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This lecture covers the design of a pressure tank, focusing on the choice of materials, wall thickness, and safety considerations. Starting with an introduction to materials science and mechanical engineering, the instructor presents a case study on selecting materials for a tank under pressure. The lecture discusses the mechanical properties of materials, criteria for crack propagation, and the importance of fatigue resistance. Various materials such as metals, polymers, and composites are evaluated for their suitability in pressure vessels. The design process involves calculating stress intensity factors, ensuring the tank's resistance to fatigue, and considering factors like corrosion resistance and cost.