What would be the net difference between the opposing forces of an automatic valve that has a 2-inch seat, an effective diaphragm area of 6 inches, and an inlet pressure of 50 pounds per square inch (psi)?

To determine the net difference between the opposing forces of the automatic valve, we first need to compute the forces acting on the diaphragm of the valve. The effective diaphragm area that generates force can be calculated using the formula:

[ \text{Force} = \text{Pressure} \times \text{Area} ]

In this case, the pressure is given as 50 psi, and the diaphragm area is stated as 6 square inches. To calculate the force produced by the inlet pressure:

[ \text{Force} = 50 , \text{psi} \times 6 , \text{in}^2 = 300 , \text{pounds} ]

This force represents the force acting to open the valve. On the other side of the diaphragm, the opposing force is generated based on the effective area of the valve seat. The area of the 2-inch valve seat can be calculated with the formula for the area of a circle:

[ \text{Area} = \pi r^2 ]

Given the diameter of 2 inches, the radius is 1 inch. Therefore:

[ \text{Area} = \pi (1 , \text{in})^2 \approx