What is the formula to calculate the total force acting on a safety valve disc based on its diameter and pressure?

The total force acting on a safety valve disc can be calculated using the formula that involves the diameter of the disc and the pressure exerted on it. The formula provided in the correct choice, which states TF = D x D x 0.7854 x P, breaks down into components that align with fundamental principles of circular area calculation and force due to pressure.

In this formula, D represents the diameter of the safety valve disc, and 0.7854 is the approximate value of π divided by 4, which is used to calculate the area of a circle (A = πr²). Since the radius is half of the diameter (r = D/2), the area can also be expressed as (π/4)D². Thus, the total area of the safety valve disc is given as 0.7854D².

When this area is multiplied by the pressure P acting on the disc, the result gives the total force (TF) acting on it, as pressure is defined as force per unit area (P = F/A). Therefore, multiplying the area by pressure yields the total force acting on the disc.

This understanding illustrates why the formula effectively calculates the force the safety valve disc experiences when subjected to a specific