Notes on Fluid Mechanics

Fluid Mechanics

Definition of Mechanics
  • Mechanics: The oldest physical science dealing with stationary and moving bodies under forces.
    • Statics: Branch dealing with bodies at rest.
    • Dynamics: Branch dealing with bodies in motion.
  • Fluid Mechanics: Science of fluid behavior at rest (fluid statics) and in motion (fluid dynamics), including fluid interactions with solids/other fluids.
Fluid Statics and Dynamics
  • Fluid Statics: Study of fluids at rest.
  • Fluid Kinematics: Study of fluids in motion excluding pressure forces.
  • Fluid Dynamics: Study of fluids in motion including pressure forces.
    • Hydrodynamics: Motion of incompressible fluids (liquids); hydraulic systems focus on liquid flows in pipes/open channels.
    • Gas Dynamics: Flow of fluids with significant density changes (e.g., high-speed gas flow).
    • Aerodynamics: Gas flow over objects (aircraft, rockets).
Understanding Fluids
  • Fluids can be liquids or gases, distinct from solids based on shear stress resistance.
    • Solid: Resists shear stress; deforms to a fixed angle.
    • Fluid: Deforms continuously under shear stress, with stress proportional to strain rate.
Characteristics of Liquids and Gases

  • Liquids:

    • Incompressible, fixed volume, takes the shape of its container, forms a free surface.
    • Molecules can move relative to each other, maintaining volume due to cohesive forces.

  • Gases:

    • Easily compressible, expands to fill the container, cannot form a free surface due to low cohesive forces.
Comparative Properties
  • Liquids vs. Gases:
    • Liquids: Hard to compress, fixed volume, forms free surface.
    • Gases: Easy to compress, no fixed volume, fills entire container.
Applications of Fluid Mechanics
  • Engineering/Science Applications:
    • Biomechanics: Blood flow, airflow in lungs, cerebral fluid movement.
    • Household Systems: Piping for water, gas, sewage; appliances like refrigerators, air conditioning.
    • Meteorology/Ocean Engineering: Air and water currents.
    • Mechanical Engineering: Pump design, aircraft analysis, engine cooling systems.
    • Civil Engineering: Sediment transport, flood control systems, pollution management.
    • Chemical Engineering: Design of processing equipment.
    • Military Applications: Missiles, vehicles, dispersion of agents.
    • Medical Use: Heart devices, drug delivery systems.
    • Energy Sector: Turbines, gas management, hydro and wind energy.
Classification of Fluid Flows

  • Viscous vs. Inviscid:

    • Viscous Flow: Friction effects significant (internal resistance due to viscosity).
    • Inviscid Flow: Negligible viscous effects, relevant in specific regions away from surfaces.

  • Internal vs. External Flow:

    • Internal Flow: Fluid flow confined within channels (e.g., pipes).
    • External Flow: Unbounded fluid over surfaces (e.g., airflow around objects).

  • Compressible vs. Incompressible Flow:

    • Incompressible Flow: Density remains nearly constant (typical for liquids).
    • Compressible Flow: Density varies significantly (typical for gases).
    • Example: Water changes density only minimally under high pressure; gases change significantly under small pressure variations.

  • Laminar vs. Turbulent Flow:

    • Laminar Flow: Smooth, orderly layers, typical for high-viscosity fluids at low velocities.
    • Turbulent Flow: Chaotic and disordered, typical for low-viscosity fluids at high velocities.

  • Natural vs. Forced Flow:

    • Natural Flow: Fluid motion due to buoyancy.
    • Forced Flow: Motion initiated by external means (pumps, fans).

  • Steady vs. Unsteady Flow:

    • Steady Flow: No change at a point over time.
    • Unsteady Flow: Changes over time.
Properties of Fluids
  • General Properties: Include pressure (P), temperature (T), volume (V), mass (m), viscosity, etc.
    • Intensive Properties: Independent of mass (e.g., temperature, pressure, density).
    • Extensive Properties: Depend on system size (e.g., total mass, total momentum).
Density
  • Defined as mass per unit volume (
    ho = rac{m}{V} ) with SI units of kg/m³.
  • Density of liquids is approximately constant; gases vary with pressure and temperature.
Specific Weight
  • Ratio of weight to volume (w=WVw = \frac{W}{V}).
Specific Volume
  • Volume per unit mass (v=Vmv = \frac{V}{m}), reciprocal of density.
Specific Gravity
  • Ratio of fluid density to standard fluid density, dimensionless (S=extDensityoffluidextDensityofstandardfluidS = \frac{ ext{Density of fluid}}{ ext{Density of standard fluid}}).
Example Problems

  1. Hydraulic Calculations:

    • Calculate specific weight, density, specific gravity given weight and volume.
    • Example 1: One liter fluid weighing 7 N:
      • Specific weight: w=7N0.001m3=7000N/m2w = \frac{7N}{0.001m^3} = 7000 N/m²
      • Density:
        ho = rac{7000N/m²}{9.81m/s²} = 713.5 kg/m³
      • Specific gravity: S=713.5kg/m31000kg/m3=0.7135S = \frac{713.5 kg/m³}{1000 kg/m³} = 0.7135

  2. Gas Calculations:

    • Given specific gravity of petrol as 0.7, calculate density, specific weight, and weight for 1 liter.
Activity
  • Calculate specific weight, density, and specific gravity for a fluid weighing 8N.
  • Find specific gravity of gasoline given its density (721 kg/m³).
  • Compare densities of two fluids based on prior calculations.