Essentials of Fluid Mechanics

Jan 21, 2025

Lecture Notes on Fluid Mechanics

Definition of a Fluid

  • A fluid is defined as a substance that deforms continuously when acted upon by a shearing stress.
  • Example: Applying force to a copper plate vs. applying force to a layer of water.
    • Copper plate deforms and stops; water continues to deform.
  • Types of fluids discussed: liquids (e.g., water, oil) and gases (e.g., air).

Differences Between Liquids and Gases

  • Liquids have stronger molecular attachments than gases.
  • Gases can spread out and do not maintain a definite shape like liquids do.

Viscosity and Shearing Stress

  • Viscosity (μ): A key property of fluids to determine shearing stress.
  • Shearing Stress (τ): Defined as force per unit area, related to viscosity and velocity gradient (du/dy).
  • Kinematic Viscosity (ν): Defined as μ/ρ.
  • Understanding these properties is critical for solving fluid mechanics problems.

Unit Systems

  • SI Units:
    • Force: Newtons
    • Mass: Kilograms
    • Length: Meters
  • British Gravitational Units:
    • Force: Pounds
    • Mass: Slugs
    • Length: Feet
  • Emphasis on being proficient in both SI and British units for problem-solving.

Key Properties of Fluids

  • Pressure: Defined as force per unit area.
  • Different types of pressure:
    • Absolute Pressure: Measured from zero pressure.
    • Gauge Pressure: Measured relative to atmospheric pressure.
  • Surface tension (σ): Defined as force per unit length, influencing fluid behavior in tubes and containers.

Important Fluid Properties

  • Density (ρ):
    • SI: kg/m³
    • British: slugs/ft³
  • Specific Weight (γ): Weight per volume, varies by unit system.
  • Specific Gravity: Dimensionless ratio comparing fluid density to water.

Solving Fluid Mechanics Problems

  1. Sketch the Problem: Helps in visualizing the scenario.
  2. Write Down Equations: Start with symbolic terms before plugging in numbers.
  3. Include Units: Ensure all units are accounted for and properly canceled out.

Practice and Preparation for Exams

  • Practice through homework and example problems.
  • Avoid copying solutions; work through the problems independently to strengthen understanding.
  • Utilize textbooks, class lectures, and office hours for additional support.

Next Steps

  • Assignments for the next two classes will be given.
  • Office hours for additional help available on Monday, Tuesday, and Wednesday.

Reminder: Drawing sketches and understanding the physical principles are crucial for success in fluid mechanics.