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Bernoulli Exercise
6

Bernoulli Exercise

Bernoulli Exercise

(OP)
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?

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

RE: Bernoulli Exercise

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
http://katmarsoftware.com

"An undefined problem has an infinite number of solutions"

RE: Bernoulli Exercise

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.

RE: Bernoulli Exercise

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?

RE: Bernoulli Exercise

(OP)
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

RE: Bernoulli Exercise

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:
https://xkcd.com/169/


RE: Bernoulli Exercise

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 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.

RE: Bernoulli Exercise

(OP)
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

RE: Bernoulli Exercise

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.

RE: Bernoulli Exercise

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
FAQ731-376: Eng-Tips.com Forum Policies
Need help writing a question or understanding a reply? forum1529: Translation Assistance for Engineers


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: http://www.engineering.com/AskForum/aff/32.aspx

RE: Bernoulli Exercise

Then you definitely do not want to ask what the difference is between "there" and "their".

RE: Bernoulli Exercise

(OP)
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

RE: Bernoulli Exercise

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.

RE: Bernoulli Exercise

(OP)
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

RE: Bernoulli Exercise

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:



The question should be in a multiple choice format.




RE: Bernoulli Exercise

Pick the most correct answer, or the least wrong?

RE: Bernoulli Exercise

(OP)
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

RE: Bernoulli Exercise

None of the above?

RE: Bernoulli Exercise

(OP)
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

RE: Bernoulli Exercise

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.

RE: Bernoulli Exercise

Might as well make that average mass flow rate.

RE: Bernoulli Exercise

So basically there is no true numerical solution because you haven't really defined the question??

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

RE: Bernoulli Exercise

IMO, we should be able to recognize the difference between orifice plates and venturi tubes, so when we see an orifice plate, we should not be thinking only about Bernoulli. I couldn't give more than 1/3 credit (at best) for a Bernoulli solution to an orifice plate problem.

RE: Bernoulli Exercise

(OP)
If mass flow rate is constant, then average is nominal and is actual at every cross section. As I said, if you go through the derivation of the API 14.3 gas measurement equations, the first step is Bernoulli (at the orifice). It may offend your sensibilities, but that is the way the equations were developed.

Yes there is an answer.

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

RE: Bernoulli Exercise

184 ft/sec?

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

RE: Bernoulli Exercise

(OP)
Exactly. Did you take more than 16 minutes on it?

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

RE: Bernoulli Exercise

I would simply have assumed that you meant the difference in velocity between the upstream (flow undisturbed by the orifice) and the downstream (far enough downstream that there is no jet remaining from the vena contracta through the orifice). If density negligibly different, the PIPE is clearly the same ID at both ends, and mass flow is constant, then the velocity upstream and far enough downstream is EQUAL, or close enough!

RE: Bernoulli Exercise

(OP)
Taking the suggestions to heart, in the future the exercise will look like



Thanks for looking at it. I don't think any of the comments made a material difference in the class outcome (I would have been very happy if any of the students had raised any of those points instead of the "its too hard" whine), but there are fewer places to find fault with the exercise in lieu of trying to solve it.

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

RE: Bernoulli Exercise

(OP)
MoltenMetal,
I had a guy in Bucharest take that approach a couple of years ago. I told him he wasn't wrong and when we talked on a break it was clear that he was just being a smart ass and knew the exercise was nearly trivial.

I'm still waiting for one of the little darlings to draw a velocity profile and ask "which velocity are you looking for?" Hasn't happened yet. Might happen if the gas measurement section were before this section instead of after it, but so far if any of them ever knew about the velocity distribution across a pipe cross section they have safely stored it in a compartment that they don't go to.

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

RE: Bernoulli Exercise

I worked it out a couple of ways.

I didn't bother looking up the compressibility of air at flowing conditions, but if Z=1.0 I end up with dV=181 ft/s. At Z=0.9 I ended up with dV=172 ft/s.

Took me about 12 minutes but I did the calculation twice in my basement man-cave in the ambience created by a screaming 11-week old Mini-Aussie puppy, using a ruler with my pencil and paper because after 33 years of hating crooked lines separating numerator and denominator, old habits are hard to break.

RE: Bernoulli Exercise

"Ideal venturi" would signal that Cd = 1, and you should get no more vena contracta questions/diversions. Of course, if you do, it gives you additional justification to mentally drop kick them across the room!

Good luck,
Latexman

Technically, the glass is always full - 1/2 air and 1/2 water.

RE: Bernoulli Exercise

(OP)
At 100 psia, air is really close to an ideal gas (Z=1.0). We cover that in Section 1 (this is in Section 4 and if someone forgot the previous day's work there is no hope for them, I warn them that each section builds on the previous and in the exercises they are responsible for what came before). The answer I got (using MathCad and not resorting to numbers until the last step) was 184.065 ft/s. 181 ft/s likely comes from a slightly different value for density (I got 0.492 lbm/ft^3). The key step is:

v1=[(2/15)*(P1-P2)*144/ρ/gc]1/2

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

RE: Bernoulli Exercise

Another assumption would have to be that there is no energy loss across the orifice plate.

Where is the energy loss across the orifice plate factored in? The energy loss is not because of friction.

ASME estimates the pressure drop that is permanently lost with a sharp edged orifice plate varies from about 45% to nearly 100% of the sensed DP based principally on the Beta ratio (d/D). The smaller the Beta ratio the higher the drop. A properly sized orifice plate will typically lose 40% of the sensed DP to permanent pressure loss. This loss is from the turbulence being converted to heat energy.

RE: Bernoulli Exercise

I'm obviously struggling with the unit conversions; I did everything in metric. I get the [2/15*{P1-P2}/r]^0.5 term. The density I used was 7.89 kg/m^3 which is 0.4926 lbm/ft^3. Been in Canada too long. Anyway, 181 versus 184 aside, it's a problem they should readily be able to solve in the time allotted.

RE: Bernoulli Exercise

(OP)
bimr,
The underlying assumptions for Bernoulli are a page long two slides before the exercise. I worked on the API sub-committee that published the permanent pressure drop calculation (it is a bit more complex than a simple conversion of dP to heat). That is one of the reasons that I just looked at upstream and in the plane of the plate. Calculating the downstream pressure would have gotten into all of that rebound effect stuff that has no place in this exercise.

SNORGY,
That is the density I used and got a Δv of 56.087 m/s.

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

RE: Bernoulli Exercise

That's Fast.

RE: Bernoulli Exercise

OK so I did the dP = 20000 Pa; if I do a hard conversion for dP = 3 psi, it is 20684.2 Pa, and then I get your numbers exactly.

RE: Bernoulli Exercise

(OP)
About 6.7 MMSCF/day in a 6-inch pipe, pretty fast, but not outrageous. I would be happy with a 0.5 β tube with 83 in H2O dP at 100 psia. (I didn't see the deleted posts until they were deleted, I'm not sure what is going on with that calculator I played with it for a few minutes but couldn't make heads or tails of the output).

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

RE: Bernoulli Exercise

The output looks more or less correct. I eventually discovered that the input had to be Pa, not kPa. And the velocity is calculated at the approach, not in the throat, so for the 3"/6" it is 4 x 18 something m/s. Anyway the velocity was much higher than what I was thinking. Guess that's why we always used higher Β ratios than 0.5

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