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Bernoulli Exercise 6

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zdas04

Mechanical
Jun 25, 2002
10,274
I recently had a class full of engineers (range from 6 months to 22 years experience with the average around 6 years) try to work this exercise. The comments were mostly "its too hard" and "you didn't give us enough information". I allowed 16 minutes for them to work on it and let them work in groups (I'm too easy). I figured that most of the class would finish in less than 5 minutes and have a long break. When no one was finished in 16 minutes I gave them a 15 minute break and let them continue if they wanted. After 31 minutes there was still no solution (this exercise comes at the end of a discussion of the Bernoulli Equation so they have that equation on the previous page).

Is it really that hard a problem for practicing engineers? Do I need to dumb it down for the little darlings?

Exercise04-1_lc8pwn.jpg


David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
 
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David, between which two planes are you looking for the change in velocity? If it is between the planes through the tapping points P1 and P2 then I do not think Bernoulli is the right tool to use. In fact, I don't think Bernoulli has a lot to do with pressure drop through orifices at all.

Katmar Software - AioFlo Pipe Hydraulics

"An undefined problem has an infinite number of solutions"
 
A trick question?

If density is the same the velocity through the centre of the orifice compared to some distance either side of the orifice is going to be 4 times as much (3^2)/(6^2) ??

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
 
It's mathematics and if you do not have to work with formulars with more than one unknown every few weeks.... Hey, you forgot what you learned years ago at the university. But it surprises me that nobody found the solution and NO, I do not think it is too difficult for a class of engineers who can work in groups. Was it the first time that this happened?
 
Katmar,
If anyone had asked that question I would have given them full marks, but they all assumed that the upstream plane was "infinitely far upstream of the orifice" (i.e. a couple of inches) and the second plane was at the plane of the orifice plate. This is the configuration used to develop gas measurement equations, and that derivation starts with Bernoulli and adjusts for real exit effects.

LittleInch,
Good first step (that is the step that no one got), but the question is looking for a velocity difference.

micalbrch,
This was the first time that No One got past the step that LittleInch found in 30 seconds. Usually about half the groups get that far from the continuity equation (i.e., mass flow rate and density are constant, so the relative velocity known and Bernoulli becomes an equation with one unknown). This time I was shocked that they all worked diligently for 30 minutes and no one made it through the first step.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
 
I got to where LittleInch is immediately, i.e. v(2)=4*v(1). I couldn't figure out the answer without the density.
What's the trick?
Not sure this is warranted, but:
 
I agree with Katmar...

Sorry LI, you're close, but it is not 4X. The velocity through an orifice is measured at the Vena Contracta which is less than the 3" diameter of the hole
Flow_across_orifice_plate_imom9w.png
in the orifice plate and is a function of a number of parameters. We can't do this problem, due to lack of details concerning the orifice plate. It kinda looks like a sharp-edge orifice, but it could be a square-edge orifice. Technically the thickness of the orifice also can have some bearing on the answer as well. OK maybe it is a thin plate, but you didn't tell us enough to estimate orifice plate effects, diameter of the vena contracta, or its discharge coefficient. In fact those formulas don't look quite right either, because as I recall the ratio of orifice diameter to pipe inside diameter also has an effect and all I see there is diameter of the orifice.

Maybe you want to change the problem to a venturi tube in laminar flow with two pressure taps. It doesn't demand quite so much attention to detail.
 
jgailla,
The there is enough information to calculate the gas density (and since density is given as constant, the course recommends using a simple average pressure).

BigInch,
You didn't quite get that right. As you say, the minimum flow area is at the vena contracta, which is smaller than the bore of the square-edged orifice. That doesn't mean you cannot calculate a velocity in the plane of the orifice plate, just that a velocity calculated there will not be a maximum (this physical reality is one of the main drivers for why the API 14.3 equations do not look like Bernoulli and β-ratio is a big deal in 14.3, but not here). If any of the students (who couldn't get rid of the second velocity term if they assumed that they should use the plane of the plate, remember) had raised that point I would have been encouraged, but they didn't.

Also, this problem is air flow, and the calculation for the vena contracta in a low velocity gas stream is different from water. And is the nomenclature in your image right? "SG: water gravity in kg/m3)"? That makes the units in the radical really messy (but the square root of kPa is pretty messy all by itself). Water "Specific Gravity" is usually defined as density/1000 kg/m3 or density/62.4 lbm/ft3, so SG doesn't have units.

Any equation with a discharge coefficient is empirical. The course was still looking at closed form equations at that point. The next section gets deeply into empirical equations and real responses.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
 
Nice try zdas. Then you didn't say, change in velocity from where to where, did you? Vena contracta is the default unless stated otherwise, as we're usually interested in the maximum velocity attained, no others being of any importance. The change in velocity is different at each point along its path, as the fluid accelerates through the orifice, or did all that happen magically too? Come on ... accept it. It's a flawed question.
 
Having bad students isn't anything new; the question is always nature, or nurture?

I've been in classes were MSEE students, who were already employed, had trouble with really simple questions.

TTFN
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Need help writing a question or understanding a reply? forum1529


Of course I can. I can do anything. I can do absolutely anything. I'm an expert!
There is a homework forum hosted by engineering.com:
 
Then you definitely do not want to ask what the difference is between "there" and "their".
 
BigInch,
No I didn't specify the planes and if anyone had said "indeterminate because you didn't specify the two planes" or "zero, since I picked both planes in the 6-inch pipe", I'd have given them full marks. By saying that ID1 is 6-inch and ID2 is 3 inch, a reasonable person (including everyone who has ever taken this class) would assume that they could use those two numbers rather than reaching for extra hoops to jump through.

I can't find where I messed up "there" and "their". Just call me illiterate.


David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
 
Sorry I didn't say you used their/there. Just a general comment.

I did more than a few years designing power station fuel gas delivery installations, well production measuring stations, gas pipeline interconnection sales stations, town border laterals, tie-ins and meter stations, including specifying lengths of tubes, flow straighteners and precise, machined IDs of tubes and sizes and thicknesses and beta ratios of orifice plates in Daniel flowmeters, so I do slightly remember that "theirs" a pronounced difference between orifice plates and venturi tubes. Change it to a venturi problem and I won't argue any more about it.
 
Yeah, I filled in as Amoco's Denver Region measurement engineer for a couple of years while management didn't think we needed one (an extra assignment that had me going to the International School of Hydrocarbon Measurement 4 yeas in a row). I also did some consulting with one of the API 14.3 sub committees a couple of times when an Amoco guy chaired the sub committee. Also presented a meter proving paper at Southwest Research, and tested several meter skids at CEESI. It is an area where I remain interested, but I haven't installed a new Daniels Square Edged Orifice Meter in 15 years. My go to meter today is V-Cone because they are self conditioning.

I'll look at changing it to a converging/diverging nozzle. If I do, I'll clearly define the planes of interest.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
 
Regarding "That doesn't mean you cannot calculate a velocity in the plane of the orifice plate"

You question does not actually state where the velocity should be calculated.

Here is a better image:

figure2104_ezeffd.jpg


The question should be in a multiple choice format.
 
Pick the most correct answer, or the least wrong?
 
bimr,
Some of these "kids" are pretty sure that their jobs should be multiple choice. I don't think it helps them to pander to that. I was "nice" on this exercise in that I gave them everything they needed with no extra info (unusual in this course). No one cares what the answer is (least of all me), I want them to set up the problem and develop their assumptions and solution steps. If they miss a required gc or cancel feet with inches they get an answer far different from the rest of the class and most of them will work really hard to find their error. That makes for a learning experience. Guessing "C" doesn't really do that.

The pre-test is multiple choice because I don't have time between when I have the student list and the first day of class to grade a real engineering test. If anyone wants to give it a try, send me an e-mail (address is on my web page). Being multiple choice doesn't seem to help much since the average score has been 37% so far.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
 
I think that works with most bosses something on the order of zero times.

David Simpson, PE
MuleShoe Engineering

In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, Italian Physicist
 
The only quibble that I would have with the question is to say that the mass flow rate is the same at every "cross-section in the pipe" rather than "every point" in the flow". However, every engineer should realize that without needing to be told.
 
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