Understanding Drag Force and Flow Separation in Fluid Mechanics
Assumptions in Parallel Plate Flow
- No local acceleration and no hydrostatic effects
- Pressure is constant along the plate
Definition of Drag Force
Resistance force caused by movement of a body through a fluid. Two types: Pressure Drag and Viscous Drag.
Pressure Drag
Rises from pressure difference between front and rear of object moving through fluid. Shape of object influences pressure drag.
Viscous Drag
Caused by friction between fluid and object surface. Depends on surface area, roughness, and fluid velocity.
Which Force is Stronger?
- At low Reynolds numbers, viscous drag is stronger
- At higher Reynolds numbers, pressure drag tends to become stronger
Lift Force
Sum of forces that raise object and act perpendicular to fluid direction.
What is a Wake?
Area after object where flow is not streamline, separating.
Flow Separation
Occurs when flow encounters object, modifies path, and vortices appear due to low pressure areas.
Approaches in Fluid Mechanics
Inviscid Approach
Assumes zero viscosity, no frictional dissipation of energy.
Viscous Approach
Considers fluid viscosity, introduces shear stresses and no-slip condition at boundaries.
Objective of Streamlining
Change object geometry to minimize drag force by delaying separation point.
Drag Crisis
Transition from laminar to turbulent regime affects drag coefficient.
Von Kármán Vortex
Repeating pattern of swirling vortices caused by flow separation.
Flow through Packed Beds
High resistance, pressure loss. Analogy with parallel channels.
Boundary Layer Evolution
Reynolds number as function of distance on flat plate.
Reducing Friction Coefficient
Strategies to reduce friction of rounded objects.
Flow Around Cylinders
Symmetric eddies, oscillating forces, and pressure differences.
Parallel Plate Flow Areas
Laminar, Transition, Turbulent flow.
Golf Balls vs. Cars
Aerodynamic differences and design considerations.
Navier-Stokes Equations
Numerical solutions for turbulent and laminar regimes.
Hagen-Poiseuille Flow
Exact solution for laminar flow in circular pipe.