This topic will introduce the fundamental concepts of fluid mechanics, including properties of fluids, fluid statics, and the difference between liquids and gases.
(A concise, structured overview for beginners)
| Concept | Description | Typical Units |
|---|---|---|
| Fluid | Substance that continuously deforms under shear stress; cannot sustain a static shear force. | — |
| Continuum Hypothesis | Treats fluids as continuous matter, ignoring molecular discreteness. Valid when characteristic length ≫ mean free path. | — |
| Control Volume | A fixed region in space through which fluid may flow; used for applying conservation laws. | m³ |
| Particle (or Fluid Element) | An infinitesimally small mass of fluid that moves with the flow. | kg |
| Density (ρ) | Mass per unit volume. | kg·m⁻³ |
| Viscosity (μ, η) | Internal friction; resistance to relative motion of adjacent layers. | Pa·s (dynamic) or m²·s⁻¹ (kinematic) |
| Pressure (p) | Normal force per unit area exerted by the fluid. | Pa (N·m⁻²) |
| Surface Tension (σ) | Force acting along a fluid surface that minimizes surface area. | N·m⁻¹ |
Mass (Continuity Equation)
[
\frac{\partial \rho}{\partial t} + \nabla!\cdot(\rho\mathbf{V}) = 0
]
Momentum (Navier–Stokes Equations)
[
\rho!\left(\frac{\partial \mathbf{V}}{\partial t}+ \mathbf{V}!\cdot!\nabla\mathbf{V}\right)= -\nabla p + \mu \nabla^{2}\mathbf{V}+ \rho\mathbf{g}
]
Energy
[
\rho!\left(\frac{\partial e}{\partial t}+ \mathbf{V}!\cdot!\nabla e\right)= -p,\nabla!\cdot\mathbf{V}+ \Phi + \nabla!\cdot(k\nabla T)+ \dot{q}
]
| Number | Formula | Physical Meaning |
|---|---|---|
| Reynolds (Re) | (\displaystyle Re = \frac{\rho V L}{\mu} = \frac |