Critical depth in open flow trapezoidal channel

[DuckFlats]

This problem requires using the solve function on the calculator. My Casio fx-115ms will solve the equation, but only gives one value, when typically there are multiple answers. I cannot figure out how to show both answers. Should I expect to see an open flow problem asking for critical depth on a trapezoid? It seems like that question is testing your calculator more than your knowledge. Especially because it takes about 30 seconds for the calculator to even give an answer. 

 

[matt267 PE]

Should I expect to see an open flow problem asking for critical depth on a trapezoid?

This type of question is fair game on the exam. What references are you using for open channel flow? There are equations, table, and charts that can provide the critical depth for you. (I don't have them in front of me at this time.)

 

[DuckFlats]

I am using the equation: Q^2/g=A^3/T, I am given b, water depth,Q and that it is a trapezoid. With 3:2(h:v) slopes.

 

[DuckFlats]

And I realize you can essentially guess a critical depth and solve by trial and error, but that seems time consuming compared to equation solver on the calculator.

 

[matt267 PE]

What are you using for an open channel reference?

There is a chart and a table that I studying with that allowed me to find the critical depth without have to use the equation solver. With out that, trial and error might be the best bet for the exam.

 

[matt267 PE]

Check out this page: http://astonishingengineering.com/power/hydro/hydraulic-energy-dissipators/296-criticai-depth-determination.html

the graph on the bottom is similar to what I used while studying.

 

[DuckFlats]

Printed! Thanks a lot. My calculator actually started giving the correct answer. But that chart is much better to use. Trial and error would waste some valuable time

 

[matt267 PE]

Excellent. Good luck on the exam.

 

[civilized_naah]

 

[civilized_naah]

Check:

For depth d = 3.096 ft

Top width T = 12 + 2x2x3.096 = 24.384 ft

A = 3.096 x 18.192 = 56.322 ft2

A3g = 5.753x106

Q2T = 6.096x106

5% difference

Exact answer d = 3.147 ft

 

[ptatohed]

Dr. G., You're alive!