What total force is exerted on a piston that has a diameter of 3" under a pressure of 100 psig?

To determine the total force exerted on the piston, it's important to use the formula that relates pressure, area, and force. The pressure exerted on the piston is measured in pounds per square inch (psi), and the area of the piston can be calculated from its diameter.

1. Calculate the radius of the piston, which is half the diameter. With a diameter of 3 inches, the radius is 1.5 inches.

2. Use the formula for the area of a circle, A = πr². Substituting the radius:

A = π(1.5 inches)²

= π(2.25)

= approximately 7.07 square inches.

3. The pressure given is 100 psig (pounds per square inch gauge). To find the total force (F), use the formula:

F = Pressure × Area.

F = 100 psi × 7.07 square inches

= 707 (rounded to one decimal place).

This calculation results in a total force of approximately 706.5 pounds, confirming that the answer of 706.5 psi reflects the total force exerted on the piston under the specified conditions. This approach illustrates how pressure and