Introduction to Fluid Mechanics

Introduction to Fluid Mechanics
(A concise, organized overview for quick study and reference)

1. What Is Fluid Mechanics?

• Definition: The branch of physics that studies the behavior of fluids (liquids and gases) at rest (fluid statics) and in motion (fluid dynamics).
• Why It Matters: Applications span aerospace, automotive, civil engineering, biomedical devices, environmental science, and everyday phenomena (e.g., weather, blood flow).

2. Fundamental Concepts

3. Governing Equations

3.1 Conservation of Mass – Continuity Equation

• Differential form (incompressible fluid):
  [ \nabla \cdot \mathbf{V} = 0 ]
• Integral form (general):
  [ \frac{d}{dt}\int_{CV}\rho , dV + \int_{CS}\rho \mathbf{V}\cdot \mathbf{n}, dA = 0 ]

3.2 Conservation of Momentum – Navier‑Stokes Equations

• General vector form:
  [ \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} ]
• Key terms:
  • Inertia (left side)
  • Pressure gradient, viscous diffusion, body forces (right side)

3.3 Conservation of Energy – Energy Equation

• Simplified for incompressible flow (steady, no heat generation):
  [ h + \frac{V^{2}}{2} + gz = \text{constant along a streamline} ]
• Full form includes: internal energy, heat conduction, viscous dissipation, work of pressure forces.

4. Fluid Properties

5. Dimensionless Numbers

| Number | Definition |