1.2 Classification of Fluid Flows

Fluid flows can be classified based on viscosity, compressibility, and flow regime. These factors determine how fluids behave under different conditions, affecting their motion and properties.

Understanding flow types is crucial for engineering applications. Laminar vs turbulent, steady vs unsteady, and internal vs external flows all have distinct characteristics that impact fluid behavior and system design.

Classification of Fluid Flows

Classification of fluid flows

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• Viscosity describes a fluid's internal resistance to flow
  • Viscous flows have significant internal resistance (honey, oil, syrup)
    • Viscous forces dominate over inertial forces
  • Inviscid flows have negligible internal resistance (water, air at low speeds)
    • Inertial forces dominate over viscous forces
• Compressibility relates to how fluid density changes with pressure
  • Compressible flows have fluid density that varies significantly with pressure changes (high-speed gas flows, supersonic flows)
    • Mach number (ratio of flow speed to speed of sound) > 0.3
  • Incompressible flows have fluid density that remains nearly constant with pressure changes (liquids, low-speed gas flows)
    • Mach number < 0.3
• Flow regime categorizes flows based on their behavior and characteristics
  • Laminar flows have fluid particles moving in smooth, parallel layers
  • Turbulent flows have fluid particles moving in a chaotic and irregular manner

Laminar vs turbulent flows

• Laminar flows exhibit smooth, parallel layers of fluid motion
  • No mixing occurs between layers
  • Low Reynolds number ($Re < 2300$ for pipe flows)
  • Velocity profile is parabolic in fully developed pipe flows (slow-moving fluids, small pipes, high-viscosity fluids)
• Turbulent flows display chaotic and irregular fluid motion
  • Mixing occurs between layers
  • High Reynolds number ($Re > 4000$ for pipe flows)
  • Velocity profile is flatter compared to laminar flows (fast-moving fluids, large pipes, low-viscosity fluids)

Steady vs unsteady flows

• Steady flows have flow properties that do not change with time at any point
  • Velocity, pressure, and density remain constant
  • Mathematically represented as $\frac{\partial}{\partial t} = 0$
  • Examples include fully developed pipe flows and constant flow rate from a tank
• Unsteady flows have flow properties that change with time at any point
  • Velocity, pressure, and density vary over time
  • Mathematically represented as $\frac{\partial}{\partial t} \neq 0$
  • Examples include starting or stopping of a flow, pulsating flows, and waves

Internal and external flows

• Internal flows are confined by boundaries on all sides
  • Examples include pipe flows, duct flows, and flow through a nozzle
  • Applications involve piping systems, HVAC ducts, and hydraulic systems
• External flows occur over a surface or body, with at least one side not confined by a boundary
  • Examples include flow over an airfoil (wings), flow around a car (vehicle aerodynamics), and flow past a building (wind engineering)
  • Applications involve aerodynamics, wind engineering, and hydrodynamics