How many cubic feet per second of liquid flow are in a gallon per minute?

This is a pretty straightforward conversion. One cubic foot is equal to 7.48 gallons (US). If you take the reciprocal of that figure (1 / 7.48), you can determine how many cubic feet are in one gallon: 0.134. That is, one gallon is equal to 0.134 cubic feet. So, one gallon per minute equals 0.134 cubic feet per minute. But you're not done, yet. Since there are 60 seconds in a minute, you must divide that figure by 60 to determine how many cubic feet flow in just one second. 0.134/60 = 0.00223 = 2.23E-3 cubic feet per second. That's a pretty small number to work with. It might be more useful to convert that to cubic inches per second (although you didn't ask for the answer in those units). Since a cubic foot is equal to 1728 cubic inches, you can multiply the answer above by that number: 2.23E-3 x 1728 = 3.85 cubic inches per second (in3/s).