This lesson covers the exact solutions of Navier Stokes equations in Cartesian coordinates, focusing on plane Poiseuille flow with slip at the wall. The lesson explains the assumptions made for the flow, such as laminar steady incompressible flow with constant fluid properties and fully developed flow. It also discusses the governing equation and how to integrate it to get the velocity profile. The lesson further explains how to apply boundary conditions to find the integration constants and how to calculate the volume flow rate and mean velocity. The lesson concludes with a discussion on shear stress distribution inside the flow domain and how to calculate the wall shear stress.

- The Navier Stokes equations can be solved exactly for plane Poiseuille flow with slip at the wall.
- Assumptions for the flow include laminar steady incompressible flow with constant fluid properties and fully developed flow.
- The governing equation can be integrated to get the velocity profile.
- Boundary conditions can be applied to find the integration constants.
- The volume flow rate and mean velocity can be calculated.
- The shear stress distribution inside the flow domain can be determined and the wall shear stress can be calculated.

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