Goswami Practice Exam, Breadth Exam 2, Problem 119

[turbo83lude]

Need help understanding/solving this problem.

The 1-hr unit hydrograph of excess precipitation is shown in the table below.

Time (hr) 0 1 2 3 4 5

Discharge Q (cfs/in) 0 35 75 105 40 0

A 2-hr storm produces 1.7 in. of runoff during the first hour followed by 0.8 in. of runoff during the second hour. The peak discharge (cfs/sec) due to this storm is most nearly:

A. 210

B. 239

C. 263

D. 287

The answer is B.

Can anyone help??

 

[bradlelf]

Here you go:

The first hour rain event (1.7 " runoff) peaks at T=3 hr. So 1.7*105 = 106.7 cfs

The second storm hits at T=1 hr with 0.8 " runoff.

Since 1.7">0.8" we know that the ultimate peak will happen at T=3 hrs.

So, since the second storm started at T=1 hr ... you need to use the 75 cfs/in (T=2 hr) factor for the second storm. 2+1 = 3rd hour.

(1.7 * 105) + (0.8 * 75) = 238.5 cfs

 

[bradlelf]

Hour 0 Hour 1 Hour 2 Hour 3 Hour 4 Hour 5 Hour 6 Storm 1 1.7 in 0 cfs/in 0.0 cfs 35 cfs/in 59.5 cfs 75 cfs/in 127.5 cfs 105 cfs/in 178.5 cfs 40 cfs/in 68.0 cfs 0 cfs/in 0.0 cfs 0 cfs/in 0.0 cfs Storm 2 0.8 in 0 cfs/in 0.0 cfs 0 cfs/in 0.0 cfs 35 cfs/in 28.0 cfs 75 cfs/in 60.0 cfs 105 cfs/in 84.0 cfs 40 cfs/in 32.0 cfs 0 cfs/in 0.0 cfs Total 0.0 cfs 59.5 cfs 155.5 cfs 238.5 cfs 152.0 cfs 32.0 cfs 0.0 cfs

 

[bradlelf]

That did not paste correctly apparently ... let me know if you have any other questions.

 

[miloc]

I don't quite well get the rationale behind, but, now I know how to address a question like that. Thanks.

 

[turbo83lude]

Thank you very much for the response. Question: Why can't solve this problem using the s-curve method? When would you typically use the s-curve method?

 

[Lucky1]

Good question. I have the same issue not knowing when to mathmetically solve like above or use the curve.

 

[bradlelf]

When you say S curve ... do you mean Unit hydrograph?

 

[Lucky1]

Yes, hydrograph.

 

[bradlelf]

You use the SCS Unit hydrograph when you need to use a synthetic storm distribution. I doubt you would have to do this by hand on the exam since it would take over 6 minutes to do so.

Are you possibly confusing hyetographs with hydrographs?

Hyetograph = rainfall vs time

Hydrograph = flow vs time

 

[bradlelf]

https://documents.cloud.autodesk.com/Public/Details?hash=mJpHIah

https://documents.cloud.autodesk.com/Public/Details?hash=mJ9L6a6

Try these for a better explanation. For this problem they gave you the unit hydrograph. If you plot both storms using the rainfall amount (since the unit hydrograph is based upon 1" of rainfall) you get the correct answer. The important item in this problem is 2 storms starting at 2 different times.