Gas Dynamics Lecture Notes

What is Gas Dynamics?

• Gas dynamics is the study of the flow of gases, particularly when they are compressible.
• Difference from Fluid Dynamics:
  • Fluid Dynamics: Density remains roughly constant.
  • Gas Dynamics: Density varies significantly (compressible flow).

Compressibility

• Definition: Measure of how much a gas's density changes with pressure and temperature changes.
• Factors Affecting Density:
  • Change in pressure
  • Change in temperature
• Notation: Specific volume (volume per unit mass) is used, denoted as v.
• Mathematical Expression:
  • Differential change in specific volume: d(v)/v = ...
  • Two terms:
    • Expansion (heat at constant pressure)
    • Isothermal compressibility (constant temperature)

Coefficient of Compressibility

• High coefficient implies high compressibility.
• Can also be expressed in terms of density.
• Reciprocal Relation: Per unit volume inversely related to density.

Mach Number

• Definition: Ratio of fluid flow velocity to the speed of sound at that location.
• Interpretation:
  • Mach number << 1: Incompressible flow
  • Mach number > 1: Compressible flow

Concepts of Wave and Compressibility

• Sound waves in solid vs gas: transfer due to molecule collisions.
• High density in solids means faster transmission of waves (higher speed of sound).
• Speed of sound in air at room temperature: ~340 m/s; in metal: 5000-6000 m/s.

Historical Context of Mach Number

• Named after Ernst Mach, who studied sound and shockwaves.

Course Objectives

• Start from basics and build to advanced graduate-level analysis.
• Emphasize physical intuition along with mathematical derivation.
• Main focus: Understanding and visualizing wave and flow phenomena.

Review of Basic Thermodynamics

Systems and Surroundings

• System: Part of the universe we are interested in.
• Surroundings: Everything else in the universe.
• Types of Systems:
  • Closed (no mass exchange)
  • Open (mass exchange allowed)
  • Isolated (no interaction with surroundings)

State and Process

• State: Complete description of a system (e.g., pressure, temperature, volume).
• Process: Transition between states.
• Path: Sequence of states a system goes through during a process.

Intensive and Extensive Properties

• Intensive: Independent of mass or size (e.g., pressure, temperature).
• Extensive: Depends on mass or size (e.g., volume).

Defining Systems

• Two intensive properties are typically used to define a state.
• Sometimes one intensive and one extensive property are used.

Laws of Thermodynamics

Zeroth Law

• Definition: If two systems are in equilibrium with a third system, they are in equilibrium with each other.
• Equilibrium Concepts: Thermal (temperature), mechanical (pressure), chemical (composition).

First Law

• Definition: Energy cannot be created or destroyed; energy is conserved.

Second Law

• Definition: There exists a quantity called entropy; in any natural process, entropy must increase.
• Spontaneity: Process occurs if the entropy of the universe increases.

Example Discussions

• Isolated system interactions and equilibrium
• Practical example: Refrigerators and entropy
• Entropy: Measure of disorder and 'happiness' of molecules

Anticipation for Next Class

• Topics: Define gas, perfect gas, thermodynamic processes, and laws of mechanics.