Design for Stormwater Drainage: Calculation of Runoff and Pipe Sizing

Design for Stormwater Drainage: Calculation of Runoff and Pipe Sizing

Stormwater drainage systems are designed to control surface runoff, thus avoiding flooding and reducing soil erosion. This article guides step-by-step instructions on calculating stormwater runoff and finding the size of the right pipe to drain effectively using some practical examples.

What is stormwater runoff?
Stormwater runoff is the surface flow of water during rainfall that doesn't get absorbed into the ground. Therefore, calculating runoff is critical in designing a stormwater system to handle peak flows during rain events. Runoff Calculation Using the Rational Method

The Rational Method is a widely used approach for calculating peak stormwater runoff. The formula is:

Q = C x I x A

Where:

• Q = Peak runoff (m³/s)
• C = Runoff coefficient (dimensionless)
• I = Rainfall intensity (mm/hr or m/s)
• A = Drainage area (hectares or m²)

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Step-by-Step Example: Runoff Calculation

Step 1: Determining the Runoff Coefficient (C)

The runoff coefficient depends on the surface type:

• Asphalt or concrete: 0.7 to 0.95
• Grass: 0.15 to 0.35
• Gravel: 0.25 to 0.40

Let’s assume a concrete surface for a small parking lot, and the coefficient is C = 0.85.

Step 2: Rainfall Intensity (I)

The rainfall intensity (I) is usually provided by local meteorological departments. For this example, we will use I = 30 mm/hr, which is a common storm value for urban areas.

Convert 30 mm/hr into meters per second:

I = 30 / 1000 = 0.03 m/hr

Convert to seconds:

I = 0.03 / 3600 = 0.00000833 m/s

Step 3: Area of the Drainage Basin (A)

Next, calculate the drainage area (A). Let’s assume a parking lot with an area of 2000 m².

Convert the area to hectares (since 1 hectare = 10,000 m²):

A = 2000 / 10,000 = 0.2 hectares

Step 4: Calculating Runoff (Q)

Now, we can calculate the peak runoff using the formula:

Q = C x I x A

Q = 0.85 x 0.00000833 x 0.2

Q = 0.000001416 m³/s = 1.416 L/s

The peak runoff (Q) for this parking lot is 1.416 L/s.

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Pipe Sizing for Stormwater Drainage

After calculating the runoff, the next step is to determine the appropriate pipe size to handle the flow. Manning’s equation is used to calculate the flow capacity of the pipe:

Q = (1 / n) x A x R^(2/3) x S^(1/2)

Where:

• Q = Flow rate (m³/s)
• n = Manning’s roughness coefficient (typically 0.013 for concrete pipes)
• A = Cross-sectional area of the pipe (m²)
• R = Hydraulic radius (m)
• S = Pipe slope (m/m)

Step 1: Cross-sectional Area of the Pipe (A)

For a circular pipe, the area is calculated as:

A = π x D² / 4

Where D is the pipe diameter (in meters).

Step 2: Hydraulic Radius (R)

The hydraulic radius for a pipe flowing full is:

R = D / 4

Step 3: Pipe Slope (S)

The slope is the vertical fall over the length of the pipe. Let’s assume a slope of S = 1%, which means S = 0.01.

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Step-by-Step Example: Pipe Sizing

We now calculate the pipe size to handle the runoff (Q = 1.416 L/s = 0.001416 m³/s) from the previous section.

Step 4: Iteration to Solve for Pipe Diameter

Assume a slope of S = 0.01 and a Manning’s roughness coefficient n = 0.013 for a concrete pipe.

Using trial and error (or pipe-sizing charts), we will try different pipe diameters until we find one that meets the required flow.

For D = 200 mm (0.2 m):

A = π x (0.2)² / 4 = 0.0314 m²

R = 0.2 / 4 = 0.05 m

Now, calculate the flow using Manning’s equation:

Q = (1 / 0.013) x 0.0314 x (0.05)^(2/3) x (0.01)^(1/2)

Q = 76.923 x 0.0314 x 0.079 x 0.1

Q = 76.923 x 0.002478 x 0.1

Q = 0.01905 m³/s = 19.05 L/s

Since 19.05 L/s is greater than our required 1.416 L/s, a 200 mm pipe would be sufficient to handle the peak runoff.

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Conclusion

Designing an effective stormwater drainage system requires careful calculation of runoff and appropriate pipe sizing. Using the rational method for runoff and Manning’s equation for pipe sizing ensures that your system can handle peak flows during storm events. In this example, a 200 mm diameter pipe is sufficient to manage runoff from a 2000 m² concrete parking lot during a 30 mm/hr storm.