Fluid Dynamics: Understanding Drag Force

Introduction

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• Focus: Drag force in fluid mechanics. Lift will be covered separately.

Components of Force on Object in Fluid

• Drag: Force in the same direction as fluid flow.
  • Aerodynamic forces: For gases (ex: air).
  • Hydrodynamic forces: For liquids (ex: water).
• Lift: Force perpendicular to fluid flow.

Importance of Drag Forces

• Usually undesirable, affecting fuel consumption and performance of vehicles.
• Engineers try to minimize drag to save costs and improve efficiency.

Sources of Drag Forces

• Wall Shear Stresses: Tangential stresses caused by fluid viscosity (frictional forces).
• Pressure Stresses: Perpendicular stresses caused by pressure distribution around the object.
• Components of Drag:
  • Friction Drag: Caused by shear stresses.
  • Pressure Drag/Form Drag: Caused by pressure stresses.

Pressure Drag and Flow Separation

• Significant for blunt bodies (ex: sphere).
• Flow Separation: Boundary layer detaches, creating a wake (low-pressure area) behind the body, increasing drag.
  • Factors Influencing Flow Separation:
    • Favorable pressure gradient (decreasing pressure initially).
    • Adverse pressure gradient (increasing pressure leading to flow reversal and separation).
  • Example: For a smooth sphere in laminar flow, separation at 80°; in turbulent flow, at 120°.
  • Applications: Golf ball dimples create turbulence to delay flow separation and reduce drag.

Techniques to Reduce Drag

• Streamlined Design: Teardrop shapes for minimizing flow separation (ex: airplane wings).
• Turbulence Generators: Used to delay separation (ex: vortex generators on airplane wings).
• Friction Drag Considerations: Increase with fluid viscosity and significant for large surface area bodies.
• Hybrid Laminar Flow Control: Suction to pull air, delaying turbulence (ex: on aircraft wings).
• Artificial Shark Skin: Mimics shark scales to reduce friction drag via microscopic ridges.

Balancing Drag Forces

• Geometry Impact: Orientation impacts pressure and friction drag.
  • Example: Flat plate at 90° has high pressure drag but low friction drag, rotated 90° trades off.
• Angle of Attack: Large influence on drag for airfoils.

Drag Equation

• Used to represent total drag force.
  • Terms:
    • Drag Coefficient (C-D): Captures geometry and flow effects, determined experimentally or via simulations.
    • Fluid density (Rho), Velocity (V), Reference area (A).
• Drag Coefficient Variations:
  • Flat plate: Almost constant with Reynolds number.
  • Blunt bodies: Decreases significantly with transition to turbulent flow.
  • Streamlined bodies: Gradual decrease with Reynolds number, increase after turbulence onset.
• Stokes’ Law: Specific case for low Reynolds numbers (Re < 1).
  • Derives terminal velocity for spheres, useful in viscometers for fluid viscosity measurement.

Named Drag Components in Aviation

• Induced Drag: Due to lift creation.
• Wave Drag: Due to shock waves in high-speed flight.
• Interference Drag: Due to intersections of different parts of an aircraft.

Additional Content

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