Fluid Mechanics Fundamentals

This lecture covers the fundamentals of fluid mechanics, starting with differential conservation laws and empirical stress-strain relationships to describe fluid flow. The instructor explains the derivation of mass conservation and momentum conservation equations, emphasizing the importance of understanding the logic behind the process. The lecture delves into Newton's second law, discussing the conversion of Lagrangian laws to Eulerian laws and the role of external forces. The concept of viscous stresses and the Cauchy stress tensor are introduced to analyze surface forces on fluid elements. The application of the Gauss theorem to convert surface integrals to volume integrals is demonstrated, with a focus on incompressible flows and the outer product of vectors.