This lesson covers the derivation of the Navier-Stokes equation, a fundamental principle in fluid dynamics, starting from the Reynolds Transport Theorem. The lesson explains the integral form of linear momentum conservation from the Reynolds Transport Theorem and then transforms it into a differential equation for linear momentum conservation. The lesson also discusses the concept of extensive and intensive properties, the rate of change of momentum, and the net external force acting on a system. It further explains the concept of surface forces and body forces acting on a fluid element. The lesson concludes with the derivation of the Navier-Stokes equation for incompressible fluid flow in both conservative and non-conservative forms.

- The Navier-Stokes equation is derived from the Reynolds Transport Theorem.
- The equation is first derived in integral form and then transformed into a differential equation.
- The rate of change of momentum and the net external force acting on a system are key concepts in the derivation.
- Surface forces and body forces are two types of forces acting on a fluid element.
- The Navier-Stokes equation for incompressible fluid flow can be expressed in both conservative and non-conservative forms.

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