Determine the driving force in your pipe. The driving force is determined by either the maximum pressure capacity of the pipe or, if the pipe is not filled completely, the pressure created by the pump. Both pumps and pipes include a pressure spec in pounds per square inch (psi) in basic system information, usually printed along the pipe. Use the pump psi reading only if it is lower than the psi reading on your pipe. A standard pipe is usually around 250 psi.
Determine the change in elevation along the pipe's length. This factor, usually called "head" is simply the elevation of the end of the pipe subtracted from the beginning, and can be either positive or negative. A pipe flowing from 600 feet above sea level to 800 feet above sea level, for example, has a negative head of 200 feet.
Convert your psi reading to feet of water by multiplying by 2.31, the given conversion factor between the two measurements. Two hundred fifty psi, to return to the example, is 577.5 feet of water.
Set up the Hazen-Williams equation to determine the relationship between friction and flow. The equation is given by H(friction) = 0.002083 * L * (100/C)^1.85 * ( gpm^1.85/d^4.8655), where "L" is the length of pipe, "C" is a roughness factor and "d" is the pipe diameter. Gpm is the flow in gallons per minute.
Insert all known values. The roughness factor is often given by pipe manufacturers, but you can use 120 as a standard value for most types of steel or PVC pipe. Also, insert values for your pipe length and diameter, so the only two remaining variables are H (friction) and gpm (flow).
Draw an axis on a sheet of graph paper, where your x (horizontal) axis represents flow (gpm) and the y (vertical) axis represents friction.
Plug in hypothetical flow values into the equation to calculate the corresponding friction values. Use values of 10, 20, 30, 40, 50 and 60 gpm, and plot each of the values on your graph at the intersection of the flow and friction values on your axis. The resulting line between the points should be a curve, the system curve that predicts how flow changes as a result of resistance.
Subtract your head value from the psi reading converted to feet. In the example, a pipe with 200 feet of negative head and 250 psi (577.5 feet) of pressure has a total difference of 377.5 feet (577.5 - 200).
Find the point on the y axis with the value you just calculated, 377.5 feet in the example. Draw a horizontal line from that point to the curve, where the intersection gives you both the desired friction and flow (gpm) values for the pipe system.