Key Difference: Fluid dynamics typically assumes constant density (incompressible), whereas gas dynamics involves varying density (compressible flow).
Compressibility
Definition: Compressibility relates to how the density of a gas changes under various processes such as pressure change or temperature change.
Notation: Specific volume (volume per unit mass) is used, denoted as ν (with a cut) to differentiate from velocity.
Equations: Utilizes differential calculus to express changes in specific volume (dν/ν), considering pressure and temperature variations.
Isothermal Compressibility: Relates to changes in volume at constant temperature.
Physical Interpretation: High compressibility means a small pressure change can significantly change the specific volume.
Alternate Definition: Related to bulk modulus.
Mach Number
Definition: The ratio of the fluid flow velocity to the speed of sound at that point in the flow.
Criteria: If Mach number < 1 (incompressible); if Mach number ≥ 1 (compressible).
Speed of Sound: Influenced by the medium's properties (e.g., 340 m/s in air, 5000–6000 m/s in steel).
Ernst Mach: Scientist known for his work on shock waves and blast waves, giving his name to Mach number.
Energy Transmission and Sound Waves
Example: Comparing hitting a metal rod vs. an air column with a hammer to demonstrate wave propagation speed differences attributable to compressibility and molecular arrangement.
Speed of Sound: Determined by how quickly molecules can transmit compression-expansion waves.
Laws of Thermodynamics
Zeroth Law
Definition: If two systems are each in equilibrium with a third system, they are in equilibrium with each other.
Thermal Equilibrium: Defined using temperature.
Mechanical Equilibrium: Defined using pressure.
Chemical Equilibrium: Requires the same gas composition.
First Law
Definition: Energy cannot be created or destroyed (Energy Conservation Law).
Implication: Introduces energy as a fundamental quantity for state descriptions.
Simple Compressible Substances: Only thermal and mechanical interactions are considered (heat exchange and compression/expansion work).
Second Law
Definition: Entropy of an isolated system can never decrease; it must increase for spontaneous processes.
Entropy: A quantity introduced to measure system disorder or randomness.
Practical Example: Refrigerator system illustrating entropy changes between the system and surroundings.
Nature's Law: Entropy increase is observed universally; not man-made but a fundamental aspect of nature.
Review and Course Structure
Objective: Build understanding from basic principles to graduate-level analysis with strong physical intuition.
Focus: Emphasize understanding physical phenomena and their mathematical descriptions (differential equations, laws of physics).
Upcoming Topics: Thermodynamic variables, gas definitions, perfect gas law, thermodynamic processes, laws of mechanics.
Methodology: Combination of mathematical derivations and physical intuition.