NCEES Transportation Depth problem 531

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Predgw

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Runoff from a subdivision is collected in a basin then released at 43 CFS through a circular corrugated metal pipe. ( n=0.025) The pipe slope is 0.001ft/ft

Find the diamter (ft) of the pipe that should be used to deliver the flow.

A. 3

B. 5

C. 6

D. 18

I ran out of time yesterday and skipped this. However I just did it and while it took a few minutes I thought I had it correct. However I was wrong.

I used the same method and equation as the solution, expect the solution peformed an odd mathematical step. ( or I'm wrong)

They used the manning equation. Because the diamter is unknow they used (3.14*d^2)/4 for area and (d/4)2/3 for the R value

But when they plugged in the numbers they get 43 = (1.49/.025) * (0.785d^2)* (0.397d^2/3)* (0.001^1/2)

Where is the 0.397 coming from? I had 0.25d^2/3

Using my numbers i get a 6' pipe. There is no errata for this. WTF , am I missing something very obivous here? I do feel like I'm starting to burnout a little.

Thanks

 
Pred, you are getting burned out. ;) The 0.397 is simply (1/4)(2/3)

Q = (1.49/n)(pid2/4)(d/4)2/3(S)1/2

----> 43 = (1.49/.025)(.785d2)(.397d2/3)(.0011/2)

Right?

 
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