NCEES 2011 Problem 510 (WR/E)

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matt267 PE

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Question 510 states:

The figure shows a sluice gate in a 35-ft rectangular channel. At Section 1, Y1 is 3.8 ft and the velocity is 50 ft/sec. The Froude number at Section 2 is most nearly:

To solve, I used this equation to find Y2:

01.png (edit: d1=y1)

and this equation to find the Froude number:

02.png

I got Fr=6.83 which is wrong.

The solution used this formula to solve for Fr1:

03.png

This formula to solve for Y2:

04.png

This to solve for V2:

05.png

and this to solve for Fr2:

06.png

They got Fr2=0.31

Can anyone provide some insight on why my method was wrong?

 
Last edited by a moderator:
@matt267,

For a rectangular channel with Fr2, the equation is d1/d2 (not d2/d1 as you typed.)

You were using the wrong equation.

Harry

 
Last edited by a moderator:
Harry,thanks for the reply. You are absolutely correct.

FYI to others: I used equation 19.92 and 19.93b from the 13th edition of the CERM to get the correct answer.

Thanks again Harry!

 
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