Using the thin-walled cylinder theory, how does the 30-inch boiler compare to the 60-inch boiler in terms of working pressure?

In the context of the thin-walled cylinder theory, which is often applied in engineering to analyze the strength and pressure capabilities of cylindrical structures, the ability of a cylinder to withstand pressure is related to its diameter.

The formula for determining the hoop stress (circumferential stress) in a thin-walled cylinder under uniform internal pressure is given by:

[ \sigma = \frac{P \cdot d}{2t} ]

where ( \sigma ) is the hoop stress, ( P ) is the internal pressure, ( d ) is the diameter of the cylinder, and ( t ) is the thickness of the cylinder wall. From this relationship, you can see that for a constant wall thickness, the hoop stress is directly proportional to the diameter.

For a 30-inch boiler compared to a 60-inch boiler, if we consider both to have the same wall thickness, the 60-inch boiler has a diameter that is twice that of the 30-inch boiler. This means the hoop stress for the 60-inch boiler would also be ideally twice as great if the working pressure ( P ) remained constant across both cylinders. Therefore, the working pressure that the 30-inch boiler can sustainably manage would be half of