Detention Storage Volume Calculator

Compute storage volume for detention basins to attenuate peak discharge from a design storm.  Can use one or more ponds / basins to achieve required volume.

Software based on the USA Soil Conservation Service publication TR-55 (1986): Urban Hydrology for Small Watersheds

 To:  SCS TR-55 Peak Discharge Calculator 
Time of Concentration Calculator  Rational Equation Peak Discharge Calculator
 Unit Conversions Calculator 
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Topics on this page:  Introduction    Equations   Error Messages   References

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Introduction                                                Top of Page
Communities usually have guidelines stating that 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 runoff volume and peak discharge from the watershed.

Detention storage can be incorporated into developments to attenuate (reduce) the peak 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 peak discharge to the pre-development value of 150 cfs at the specified location.  The engineer can use our calculation to determine the detention 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 runoff depth and pre- and post-development peak discharge, use our SCS TR-55 Peak Discharge Calculator or Rational Method Peak Discharge Calculator.)

Our detention storage 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 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)                            Top of Page
The following equations are used for the calculation:

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

where: 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.

Storage Required vs. Discharge

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

"qo / qi  must be 0.1 to 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  
                                                        Top of Page
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.info.usda.gov/CED/ftp/CED/tr55.pdf .

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LMNO Engineering, Research, and Software, Ltd.

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