Detention Basin Storage (Modified Rational)
Estimates the storage a detention basin needs so that a developed site releases no more than an allowed peak flow. It finds the peak runoff by the rational method and sizes the pond by the Aron and Kibler rational-hydrograph method [1][2]. Use it at the concept stage, before routing a storm through a real pond.
Equations
Qp = C·Cf·i·A / 360 Vs = Qp·td − Qa·(td + tc)/2 with td = tc: Vs = tc·(Qp − Qa)
Qp is the peak inflow in m³/s, C the runoff coefficient, i the rainfall intensity in mm/hr for the storm duration td, and A the drainage area in hectares. Cf is the HEC-22 Table 3-2 frequency factor [4]; C·Cf is capped at 1. The Surface / Land Use list fills C with the midpoint of its HEC-22 Table 3-1 range [4]. Qa is the allowable release rate, usually the predevelopment peak, and tc the time of concentration (in seconds in Vs, which is in m³).
The inflow is a trapezoid: up to Qp over tc, level until the rain stops at td, down to zero at td + tc. The outflow rises in a straight line until it meets the falling limb at Qa; Vs is inflow less outflow up to then. With one intensity the page uses td = tc: a triangular inflow of base 2tc, with the outflow reaching Qa at tc·(2 − Qa/Qp).
Limits and common mistakes
- Aron and Kibler size the pond for the critical duration, the storm needing the most storage, which can be longer than tc when Qa is small. Evaluate Vs for longer td, with Qp from each duration’s intensity, and keep the largest.
- Read i for duration tc and the chosen return period from the local IDF curve.
- The straight-line outflow approximates an orifice or weir. Confirm the final design by routing the storm.
- The rational method suits small catchments, typically under about 80 ha. Use a hydrograph method such as TR-55 [3] for larger ones.
Worked example
A 3 ha light industrial site may release no more than its predevelopment peak of 0.2 m³/s in the 25-year storm. Its time of concentration is 15 min, and the 25-year, 15-minute intensity is 120 mm/hr. How much storage does the basin need?
- Choose Surface / Land Use Industrial, light areas, which sets Runoff Coefficient (C) to 0.65.
- Choose Design Storm Return Period 25 years (Cf = 1.1).
- Enter Rainfall Intensity (i, mm/hr) 120, Drainage Area (A, ha) 3, Time of Concentration (tc, min) 15 and Allowable Release Rate (Qa, m³/s) 0.2.
- Press Solve. The Solution shows:
Peak inflow Qp = C·i·A / 360: 0.715 m³/s
Hydrograph time base (2·tc): 30 min
Outflow reaches Qa at tc·(2 − Qa/Qp): 25.8042 min
Required storage volume Vs = tc·(Qp − Qa): 463.5 m³
Required storage volume Vs = tc·(Qp − Qa): 606.235 yd³
Frequency factor Cf: 1.1
Design coefficient C·Cf (at most 1): 0.715
Check by hand. The inflow triangle holds 0.715 × 900 s = 643.5 m³. By 25.804 min (1,548.25 s), 0.5 × 0.2 × 1,548.25 = 154.825 m³ has left and 0.2² × 900 / (2 × 0.715) = 25.175 m³ of inflow is still to come, so the pond holds 643.5 − 25.175 − 154.825 = 463.5 m³. Then check longer storms.
