A Square Parking Lot Of 250m On A Side

A Square Parking Lot Of 250m On A Side The Surface Of The Lot Is Plan

A square parking lot with a side length of 250 meters has a plan surface that is sloped toward one of its edges where a gutter is located. This gutter drains the entire parking lot and is inclined from both ends toward a sewer inlet at its center. The time of concentration for runoff from this lot is estimated to be 20 minutes, with 18 minutes attributable to overland flow across the surface and 2 minutes for water to travel down each half of the gutter. Assuming the rational runoff formula applies, with a runoff coefficient of 0.75, determine which of the following storm events will produce the highest peak runoff rate, and calculate that peak runoff rate for each case:

a) A 100 mm/h rainfall intensity lasting 10 minutes

b) A 25 mm/h rainfall intensity lasting 40 minutes

c) A 15 mm/h rainfall intensity lasting 66.7 minutes

Paper For Above instruction

Introduction

Rainfall-runoff modeling is a critical component in hydrological engineering, particularly in urban areas such as parking lots where surface runoff management is essential for stormwater control. The rational method is widely used due to its simplicity and applicability for small catchments with relatively uniform rainfall and runoff characteristics. In this paper, we analyze a square parking lot with a specific configuration and hydrological parameters to determine which storm intensity results in the highest peak runoff rate. This involves calculating the runoff for different storm durations and intensities, comprehending the influence of the catchment’s physical and hydrological properties, and applying the rational formula appropriately.

Site and Hydrological Parameters

The study area consists of a square parking lot measuring 250 meters on each side, giving a total area of:

Area, A = 250 m × 250 m = 62,500 m²

The catchment is characterized by an average runoff coefficient (C) of 0.75, indicating significant imperviousness, typical for parking surfaces. The time of concentration (Tc), which includes overland flow and gutter flow, is approximately 20 minutes, with overland flow taking about 18 minutes and gutter flow 2 minutes. The catchment’s hydrological response is characterized by this Tc value, and the selected storms are compared based on their intensity, duration, and resulting peak runoff.

Methodology

The rational formula expresses the peak runoff rate (Qp) as:

Qp = CiA

Where:

- C = runoff coefficient (dimensionless)

- i = rainfall intensity (mm/hr)

- A = area of the catchment (m²)

- Qp = peak flow rate (m³/sec)

To ensure consistent units, rainfall intensity is converted to m/sec:

i (mm/hr) / 1000 / 3600 = i (m/sec)

The critical aspect of the analysis involves selecting the rainfall intensity that matches or exceeds the maximum required to produce a peak flow, considering that the effective rainfall duration cannot be less than the time of concentration for the peak to develop fully.

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Case (a): Rainfall intensity of 100 mm/h over 10 minutes

Conversion of intensity:

100 mm/h = 0.1 m/h = 0.1 / 3600 ≈ 2.78 × 10⁻⁵ m/sec

Duration in hours:

10 min = 10 / 60 ≈ 0.167 hours

Since the duration (10 minutes) is less than the time of concentration (20 minutes), the effective rainfall duration for calculating the peak is typically assumed to be at least the time of concentration or the duration of the storm if it exceeds Tc. Here, the duration is less, but since the storm intensity applies only for 10 minutes, the maximum intensity that can be sustained is 100 mm/h for the entire Tc.

Alternatively, the peak runoff occurs when the rainfall duration equals or exceeds Tc. As the storm duration is less than Tc, the effective rainfall duration is the storm duration, and the peak flow is governed by the intensity during this period, or the intensity corresponding to the storm.

The peak runoff rate:

Qp = C × i × A

Expressed in m³/sec:

Qp = 0.75 × 2.78 × 10⁻⁵ m/sec × 62,500 m² ≈ 1.30 m³/sec

Case (b): Rainfall intensity of 25 mm/h over 40 minutes

Conversion:

25 mm/h = 0.025 m/h = 0.025 / 3600 ≈ 6.94 × 10⁻⁶ m/sec

Duration:

40 min = 40/60 ≈ 0.667 hours

Since duration exceeds Tc, the effective rainfall duration for peak runoff calculation is the time of concentration, 20 minutes or 0.333 hours, for the development of the flow. The rainfall intensity to be used is that which lasts for the duration of runoff or the actual storm since the storm exceeds Tc.

The peak flow:

Qp = 0.75 × 6.94 × 10⁻⁶ × 62,500 ≈ 0.32 m³/sec

Case (c): Rainfall intensity of 15 mm/h over 66.7 minutes

Conversion:

15 mm/h = 0.015 m/h = 0.015 / 3600 ≈ 4.17 × 10⁻⁶ m/sec

Duration:

66.7 min ≈ 1.111 hours

Since the storm duration exceeds Tc, the effective rainfall duration for calculating peak flow is 20 minutes, meaning the rainfall intensity used is that which influences the peak, i.e., the storm’s intensity, or the storm should be considered to match or exceed Tc. Because the storm duration is longer, the maximum intensity relevant for the peak is the storm's average intensity during the development period.

The peak runoff:

Qp = 0.75 × 4.17 × 10⁻⁶ × 62,500 ≈ 0.20 m³/sec

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Results and Discussion

Comparing the calculated peak runoff rates:

- Scenario (a): approximately 1.30 m³/sec

- Scenario (b): approximately 0.32 m³/sec

- Scenario (c): approximately 0.20 m³/sec

The highest peak runoff occurs under storm (a), with 100 mm/h rainfall intensity over 10 minutes, despite the shorter duration, because the rainfall intensity is significantly higher, leading to a higher instantaneous runoff. Typically, the peak runoff is controlled by the highest effective rainfall intensity during the development of the flow, and in this analysis, the storm with 100 mm/h yields the maximum flow due to its high intensity, despite its short duration.

Furthermore, the rational method supports the conclusion that higher rainfall intensities generate higher peaks, provided the storm duration is sufficient to produce the flow or matches the time of concentration. Since the storm's duration in case (a) is less than Tc, the peak is effectively governed by the storm intensity, which is significantly higher than in other cases.

Conclusion

Out of the three storm scenarios considered, the storm with a rainfall intensity of 100 mm/h for 10 minutes produces the highest peak runoff rate of approximately 1.30 m³/sec for the parking lot. The analysis underscores the importance of considering both rainfall intensity and duration relative to the catchment’s time of concentration for estimating peak runoff. Urban stormwater management must account for these peak flows to ensure adequate drainage capacity, especially during high-intensity short-duration storms.

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