AS

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.