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?
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
Katmar Software - AioFlo Pipe Hydraulics
http://katmarsoftware.com
"An undefined problem has an infinite number of solutions"
RE: Bernoulli Exercise
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
RE: Bernoulli Exercise
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
What's the trick?
Not sure this is warranted, but:
https://xkcd.com/169/
RE: Bernoulli Exercise
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
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
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
RE: Bernoulli Exercise
I've been in classes were MSEE students, who were already employed, had trouble with really simple questions.
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RE: Bernoulli Exercise
RE: Bernoulli Exercise
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
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
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
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
RE: Bernoulli Exercise
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
RE: Bernoulli Exercise
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
RE: Bernoulli Exercise
RE: Bernoulli Exercise
Remember - More details = better answers
Also: If you get a response it's polite to respond to it.
RE: Bernoulli Exercise
RE: Bernoulli Exercise
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
Good luck,
Latexman
Technically, the glass is always full - 1/2 air and 1/2 water.
RE: Bernoulli Exercise
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
Good luck,
Latexman
Technically, the glass is always full - 1/2 air and 1/2 water.
RE: Bernoulli Exercise
RE: Bernoulli Exercise
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
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 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
Good luck,
Latexman
Technically, the glass is always full - 1/2 air and 1/2 water.
RE: Bernoulli Exercise
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
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
RE: Bernoulli Exercise
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
RE: Bernoulli Exercise
RE: Bernoulli Exercise
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