This lesson covers the fundamental concepts of hydrodynamics, focusing on incompressible Navier-Stokes equations. It delves into the governing equations, vorticity, conservation laws, and provides illustrative examples to explain these concepts. The lesson also discusses the continuum approximation, incompressible flows, and the continuity equation. It further explains the concept of nondimensionalization and its importance in fluid mechanics, plasma physics, and other fields. The lesson concludes with a discussion on the material derivative and its applications in various fields.

- The Navier-Stokes equation is a fundamental principle in fluid dynamics that describes the motion of viscous fluid substances.
- The continuum approximation is used when the length of interest is much larger than the mean free path length.
- Incompressible flows are assumed when the fluid's speed is much lower than the sound speed.
- The continuity equation is a mathematical representation of the conservation of mass.
- Nondimensionalization is a critical tool in fluid mechanics and other fields as it helps to map one system to another.
- The material derivative, also known as the total derivative, is used to determine how a quantity (like energy or velocity field) changes as it moves with the fluid.

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