Fluid Mechanics: Control Volume Approach and Energy Conservation

This lecture covers the control volume approach in fluid mechanics, focusing on the Reynolds transport theorem and its application to mass, momentum, and energy conservation. The instructor begins by recapping the fundamental laws of physics necessary for Eulerian descriptions of fluid flow. The lecture details how to convert Lagrangian laws into Eulerian laws using the Reynolds transport theorem, leading to the continuity equation for mass conservation. The instructor then discusses Newton's second law in the context of a control volume, explaining how the rate of change of linear momentum relates to external forces. The first law of thermodynamics is also addressed, emphasizing the relationship between energy conservation and the Bernoulli equation. The instructor illustrates these concepts with examples, including the use of hydropower plants for energy storage. The lecture concludes with a discussion on the importance of understanding the fundamental laws of physics and making appropriate assumptions when analyzing fluid systems.