Water resource - Open channel flow

[cantaloup]

Attached you can find 2 open channel problems. They are similar. The first one is from the NCEES sample PE question, page 109. The second one is for you to practice. Take out your calculator, reference book and start your stopwatch, start to solve it.

Obviously if you want to take the exam in October you should know how to solve the problem Hmmm BUT HOW FAST AND ACCURATE CAN YOU DO IT ? I'll discuss a shortcut tomorrow.

PE_question_traperzoid_channel_1.pdf

 

[GTScott]

I used an approximate method and did not get either answer directly on, but based upon the way I leaned in picking some values, I will do with...

1 - D (I calculate it at about 14")

2 - C (I calculate it at about 21")

If your shortcut and my shortcut involve using the same chart, I would love to get my hands on a larger scale version of it.

-GT

 

[Road Guy]

A=(d(b=md) = 2d+3d^2

P=w+2dSQ(1+m^2) = 2+2d(3.1623) = 2+6.32d

R=A/P

Q=[1.49/n]*A*[R^(2/3)][(S)^(1/2)]

plug & chug

5.7 = [2d+3d^2]*[(2d+3d^2)/2+6.32d)]^(2/3)

then I did the "long way" solved for each...and ended up with 5.7=5.9

so D. = 15"

Shortcut sure would be sweet

 

[GTScott]

How long did that take you going the long way?

I did the first one using my shortcut in about 5 minutes (realized I did not really know how to do the shortcut so I had to go back a time or two) and then did the second one in about a minute and a half.

-GT

 

[Road Guy]

I think it took about 8 minutes.

Whats the shortcut?

 

[GTScott]

I think it took about 8 minutes.
Whats the shortcut?

Not sure if the original poster and I have the same shortcut, but I have a table that plots (AR^2/3)/b^8/3 vs. yo/b for circular, rectangular, and trapezoidal (word of the day) channels. It is from Open Channel Flow, Sturm 2001. Sturm was actually my undergrad hydraulics prof - one of the most intellectual human beings you will ever encounter. The table may be elsewhere. I will look.

If there is another shortcut, I would be interested in seeing it.

This question does being up another good point though, everyone should have manning's rearranged based on what you are given...I think I have it for Q (duh), V, and S thus far.

-GT

 

[Road Guy]

I need to program the manning equation in my crappy HP33S to save me some time when I see one of these on the exam, regardless which order I start the problem(solving for the answers) the correct one is always the last one I "plug & chug"

 

[cantaloup]

Shortcut #1 : Using the chart from some hydraulic textbooks, but the answer you get will be approximate.

Shotcut #2 : Using HP33s calc equation solver function. First, store in the calculator the equation. When you encounter a similar problem, bring up the equation in the calculator, punch "SOLVE" button , carefully punch in variables then relax, stretch, yawn and wait for Y (depth) to show up on the screen. Piece of cake huh ?

Attached is the file. Note: this one equation can be used to solve also rectangular shaped, V shaped channel, also solve for width, slope, flow, etc. of the channel.

Trapezoid_channel_depth_HP33s_equation.pdf

 

[GTScott]

Very cool. I had decided against programming this ^&*^* calculator but manning's would not be a bad one to get in there. Thanks for posting all of that.

What were the correct answers? I wanted to see if my approximate method worked out close enough.

 

[cantaloup]

Answer

Question 1 is 15" (14.89" to be precise).

Question 2 is 20" (20.22")

 

[mmmbeer]

Trapezoid_channel_depth_HP33s_equation.pdf ( 0bytes ) Number of downloads: 22

would LOVE to see this attachemnt

but i get an error message when i click on the link!!

can ya help a dude out??

THANKS

!!

 

[Road Guy]

we lost a lot of the attachments when we transfered the board recently