Introduction to Fluid Mechanics

Introduction to Fluid Mechanics

• Fluid mechanics is a branch of physics studying fluid (liquid and gas) behavior and forces acting on them.
• Applications range from blood flow to airplane flight.
• Based on physics and mathematics principles.
• Used in engineering for designing pipelines, aircraft, and ships.

Properties of Fluids

• Density (ρ): Mass per unit volume; higher density means more mass in a given space.
• Specific Weight (γ): Weight per unit volume; related to density by γ = ρg, where g is gravity.
• Viscosity (μ): Fluid's resistance to flow; higher viscosity indicates greater resistance. Also called dynamic viscosity.
• Kinematic Viscosity: Viscosity divided by density; measure of resistance to flow related to density.
• Surface Tension: Liquid surface minimizing its area due to intermolecular forces.
• Compressibility: Fluid's density change due to pressure changes; gases are compressible, liquids nearly incompressible.

Fluid Statics

• Fluid statics studies fluids at rest.
• Pressure: Force per unit area exerted by a fluid; increases with depth in a static fluid.
• Pascal's Law: Pressure applied to a confined fluid is equally transmitted in all directions.
• Pressure Distribution: Pressure at any point in a confined static fluid is the same in all directions.

Fluid Dynamics

• Fluid dynamics investigates fluids in motion.
• Streamlines: Curves tracing fluid particle paths, tangent to velocity vectors.
• Steady Flow: Fluid velocity at a point remains constant over time.
• Unsteady Flow: Fluid velocity at a point changes over time.
• Laminar Flow: Smooth, layered flow with parallel streamlines.
• Turbulent Flow: Irregular, chaotic flow with eddies and swirls.
• Reynolds Number (Re): Dimensionless number indicating laminar or turbulent flow; ratio of inertial to viscous forces (Re = ρVD/μ).
• Continuity Equation: Conserves mass in fluid flow; in incompressible flow: A₁V₁ = A₂V₂
• Bernoulli's Equation: Relates pressure, velocity, and elevation in steady, incompressible, inviscid flow; reflects energy conservation (P₁ + ½ρV₁² + ρgh₁ = P₂ + ½ρV₂² + ρgh₂).

Applications of Fluid Mechanics

• Hydraulic Systems: Use pressurized liquids to transmit and multiply forces.
• Hydropower: Harness energy from flowing water.
• Aerodynamics: Designs effective and efficient aircraft.
• Ship Design: Creates stable and efficient ships.
• Piping Systems: Designs pipelines for fluid transport, minimizing pressure loss and considering flow rate.
• Meteorology: Studies air mass movement.
• Medicine: Understands blood flow and designs cardiovascular devices.

Key Concepts & Equations

• Density (ρ): Mass per unit volume
• Pressure (P): Force per unit area
• Viscosity (μ): Fluid's resistance to flow
• Continuity Equation: Conservation of mass in flowing fluid
• Bernoulli's Equation: Conservation of energy in flowing fluid
• Reynolds Number (Re): Describes the nature of fluid flow.