What is the force output of an extending cylinder if the piston diameter is 2", the rod diameter is 0.5", and the fluid pressure is 65psi?

To calculate the force output of an extending cylinder, you must first determine the effective area of the piston that is pushing against the fluid pressure. The force exerted by the piston can be calculated using the formula:

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

First, we need to find the area of the piston. The area of a circle is calculated using the formula:

[ \text{Area} = \pi \times \left(\frac{D}{2}\right)^2 ]

where ( D ) is the diameter of the piston. In this case, the diameter of the piston is 2 inches. Thus, the radius is 1 inch:

[ \text{Area}_{\text{piston}} = \pi \times (1)^2 = \pi \text{ square inches} \approx 3.14 \text{ square inches} ]

Next, we need to account for the area of the rod, since it will subtract from the effective area of the piston. The diameter of the rod is 0.5 inches, so the radius of the rod is 0.25 inches:

[ \text{Area}_{\text{rod