Which formula correctly describes the force of retraction of a double-acting cylinder?

The correct formula for describing the force of retraction of a double-acting cylinder is based on the principle of calculating the effective area of the cylinder and the pressure acting upon it.

In this case, the formula ( F = \frac{\pi d^2}{4} \times p_e ) accurately represents the force generated by the cylinder when it is retracted. Here, ( d ) represents the diameter of the cylinder, and ( p_e ) denotes the effective pressure applied to the cylinder. The term (\frac{\pi d^2}{4}) calculates the area of the circular face of the cylinder since the area ( A ) of a circle is given by ( A = \frac{\pi d^2}{4} ).

The pressure ( p_e ) acts over this area to produce a force, and the product of pressure and area yields the total force exerted. Thus, this formula provides a clear and precise method for calculating the retraction force of a double-acting cylinder, which is essential for understanding how pneumatic or hydraulic systems operate.