You can convert pipe size to gallons per minute of flow by calculating the cross-sectional area of the pipe and making some reasonable assumptions about pipe volume and the rate of flow. Pipe sizing is measured by the internal diameter of the pipe, not the overall outside diameter. Once determined, the overall volume can be calculated. Pipe flow is described in gallons per minute. Shorter lengths of pipe will have a greater flow than a longer length of the same diameter. This is caused by internal resistance of the pipe itself. By the same reasoning a larger diameter pipe will have a greater flow or GPM than a smaller pipe at the same pressure or flow rate. Pressure is described as pounds per square inch. The square-inch measurement is determined by the area of the pipe. The pounds are the amount of force that is placed on the liquid to push it through the enclosed space.With that background, you can estimate the flow based on the pipe size.
Find the cross-section area of the pipe. Area is equal to pi times the radius squared or a = 3.14 x r2. A two-inch diameter pipe would have a cross-section area of 3.14 x 12 or 3.14 square inches.
Understand that water has a certain pressure associated with the height of that water. One pound of water pressure, or 1 PSI, is equal to 2.31 feet of elevation in height. In other words, a 1-inch column or pipe of water that is 2.31 feet high will have a pressure of 1 PSI. The overall height -- not volume -- of the pipe corresponds to the pressure. A 6-inch diameter pipe that is 2.31 feet high will only have 1 PSI.
Find the volume of the 2-inch diameter pipe in Step 1 that has a length of 10 feet. Ten feet is equal to 120 inches. Multiply 3.14 square inches, the cross sectional area, times the length. The volume of the pipe is equal to 376.8 cubic inches of volume.
Convert cubic inches into cubic feet. One cubic foot equals 1,728 cubic inches. Divide 376.8 cubic inches by 1,728 cubic inches per cubic foot and the answer is .218 cubic feet. This means that the 2-inch diameter pipe that is 10 feet long has an internal volume of .218 cubic feet.
Calculate the amount of water that can be contained in the section of pipe at any given time. One cubic foot of water is equal to 7.48 gallons. Multiply 7.48 gallons by .218 cubic feet and the amount of water in the pipe is equal to 1.63 gallons.
Find the GPM if the flow of water is one foot per second. Multiply the one-foot per second flow by 60 seconds per minute and the flow is now 60 feet per minute. In other words the water will flow through the 10-foot pipe six full volumes for every minute. Since the piping contains 1.63 gallons per 10 feet of pipe, multiply 1.63 by six and the final GPM is equal to 9.78 GPM of water flow from the 2-inch diameter pipe.
TL;DR (Too Long; Didn't Read)
The above estimation does not take into account frictional losses due to internal piping threads, connections or the use of special connectors.