Critical duration under TC 1

[SMIAH]

Might be an easy one (yes or no) :

When seeking a volume from the Modified Rational Method,the calculation is performed at multiple durations with corresponding intensities to produce a series of trapezoidal hydrographs.
Once the allowable discharge is subtracted the hydrograph with the greatest volume is then your critical storm duration for that analysis.

But do you check for duration < time of concentration (e.g. duration of 5 min while the tc is 15 minutes) ?

 

[psmart]

The critical duration will be greater than or equal to the Tc. A smaller duration will always produce a lower volume and peak. Try it and see...

Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[SMIAH]

It depends on the IDF curve!

In my case, it's under tc : critical duration (max volume) occurs at 10 min while tc = 15 min.

 

[jgailla]

Something doesn't seem right there. How can the critical be less than the tc?

 

[SMIAH]

We're talking about modified rational formula for volume calculation and not for peak flow determination.

It really depends on the IDF and the available outflow.

 

[SMIAH]

Try it (in SI) :

IDF parameters A and b = 64.96 and -0.44 (in I = A*Tc^b)

Area = 3,6 ha
C = 0,5
Qmax release = 0.5 m3/s (constant for the example).

I get 172 m3 at 10 min.

 

[jgailla]

Missed that SMIAH. Thought you were talking about peak flow.

 

[psmart]

Check your IDF data. The rainfall volume (intensity * duration) should be monotonically increasing with duration. The longer it rains, the greater the depth.

Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[SMIAH]

It does...

My point is the critical duration is 10 min. while someone could pretend that tc = 15.

We could pretend that tc = 30 minutes too... what would it do on the calculations!?

 

[psmart]

The Tc does matter. Changing the Tc will change the slope of the rising and falling limbs of the hydrograph.

I'm still doubtful that the critical duration could be less than the Tc. This duration would have a smaller runoff peak and volume, so I don't see how it could yield more storage in the pond. I would re-check your assumptions about the discharge you are subtracting.

Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[SMIAH]

Can you explain how does it matters in the calculations? Because I don't see where Tc is an input in the method.

The discharge is constant... this is not true but... reducing it wouldn't change the fact that the critical duration is 10 min (it could be worse e.g. at 5 min).

 

[psmart]

You said you're generating a trapezoidal hydrograph according to the modified rational method, correct? This means that the rise time will be equal to the Tc (assuming that Duration>Tc) The fall time will be a multiple of the Tc. For details see the illustration at

http://www.hydrocad.net/rational.htm

The critical duration depends on how you do the pond routing, which in turn depends on how you estimate the discharge. I never said the discharge was constant...




Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[SMIAH]

Sorry but this doesn't help.

My question was relatively easy and I think you're trying to say that critical duration can't be before tc.

But I'm trying to get a formal answer about this.

 

[beej67]

I'm pretty sure it can't, because of how IDF curves work. Higher Tcs always yield lower peak flows but also always yield higher total volumes.

Think back to the rectangular hyetograph that produces the trapezoidal hydrograph. The area of the hyetograph represents a volume of rainfall. Even though a longer Tc will produce a lower intensity rainfall, the area of the hyetograph is always higher for longer Tcs.

Right?

I don't use modified rational for hydrology down here, because review agencies quit accepting it because it was so heavily abused.

Hydrology, Drainage Analysis, Flood Studies, and Complex Stormwater Litigation for Atlanta and the South East -

http://www.campbellcivil.com

 

[LincolnPE]

By definition Td cannot be less than Tc.

 

[SMIAH]

I just don't see where Tc is an imput is the rational modified method.

Here's one excel sheet founded on Internet :

https://www.kalcounty.com/drain/new_pdfs/RationalMethodDetention_KalamazooCDC.xls

 

[LincolnPE]

That's not Modified Rational. No rainfall intensity averaging periods, critical duration analysis,etc.

 

[SMIAH]

"Critical duration analysis" would be that the maximum volume is obtained at 4 hour?

I don't get why this wouldn't be "Modified Rational".

There is no need to use Tc execept to adjust the runoff coefficient used in the Rational Method.

 

[psmart]

As I explained before, the rise and fall rates of the trapezoidal hydrograph are determined by the Tc.

Peter Smart
HydroCAD Software

http://www.hydrocad.net

 

[TerryScan]

There is a pretty detailed explanation of the methodology in this document:

http://www.deq.virginia.gov/Portals/0/DEQ/Water/StormwaterManagement/SWMHandbookVolume II.pdf

starting on pg 134 of the PDF