A storm drain system is laid out similar to that shown in Figure 1, with the following ch...

A storm drain system is laid out similar to that shown in Figure 1, with the following characteristics:

catchment area 1: A1 = 1.2 ha, C1 = 0.6, inlet time = 5 min

catchment area 2: A2 = 2.0 ha, C2 = 0.35, inlet time = 6 min

catchment area 3: A3 = 3.0 ha, C3 = 0.2, inlet time = 7 min

reach 1 (inlet 1 to inlet 2): L = 100 m, S = 0.0015

reach 2 (inlet 2 to inlet 3): L = 120 m, S = 0.003

reach 3 (inlet 3 to inlet 4): S = 0.010

Using the rational method, compute the design flow and required pipe diameter for each reach of the system for a 5-year storm.

FIGURE 1

Illustration for Example. Plan view of drainage area.

Example

A storm drainage system has been laid out in a street as shown in Figure 1. Individual inlet catchment areas and runoff coefficients have been determined and are shown. Inlet times have been estimated, and the pipe length and slope for each sewer reach are given. Using the rational method, compute the design flow and the required pipe diameter for each reach for a 10-year storm. Assume the pipe has a Manning's roughness coefficient n = 0.013.

Solution Reach 1: First, determine the rainfall intensity for area 1, using the inlet time as the time of concentration. Enter Figure 2 with Tc = 5 min, and read i = 150 mm/h or 0.15 m/h for the 10-year storm. The catchment area is 1 ha, or 10,000 m2. Applying the rational formula yields

and converting to m3/s gives

To determine the required diameter for reach 1, enter Manning’s nomograph with Q = 0.167 m3/s and the given slope of 0.0035; read the required diameter D = 45 cm and a flow velocity of 1.05 m/s.

FIGURE 2

Typical rainfall intensity–duration–frequency (IDF) curves. IDF curves are prepared from rainfall statistics by the U.S. National Climatic Data Center.

Reach 2: To compute the peak discharge or design flow for the pipeline between inlet 2 and inlet 3, first compute the composite runoff coefficient for the combined areas 1 and 2, as follows:

Next, compute the time of flow in reach 1, using the relationship

The total time of flow to inlet 2 is the inlet time for area 1 plus the channel flow time in reach 1, or 5 + 1.9 = 6.9 min. This is larger than the inlet time for area 2; therefore, use a time of concentration Tc ≈ 7 min for the composite area draining to inlet 2.

From Figure 2, read i = 145 mm/h for the 10-year storm.

Applying the rational formula yields

and

Now enter Manning’s nomograph with Q = 0.34 m3/s and the given slope of S = 0.002; read the required diameter D = 65 cm and flow velocity V = 1.02 m/s.

Reach 3: The total tributary area to inlet 3 is 1 + 1.5 + 2 = 4.5 ha, or 45,000 m2. The composite runoff coefficient is computed to be

The time of flow in reach 2 is 180 m ÷ 1.02 m/s = 176 s = 2.9 min. The total flow time to inlet 3 is then 5 + 1.9 + 2.9 = 9.8 min (inlet time for area 1 + travel time in reach 1 + travel time in reach 2). But this is less than the individual inlet time for area 3, which is 12 min. Therefore, the 12-min inlet time dominates and is taken as the time of concentration (or storm duration) for the design of reach 3.

Enter Figure 2 with Tc = 12 min and read i = 135 mm/h or 0.135 m/h for the 10-year storm. Now, applying the rational formula yields

and

From Manning’s nomograph, with Q = 0.47 m3/s and S = 0.0015, read D = 80 cm and V = 1 m/s.