Bernoulli Exercise 6

[zdas04]

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

 

[BigInch]

Might as well make that average mass flow rate.

 

[LittleInch]

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.

 

[BigInch]

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.

 

[zdas04]

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

 

[Latexman]

184 ft/sec?

Good luck,
Latexman

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

 

[zdas04]

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

 

[Latexman]

No, it took me about 5-10 minutes. A two equations, two unknowns kind-of-thing. I attached my calcs.

Good luck,
Latexman

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

 

[moltenmetal]

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!

 

[zdas04]

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

 

[zdas04]

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

 

[SNORGY]

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.

 

[Latexman]

"Ideal venturi" would signal that C_d = 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.

 

[zdas04]

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/g_c]^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

 

[bimr]

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.

 

[SNORGY]

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.

 

[zdas04]

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

 

[BigInch]

That's Fast.

 

[SNORGY]

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.

 

[zdas04]

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

 

[BigInch]

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