Storm Drainage Sizing for a Parking Deck
A new parking deck has a roof area of 20,000 square feet. The local plumbing code requires storm drainage to be sized based on a 100-year, 1-hour rainfall intensity of 4 inches per hour. The design uses four roof drains, each connected to a 4-inch vertical leader. The horizontal storm drain piping from the leaders to the storm sewer is 6 inches in diameter and slopes at 1/8 inch per foot. The code official must determine if the system is adequately sized. The code (e.g., IPC Appendix C or UPC Appendix D) provides tables for sizing storm drains based on rainfall intensity and pipe slope. The contractor claims that the 4-inch leaders are adequate because they are the same size as the roof drain outlets. The inspector must calculate the required flow and compare it to the capacity of the proposed piping.
1. Calculate the required storm drainage flow in gallons per minute (gpm) for this roof, and determine if the proposed 4-inch leaders and 6-inch horizontal main are adequate. Use the rational method: Q = (rainfall intensity) x (area) x (runoff coefficient). Assume a runoff coefficient of 1.0 for a roof.
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First, convert rainfall intensity from inches per hour to feet per hour: 4 in/hr = 4/12 = 0.333 ft/hr. The area is 20,000 sq ft. The flow rate Q = (rainfall intensity in ft/hr) x (area in sq ft) x (runoff coefficient) = 0.333 x 20,000 x 1.0 = 6,666 cubic feet per hour. Convert to gallons per minute: 6,666 ft³/hr x 7.48 gal/ft³ = 49,862 gallons per hour. Divide by 60 = 831 gallons per minute. So the required flow is approximately 831 gpm. Now, check the capacity of the proposed piping. For a 4-inch vertical leader, the capacity depends on the head and the type of leader. Using the UPC Appendix D table for vertical leaders, a 4-inch leader can handle approximately 300 gpm at a certain head. Four leaders would handle 4 x 300 = 1,200 gpm, which exceeds 831 gpm. However, the horizontal 6-inch main at 1/8 inch per foot slope: using the Manning equation or tables, a 6-inch pipe at 1/8 inch per foot slope has a capacity of about 500 gpm when flowing full. But the total flow from all leaders is 831 gpm, so a single 6-inch main is not adequate if all flow goes through it. The problem states that the four leaders connect to a 6-inch horizontal storm drain. If all four leaders discharge into the same 6-inch main, the main must handle 831 gpm, which exceeds its capacity. Therefore, the 6-inch main is undersized. The inspector should require a larger main or multiple mains. The contractor's claim about the leaders is partially correct, but the horizontal main is the bottleneck.
2. If the rainfall intensity were 6 inches per hour instead of 4, how would that change the required flow and the adequacy of the piping?
Read the worked answer
With a rainfall intensity of 6 inches per hour, the flow rate would be: 6 in/hr = 0.5 ft/hr. Q = 0.5 x 20,000 x 1.0 = 10,000 ft³/hr. Convert to gpm: 10,000 x 7.48 = 74,800 gal/hr, divided by 60 = 1,247 gpm. The 4-inch leaders would still be adequate if their capacity is 300 gpm each (total 1,200 gpm), but 1,247 gpm exceeds 1,200 gpm, so the leaders would be slightly undersized. The 6-inch main would be even more undersized. Therefore, the system would need larger leaders and a larger main. The inspector should require a redesign based on the higher intensity.