To determine the minimum wall thickness of a solid metal casing with a hollow cylindrical hole under maximum internal pressure, the formula P = (2tSE) / (D - 2tY) is used, where P is the internal pressure, t is the wall thickness, S is the maximum allowable stress, E is the material quality factor, Y is the wall thickness coefficient, and D is the outer diameter. The discussion clarifies that the casing is not a pipe but a solid structure with a hollow section. Understanding the relationship between these variables is crucial for ensuring the casing can withstand the specified pressure. The conversation references ASME B31.3 for guidelines on pressure vessels. Accurate calculations are essential for safety and structural integrity.