What is the force in pounds exerted by a pressure of 1000 psi on a piston with a diameter of 3"?

To determine the force exerted by a pressure on a piston, you first need to calculate the area of the piston. The area can be found using the formula for the area of a circle, which is (A = \pi \cdot r^2).

In this case, the diameter of the piston is given as 3 inches. First, you need to find the radius by dividing the diameter by 2, which gives a radius of 1.5 inches. Now, calculating the area:

[

A = \pi \cdot (1.5)^2 = \pi \cdot 2.25 \approx 7.0686 \text{ square inches}

]

Next, the force can be calculated using the formula (F = P \cdot A), where (F) is the force, (P) is the pressure in psi, and (A) is the area in square inches. Here, the pressure is 1000 psi.

Now substituting the values into the equation:

[

F = 1000 , \text{psi} \cdot 7.0686 , \text{in}^2 \approx 706