V₂.

Bernoulli’s Equation

• States that total energy within a pipe remains constant:

  • Total energy = Pressure energy + Kinetic energy + Gravitational potential energy.

  • E pressure1 + E kinetic1 + E potential1 = E pressure2 + E kinetic2 + E potential2.