Stormwater Runoff Detention Basin Storage Volume

Compute storage volume for detention basin to attenuate peak discharge from a design storm. TR-55 method.

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 Select calculation, rainfall type, and units: Watershed Area, A (mi2): Compute Storage Volume Compute Outflow Discharge Inflow, qi (ft3/s): Outflow, qo (ft3/s): Rainfall Distrib Type I or IA Rainfall Distrib Type II or III Outflow/Inflow, qo/qi ratio: Runoff Depth, Q (inch): Runoff Depth in inches Runoff Depth in cm Runoff Volume, Vr (acre-ft): Area in acre Area in mile2 Area in km2 Area in hectare Storage Volume, Vs (acre-ft): Volumes in acre-ft Volumes in ft3 Volumes in gallons (U.S.) Volumes in yard3 Volumes in m3 Vs/Vr ratio: Inflow, Outflow in cfs or ft3/s Inflow, Outflow in gpm Inflow, Outflow in m3/s www.LMNOeng.com © 2015 LMNO Engineering, Research, and Software, Ltd.

Units: cm=centimeter, ft=foot, gal=U.S. gallon, gpm = U.S. gallon per minute, km=kilometer, m=meter, min=minute, s=second.

Introduction
Communities usually have guidelines stating that stormwater runoff peak discharge at some location following development cannot exceed the peak discharge prior to development. The "location" is usually somewhere in the watershed where flooding would be detrimental. Development usually involves clearing trees and brush, paving surfaces, and constructing buildings. These activities tend to increase stormwater runoff volume and peak discharge from the watershed.

Detention basin storage can be incorporated into developments to attenuate (reduce) the peak stormwater discharge. For example, say a city requires the 25-yr, 24-hr storm to be the basis for design. Prior to development, the peak discharge from this storm is, say, 150 cfs (ft3/s) at a specified location, and the peak discharge due to development is predicted to be, say, 300 cfs at the same location. The city won't approve the project unless the developer incorporates enough detention storage to reduce the predicted stormwater peak discharge to the pre-development flow of 150 cfs at the specified location. The engineer can use our calculation to determine the detention basin storage volume required to attenuate the peak discharge from 300 to 150 cfs. The storage volume can then be implemented as a single pond with that volume or several ponds, basins, or depressions that add up to the required volume. The ponds/basins/depressions must go dry between storm events and should be located just upstream of the specified location. (To compute stormwater runoff depth and pre- and post-development peak discharge, use our SCS TR-55 Peak Discharge Calculator or Rational Method Peak Discharge Calculator.)

Our stormwater detention storage basin volume calculation is based on methodology presented in Technical Release 55, Chapter 6 (SCS, 1986), of the USA Soil Conservation Service (now called the Natural Resources Conservation Service, NRCS), division of the USDA (USA Department of Agriculture). The NRCS has worked for decades developing equations and conducting experiments to determine reliable models for predicting stormwater runoff storage volume for detention basins to reduce peak discharge from storm events.

We have made the calculation useful for the international community by allowing a variety of units. Unfortunately, TR-55 only presents rainfall distribution maps for the USA. Therefore, non-USA users need to determine whether a typical 24-hr rainfall resembles a Type I or IA or Type II or III distribution.

Equations (SCS, 1986)
The following equations are used for the calculation:

Vr = QA           Vs   =  Vr (Vs / Vr)          qo  =  qi (qo / qi)

where (L=Length units, T=time units): A = watershed area [L2].  Q = Runoff Depth [L].  q i = Inflow, or post-development peak discharge upstream of detention ponds [L3/T].  q o = Outflow, or post-development peak discharge downstream of detention ponds; often the pre-development peak discharge is used as this value [L3/T].  Vr = Runoff Volume [L3].  Vs = Detention Storage Volume [L3].

SCS (1986) provides equations and a graph for  Vs / Vr   vs. qo / qi .  Our calculation uses the equations, but solves them backwards when solving for qo.

Vs / Vr  =  C0  +  C1 (qo / qi)  +  C2 (qo / qi)2   +  C3 (qo / qi)3
where:
C0 = 0.660,  C1 = -1.76,  C2 = 1.96,  C3 = -0.730  for Types I and IA rainfall distributions
C0 = 0.682,  C1 = -1.43,  C2 = 1.64,  C3 = -0.804  for Types II and III rainfall distributions
The equation and coefficients are valid for  0.1 <  qo / qi   < 0.8.

Error Messages given by calculation
"All inputs must be positive." This is an initial check of user input. No results computed.

"Need 0.1 < qo / qi < 0.8." Vs not computed. The calculation is only valid for qo / qi in the proper range.

"Vs / Vr  out of range."  qo not computed. The calculation is only valid for Vs / Vr in the proper range as indicated in the above figure, depending on the rainfall distribution type.

References
U.S. Soil Conservation Service. Technical Release 55: Urban Hydrology for Small Watersheds. USDA (U.S. Department of Agriculture). June 1986. Available from NTIS (National Technical Information Service), NTIS # PB87101580. Also available on the web in .pdf format at http://www.nrcs.usda.gov/Internet/FSE_DOCUMENTS/stelprdb1044171.pdf .

LMNO Engineering, Research, and Software, Ltd.
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