If two boilers with the same capacity are operating at 200 psi and 400 psi, what is the approximate ratio of the areas of their safety valves?

To determine the approximate ratio of the areas of the safety valves for two boilers operating at different pressures, one can utilize the relationship between pressure and the area of the safety valve based on the principle of force and pressure. Safety valves are designed to release steam when the pressure exceeds a predetermined level, and they must be sized appropriately to accommodate the pressure within the boiler.

The force exerted by the pressure in the boiler is directly related to both the area of the safety valve and the pressure of the steam. The fundamental concept is given by the equation: Force = Pressure × Area. Consequently, for two boilers with the same capacity but differing pressures, the force exerted by the steam can be compared as follows:

For the first boiler at 200 psi, the force exerted by its safety valve can be represented as:

Force1 = 200 psi × Area1.

For the second boiler at 400 psi, the force exerted can be expressed as:

Force2 = 400 psi × Area2.

Setting the forces equal to each other (since both valves are designed to handle the same steam capacity and thus need to relieve the same amount of steam safely), we can derive the ratio of the areas of the safety valves:

200 psi × Area