This lesson covers the analytical solution of Navier Stokes equations for simplified problems and simple geometry. It explains the continuity equation for Cartesian coordinate and the momentum equation for laminar incompressible flow with constant fluid properties. The lesson also discusses the components of viscous stress tensor for incompressible nutrient fluid and the vorticity component. It further elaborates on the exact solution of Navier Stokes equations, the concept of fully developed flow, and the calculation of shear stress and vorticity. The lesson concludes with the explanation of plane couette flow and two-layer couette flow.

- The Navier Stokes equations are derived from the Reynolds transport theorem.
- The continuity equation for Cartesian coordinate and the momentum equation are essential for understanding laminar incompressible flow with constant fluid properties.
- The components of viscous stress tensor for incompressible nutrient fluid and the vorticity component are crucial in fluid dynamics.
- The exact solution of Navier Stokes equations is limited to laminar, one and two-dimensional flows with constant properties and simple geometry.
- The concept of fully developed flow is essential in understanding the behavior of fluid flow in different conditions.
- The calculation of shear stress and vorticity is crucial in understanding the forces acting on a fluid element.
- The plane couette flow and two-layer couette flow are special cases of fluid flow.

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