Fluid Mechanics: Bernoulli's Equation and Applications

This lecture covers the derivation and application of Bernoulli's equation in fluid mechanics. The instructor begins by revisiting Newton's second law and its integration along streamlines, emphasizing the importance of understanding both the parallel and perpendicular components of fluid flow. The lecture introduces the concept of pressure gradients and how they relate to fluid velocity and acceleration. The instructor explains the significance of Bernoulli's equation in connecting points along the same streamline and introduces a related equation for comparing different streamlines. Practical examples, such as the operation of a pitot tube and a venturi meter, illustrate how these principles are applied in real-world scenarios. The instructor highlights the assumptions necessary for using Bernoulli's equation, including steady flow and constant density, and discusses the implications of viscous forces near boundaries. The lecture concludes with a call for students to practice applying these concepts to solve fluid mechanics problems effectively.