Calculate the speed that a piston will retract if it has a 6 inch diameter piston face, a 1 inch diameter piston rod, and a fluid supply of 15 GPM.

To determine the speed at which the piston will retract, it is essential to first calculate the effective area of the piston. The speed of the piston can be derived from the fluid flow rate and the effective area.

The diameter of the piston face is 6 inches, so the radius is 3 inches. Using the formula for the area of a circle (A = πr²), we can calculate the area of the piston face. This area will be pivotal in calculating the piston speed.

Next, the diameter of the piston rod is 1 inch, giving it a radius of 0.5 inches. We again apply the area formula to find the area of the piston rod since it affects the effective area when the piston retracts. The effective area for the retraction of the piston is computed by subtracting the area of the rod from the area of the piston face.

Once we have determined the effective area, we can use the flow rate provided (15 GPM) to find the speed of the piston. To convert gallons per minute to cubic inches per minute, it is useful to remember that there are 231 cubic inches in a gallon.

The formula used to find the speed of the piston is:

Speed (in/min) = Flow