Applied Fluid Mechanics Overview

Introduction to Fluid Mechanics

• Fluid mechanics studies the behavior of fluids (liquids and gases) under various conditions.

Fluid Properties

• Density: Measure of mass per unit volume. Varies for gases with pressure and temperature.

• Viscosity: Resistance to flow; characterized by shear stress and shear rate.

• Reynolds Number (b): Determines flow regime (laminar, turbulent, etc.).

  • Re < 2000: Laminar flow

  • Re > 4000: Turbulent flow

Hydromechanics Principles

• Eulerian vs Lagrangian Description:

  • Eulerian: Fixed control volume; properties at fixed points.

  • Lagrangian: Path of moving fluid particles.

Equations of State

• For ideal gases: $pV = nRT$

• Uses include determining pressure and volume relations under varying conditions.

Viscosity Types

• Newtonian Fluids: Constant viscosity; shear stress proportional to the shear rate.

• Non-Newtonian Fluids: Viscosity changes with the shear rate (e.g., Bingham plastics).

Buoyancy

• Archimedes' Principle: The buoyant force on an immersed object equals the weight of the fluid displaced.

Hydrostatics

• Hydrostatic pressure given by $p = p_0 + <br>ho g h$

• Fluid pressure acts perpendicular to surface.

Boundary-Layer Theory

• Boundary layers: Thin regions adjacent to surfaces where viscous effects dominate, causing velocity gradients.

• Flow characteristics differ outside boundary layer; influenced by pressure gradients.

Conservation Laws

• Mass conservation (continuity), momentum, and energy conservation integral in fluid mechanics.

• Bernoulli's Equation: Describes energy conservation for incompressible, non-viscous flow.

Flow Visualization Techniques

• Pathlines, streamlines, and streaklines describe different aspects of fluid motion.