Final answer:
It would take approximately 3.26 seconds for a 20 gpm pump to extend a 4 inch diameter cylinder through a 20 inch stroke.
Step-by-step explanation:
To calculate the time it would take for a 20 gpm (gallons per minute) pump to extend a 4 in diameter cylinder through a 20 in stroke, we first need to convert the flow rate into cubic inches per second. Since there are 231 cubic inches in a gallon, the flow rate in cubic inches per second is 20 gpm * (231 cubic inches/gallon) * (1 minute/60 seconds) = 77 cubic inches/second. Next, we need to calculate the volume of the cylinder. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Since the diameter is given as 4 inches, the radius is 2 inches. Plugging in these values, the volume of the cylinder is V = 3.14 * (2 in)² * 20 in = 251.2 cubic inches. To find the time it would take to extend the cylinder, we can divide the volume of the cylinder by the flow rate of the pump: t = V / Q = 251.2 cubic inches / 77 cubic inches/second ≈ 3.26 seconds.