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Basics of Fluid Mechanics

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1. Properties of Fluids

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  • - Density (ρ): Mass per unit volume (ρ = m/V)
  • - Viscosity (μ): Resistance to flow (e.g., honey > water)
  • - Pressure (P): Force per unit area (P = F/A)
  • - Surface Tension: Minimizes fluid surface area
  • - Specific Gravity (SG): Density ratio to water (SG = ρ_fluid / ρ_water)
  • - Compressibility: Ability to be compressed (liquids ≈ incompressible, gases = compressible)

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2. Fluid Statics (Fluids at Rest)

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  • - Hydrostatic Pressure: P = P₀ + ρgh
  • - Pascal’s Law: Pressure is transmitted equally in all directions
  • - Archimedes’ Principle: Buoyant force = Weight of displaced fluid (Fb = ρgV)

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3. Fluid Dynamics (Fluids in Motion)

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  • - Continuity Equation: A₁v₁ = A₂v₂ (mass conservation)
  • - Bernoulli’s Equation: P + ½ρv² + ρgh = constant (energy conservation)
  • - Reynolds Number (Re): Determines flow type
  • - Re < 2000: Laminar flow (smooth)
  • - Re > 4000: Turbulent flow (chaotic)

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4. Applications of Fluid Mechanics

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  • - Pumps and Turbines: Moving and utilizing fluids
  • - Hydraulics: Using fluid pressure for mechanical advantage
  • - Aerodynamics: Studying airflow around objects
  • - Biomedical: Analyzing blood flow in the human body

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5. Metacentre in Fluid Mechanics

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  • - Metacentre: The point where the buoyant force acts when a floating body is tilted.
  • - Important in ship stability analysis.
  • - Metacentric Height (GM):
  • - GM = Distance between Centre of Gravity (G) and Metacentre (M).
  • - GM > 0: Stable equilibrium (returns to original position).
  • - GM < 0: Unstable equilibrium (capsizes).

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6. Types of Fluid Flows

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  • - Laminar Flow:
  • - Smooth, orderly motion with parallel layers.
  • - Occurs at low Reynolds number (Re < 2000).
  • - Turbulent Flow:
  • - Irregular, chaotic motion with mixing of layers.
  • - Occurs at high Reynolds number (Re > 4000).

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  • - Steady Flow:
  • - Fluid properties (velocity, pressure) remain constant over time.

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  • - Unsteady Flow:
  • - Fluid properties change with time (e.g., pulsating flow).

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  • - Compressible vs Incompressible Flow:
  • - Compressible: Density changes (e.g., gases).
  • - Incompressible: Constant density (e.g., liquids).

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