The flow rate through a commercial fire sprinkler system is the sum of the flow rates through its individual sprinklers. These individual flow rates, in turn, depend on the water pressure within them. Several factors affect how each sprinkler's pressure affects its flow rate. These factors include the dimensions of the sprinkler opening and details about frictional losses in the sprinkler line. Your manufacturer provides a "discharge coefficient" in the system's documentation that takes all these factors into account.
Find the square root of the pressure at each individual sprinkler's discharge point. If, for instance, the pressure at each sprinkler is 15 pounds per square inch: 15 ^ 0.5 = 3.87.
Multiply the result by the system's discharge coefficient. If, for instance, you have a fire sprinkler with a discharge coefficient of 6.2: 3.87 x 6.2 = 24 gallons per minute.
Multiply this individual flow rate by the total number of sprinklers. If your system has, for instance, 15 sprinklers: 24 x 15 = 360 gallons per minute.