Definition of fluid mechanics by breaking down the components: fluid and mechanics.
Definition of a Fluid
A fluid is defined as a liquid or gas.
Common states of matter include:
Solid
Liquid
Gas
Key Note: Liquids and gases can often be treated similarly under certain conditions:
Negligible compressibility effects
No free surfaces (e.g., water exposed to air)
Practical Examples
Example 1: Testing a human-powered submarine in a wind tunnel.
Example 2: Studying jet engine exhaust in a water tunnel.
Comparison: Actual fluid (water) tested in air and vice versa.
Exceptions
Free Surface Effects: E.g., waves on a lake.
High-Speed Flow: E.g., rockets where compressibility is significant.
Formal Definition of a Fluid
A fluid deforms continuously under shear stress.
Definition of Stress
Stress: Force per unit area acting on a surface.
Types of stress:
Normal Stress: Acts 90 degrees to the surface.
Shear Stress: Tangential stress on a surface.
Normal Stress
Effects on Solids and Liquids:
Solids resist normal stress but deform.
Liquids can resist normal stress at rest but can compress slightly.
Pressure: The most common example of normal stress, always acts inward and normal to a surface.
Shear Stress
Effects on Solids and Liquids:
Solids resist shear stress but will distort under application.
Liquids cannot resist shear stress; they flow instead.
Conclusion: A fluid at rest cannot resist shear stress.
Free Body Diagrams
Analyze stresses on elements of solids and liquids:
For solids, both shear and normal stresses are present.
For liquids at rest, only normal stresses exist.
When shear stress is applied to a liquid, it deforms and flows, and Newton's second law applies.
Mechanics
Definition: Application of laws of force and motion.
Two branches:
Statics: Study of fluids at rest (hydrostatics).
Dynamics: Study of fluids in motion.
In statics:
Use condition: ( \sigma F = 0 ) (no acceleration).
In dynamics:
Use condition: ( \sigma F = mA ) (with acceleration).
Final Definition of Fluid Mechanics
Fluid Mechanics: Application of the laws of force and motion on a fluid, which deforms continuously under shear stress, encompassing both statics and dynamics.