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Crane paper #410 and learning Fluid Mechanics

  1. Jul 31, 2005 #1

    Clausius2

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    First question I want to arise is: what is Crane paper #410?.

    As far as I have looked for it in the web, it seems to be something like a Handbook for those engineers which are involved in fluid flow calculation in professional enterprises. It has lots of tables and formulation (which surely don't enclose any demonstration) Am I correct? I also think it has not got any differential equation into it, in order to avoid engineers a headache when solving a a practical problem.

    Am I right? If I don't, please feedback me with the right information. If I do, I will post later what is my opinion about this book and its undiscriminated use by students and professionals.

    Thanks in advance.
     
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  3. Jul 31, 2005 #2
    crane technical paper no 410

    You're right.
    Crane technical paper no 410 "Flow of fluids through valves, fitttings and pipe" is a handbook for practising engineers with the following contents
    chapter 1: Theory of flow in pipes
    chapter 2: Flow of fluids through valves and fitting
    chapter 3. Formulas and Nomographs for flow through valves, fittings and pipe
    chapter 4. Examples of flow problems
    Appendices contain data fluid properties etc.

    It is not a textbook for students but contains verypractical information
     
  4. Jul 31, 2005 #3

    Q_Goest

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    I'd agree with that, it's a reference for practicing engineers. It's so popular in fact, it's often described as the "bible" of fluid flow.
     
  5. Aug 1, 2005 #4

    Clausius2

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    I think what i am going to say is going to disturb some people. We all know the image that engineers usually project in scientific environments. They usually are guys with no capacity of explaining things which are not explicitly visible with experiments, nor they have little math capacity and they are based on the "know how" method which is based itself upon former practise and which is transmitted from one engineer to another when working.

    The long time I have been walking around PF, every you has been realised I am not an engineer already (I haven't finished my undergraduate yet), nor I wanna be the "usual" engineer I have described above. All my knowledge about my major is based in those things that maybe older engineers don't remember (integrals, Diff equations and theoretics), but on the other hand they have got the power of experience. From my humble point of view, I want to say that such Handbooks are not any bible of Fluid Mechanics, are not any source of learning, and that it is very dramatic to see how some people use it systematically and extract of it formulation they have no idea from where it comes from.

    The bibles of Fluid Mechanics are those who are filled with those things some people don't want to see: Tensors, Differential equations, integrals, and lots of algebra, because It is the esence of Fluid Mechanics Science. Such books are the books of Batchelor or Spurk both about Fundamentals of Fluid Mechanics, in where it lie the true concepts of this Science. I have seen many people here referring to rapid forms or short tables of formulation when an student ask for some question, and I do not think it is a good example to refer them to this kind of naive bibliography, because in Fluid Mech there is no possible short cut when understanding some topic.
     
  6. Aug 1, 2005 #5

    FredGarvin

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    First off, with ANY topic there is going to be a point where your knowledge stops and builds upon someone else's work. That's the nature of the beast. There's absolutely no way that we can all be Ph.D's in every topic that we have to cover on a daily basis. Even other topics you have studied I am sure you do not have the depth of knowledge you are espousing here. Dare I say, it's impossible to have that level of knowledge, especially if one works for a living and is not in academia. Honestly, how many topics in physics, or even thermodynamics, can you say that you have the utmost degree of learning in? There is a point of practicality that one has to say that they are going to make the assumptions that the building blocks for information are correct and not really necessary in 99% of the applications ever seen.

    Now, in regards to Crane's...It all depends on what you deal with on a daily basis. TP 410 is indeed a well known source for information as well as a nice reference of calculations, charts and formulas all in one handy little booklet. You would have to pry it out of my hands to get mine. It is very no holds barred as far as content, but is very complete. The practicing engineer (or anyone else for that matter) would be wise to have it. It does go into basic theory, but stops there. It does not have to go in depth simply because it would be a waste of space and would clutter up the rest of the info. Most of the infor in TP 410 is based on experimentation. This was all done back before numerical solutions of higher end stuff was feasable. It was because of this kind of work that the knowledge engineers used to build plants and pipelines was possible. It seems now a days, the theory based folks, like yourself, are able to now gt solutions for the same problems and are refining the earlier test based solutions as well as new stuff.

    If one is looking at a pipeline or some other installation, in depth boudary layer theory or the derivation of Navier-Stokes are not going to be useful at that level. Piping means getting something from point A to point B as efficiently and as inexpensively as possible. That's where resources like this come in. It's not naieve to appreciate its usefulness or it's level of insight into the realm of fluid mechanics. If anything, I would say it is, on some levels, even better than the theory based books you mention because it is based on real world observations and testing.

    Not to sound condescending, but if you really were to spend some time as a practicing field engineer, you would have a better idea of what is really necessary. I'm not saying that one can or should stop learning. I would never condone that. What I am saying is that there is a point of practicality that a good engineer should be at to be technically proficient.
     
    Last edited: Aug 1, 2005
  7. Aug 1, 2005 #6

    Q_Goest

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    Clausius, I can sympathize with your view. Empirical correlations that are provided by this paper do not stem directly from fundamental principals. How those principals are expressed mathematically, as derivatives, tensors, or straight algebra, really is less of an important feature since the question you raise is really, "Why use empirical correlations over fundamental principals?"

    The information in #410 is not based on the underlying principals, so one may ask, why is it such a widely used and highly recognized and regarded paper? Is it merely because it makes life easy by doing away with the need to solve the Navier Stokes equations? Are engineers just lazy people, or worse, so stupid that they can't figure out how to set up those equations and solve them for the given set of pipes they must analyze that runs hot water to the new bathrooms being built in an apartment building?

    There are of course fundamental principals behind how water behaves in a pipe, how it flows through a valve, how it behaves when going through an elbow, but the question one is quickly faced with outside academia is, "Why is it taking you a month to figure that out? We need it done in 15 to 30 seconds, not days! Your paycheck will reflect on your poor performance!" Or even worse, "CLAUSIUS, YOU'RE FIRED!"

    The poor engineer who has to set up the shower stalls in the new apartment building has little chance to tell his boss how important it is to utilize the Navier Stokes equations to resolve this issue. The poor engineer needs an answer to this issue immediately, and even using a computer to set up the CFD analysis and use his beloved equations based on fundamental principals, his time is not well spent. His boss questions his ability to perform even the simplest of tasks.

    Even more importantly, the engineer's judgment is brought into question. Why would one try to utilize fundamental principals that will require days or even weeks of work on a problem which quite literally should take no more than a few minutes? Once the Navier Stokes equations are resolved, will the engineer go back to basic principals to determine the proper thickness of pipe used? Will the engineer set up an FEA analysis or use Castigliano's theorem to determine wall thickness for a pipe? Does he even KNOW what codes and regulations govern the work he's performing and what equations THOSE regulations require him to use for wall thickness? And how about the thermal analysis for the water heater? How deep is he going to go? The list could go on.

    The fact is, we can't spend as much time on an analysis as we can writing posts to Physics Forum! We are coerced into using the most simple method that can provide an accurate answer by the reality of economics.

    There was a scholarly article published recently in the journal of Science (REF) that looked at the reason for transition from laminar flow to turbulent in a straight section of pipe. That's all it did, it simply tried to determine how and why turbulent phenomena emerges from the laminar condition and why. That's a big question that can't even be easily deduced doing a CFD analysis and fundamental principals. And the transition from laminar to turbulent has a very significant impact on pressure drop in a pipe. Hopefully our faithful engineer setting up those showers will not go to this level of detail. Luckily for him, most pipes are flowing at velocities that quickly set up turbulent flow so the transition is of limited importance in the real world of engineering. Nevertheless, its very important for science to go on and make headway at the most fundamental levels.

    There are two schools of thought regarding teaching students in uni. The one that is used at all the highest level schools is to teach the fundamental principals such as this transition from laminar to turbulent, and let the students learn specific short cuts such as Roark's stress analysis or the Crane paper after they graduate. The other is often used in the schools that typically don't have higher level degrees such as vocational schools. They tend to focus on the practical information such as the Crane paper. Both are useful schools to teach people what they need to know. My brother in law is a tradesman that needs to know how to solder a pipe and fix air conditioners. He's a good man that shouldn't be looked down on because he doesn't know the basic principals of the phase transitions seen in solder or freon. He can run rings around any of us when in a construction environment. And someone armed with the Crane paper will run rings around anyone armed with a CFD analysis when it comes to flow of fluids through valves and pipe. We should never frown upon one cast of society because what they do is different in some way than what we do or how we do it. We're all in this wonderful world together, so we need to understand why some people do it one way and others do it another.
     
  8. Aug 1, 2005 #7

    Clausius2

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    Agreed. I have little to say about this.

    No plant and no pipeline will be >>well<< built if the practicing engineer doesn't know the concept behind it, and in order to acquire the concept no Crane410 has it, but it lies in Batchelor, Spurk, Panton or Landau's books.

    In order to you don't misunderstand my point I will clear my position:

    "A Good student or any apprenticeship in Fluid Mechanics must know very well the basis of the stuff, which only resides in the books I have mentioned above, and never do a short cut looking at handbooks. "

    "A Good engineer must know BOTH things: he must know the practice using such Handbooks, but he has not to use it systematically forgetting all about the deep concepts, because the engineer ONLY CAN DO A WELL USE OF CRANE 410 IF HE HAS READ AND UNDERSTOOD THE THEORY BEHIND IT.

    I think it is enough clear. Surely, during your vast professional experience, you will have seen many guys desgning wrongly fluid systems, despites they surely argued to their bosses: "it was written in the Crane!!!".
     
  9. Aug 1, 2005 #8

    Clausius2

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    That's a pity. Unfortunately it is so. I know what you mean. They will be engineers, but they will never be good engineers, and the probability of failure of their systems will be higher. I don't think a thermal engineer of Nasa could dare to do things in such a way.


    I understand your point. Perhaps being an engineer is very easier than being a good engineer.


    This last way of teaching is the worse way to do it. Such students will know perfectly in which page of Crane is one formula, but they will never have the needed pillars to use it efficiently or in the right way. They will be like big buildings with weak pillars.


    Please, read my reply to Fred. I think I have replied both of you simultaneously. And thanks for participate.
     
  10. Aug 1, 2005 #9

    FredGarvin

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    I do see where you are coming from and, to a certain level, I agree with you. In my profession, when something is labelled a "handbook" it carrys a connotation that it is a guide for someone who already knows what is going on or has been educated in that area, but needs a reference that is handy and cuts right to the chase. Using a handbook to teach from is not the right thing to do. That just produces someone who parrots the contents but doesn't really understand it.

    This statement helped me to understand where you were coming from on this.

    First of all, my experience isn't at the "vast" level yet. However, I do absolutely agree with you. I have seen a lot of engineers that do a huge brain dumps when they get their diplomas. "Why would anyone want to remember all of that crap you learned in school? You won't need it anyways, right?" I have to hear that quite often. It's the deeper knowledge in these topics that make one an engineer/specialist in stead of a technician or the like. Again though, a handbook is a guide. If one doesn't know the proper methodolgy to apply what's in the handbook then there is a problem.
     
    Last edited: Aug 1, 2005
  11. Aug 1, 2005 #10

    Q_Goest

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    I think it's a bit misleading to call the Crane paper merely a reference or handbook. True, it summarizes a vast amount of knowledge and provides a workable method by which to calculate pressure drop, but as both Fred and I have pointed out, it's a resource which has used emperical methods to determine values and organize equations to solve pressure drop and fluid flow problems. Without this, there is no such thing as a method to calculate these things. I dare say that Navior Stokes equations are not only impractical, but they can't even be used in principal. I say this because I'm not aware of any CFD analysis which takes surface roughness into account, though with that, it may be possible in principal.

    So there is no other method by which to calculate pressure drops, flow rates and other phenomena which is based strictly on fundamental principals because it is too complex. I think the problem here is that one needs to review the material and understand it before one can comment on it's validity and how well it serves to educate the individual engineer on basic principals. In fact, it's exactly this issue, it's ability to provide tremendous insight into pressure drop through a system that makes it so useful. Such things as 'friction factors' correspond directly to real world methods of manufacturing pipe. The concept that a bend or elbow, and how sharp that change in fluid direction is, directly affects pressure drop is a powerful understanding that is provided by the text, equations and graphs. The way a valve is designed, be it globe, ball, gate or otherwise, and how it affects the fluid stream is better understood through the Crane paper. And further understanding is gleaned by examining how sudden contractions and expansions affect flow through those restrictions.

    The Crane paper is a bit more than a reference manual or handbook. Yes, it is that for sure. It does provide a vast amount of information used to calculate fluid flow. But it also provides valuable insight into flow that one could not obtain otherwise.

    Take for example a flow problem: The Space Shuttle needs to fill the liquid hydrogen tank in 1 hour, then maintain that liquid level to within 1 percent while the cryogenic fluid boils off. This is a fluid flow problem that's combined with first law thermo, heat transfer and other fields of engineering. The Lockheed Martin engineers that designed the liquid hydrogen transfer system used the basics of the Crane paper, I can assure you. They have a Fortran program (or did as of 9 years ago) that relies very heavily on the Crane paper. Other analysis includes looking at how two phase flow through pipes has been emperically modeled. The only way of determining the pressure drop and flow through that piping system is per the methods of the Crane paper and other additions to it that folks all over the world have created. You can't use anything else. There are no other fundamental principals which can be applied to accurately describe the fluid flow. You can't perform a CFD analysis on it, it would be incomplete and inaccurate. It wouldn't take into account the surface roughness of the pipe walls, though that might be something one could overcome with significant study. And all this wealth of knowledge one can display on a computer screen with pressure drops through each portion of the system giving the engineer a keen understanding of what in the system needs to be adjusted in a matter of minutes whereas the CFD analysis would take a few orders of magnitude longer to accomplish, leave out important information, leave you with an inaccurate result, and leave you with no better understanding of what changes need to be made to the system to ensure the Shuttle tank fueling system meets the requirements.
     
  12. Aug 1, 2005 #11

    Clausius2

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    Don't dare too much. Fluent 6.0 can deal with roughness. And do not dare to say N-S are impracticable with CFD. You have mentioned an example of NASA. I don't think NASA guys are going to base the Shuttle Fuselage design in Crane Papers, nor how a thermal shield heats up with Crane, nor how the fuel flows to combustion chamber through injectors...and so on. I doubt they only trust on empirical data, because NASA is one of the main organisations on the world dedicated to CFD development with cents of self codes made by them.

    I think the main problem here is that i have seen people in PF giving systematically Crane as a reference to students, in addition this people hadn't no idea of the real assumptions behind the formulation they were posting, besides it was wrong which comes to demonstrate the true concepts
    are oxidated lying in some place of their minds. All this people has generated a bad felling in me about Crane, because it seems they only have a superficial knowledge of what they are saying (it is superficial indeed). By the way, i am not going to call this people by their name, because we all know what we post. The next time I see Crane as a reference here given by someone I will read how it is posted carefully, hoping this bad feeling fades away.

    Do not diminish the applications of CFD for real problems. Although I haven't worked in an enterprise yet, I have many friends, family and information at hands that tells me fluid flow enterprises are full of CFD teams which deal with those typical problems as you posted every day. You didn't know about how the roughness is implemented in CFD, so you have also some misunderstanding about what CFD can do and cannot do.
     
  13. Aug 1, 2005 #12

    FredGarvin

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    I guess this is where I am going to have to disagree with you Clausius. Giving Crane as a reference is a very acceptable practice. I HIGHLY doubt you will find anyone else out there that would support your notion that TP 410 is not an acceptable source. I know of many engineers who use it and cite it. The fact that someone who the data is quoted for may not understand the underlying concepts is possible, but, as my profs used to always say "we leave the derivation as an exercise to do on your own."

    There is no way, in 75% of the systems I work, that I can afford the time or have the resources available to sit down and do or have someone do a CFD analysis of a system. Things change much too quickly and the time spent by someone else on the CFD would be, essentially, wasted. Now, if you're talking a large installation, a compressor or equally complicated system, then yes...do the CFD. The time investment in the system warrants it. I am just saying that CFD analysis isn't always a viable option.

    On this same vein, I guess we'll be shelving Machinery's Handbook, Roark's Formulas for Stress and Strain and Mark's Handbook as well? I cite them as others do quite often.
     
  14. Aug 1, 2005 #13

    Q_Goest

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    Clausius, thanks for the info on surface roughness options in Fluent, I stand corrected. Then in principal, one can in fact model a piping system using CFD.

    Regarding the applicability of Crane, please note it is a tool for internal fluid flow, especially for piping systems containing valves and other restrictions. It is not used for flow across a fuselage or external flow. It isn't intended for calculating the pressure distribution inside a turbine or expander either, though it certainly could be used for nozzles and diffusers as long as conservation of momentum and thermodynamic principals are also applied. I've used it as part of an analysis to design an eductor, so it is applicable for other things. I'd recommend you also get a copy and read it through with an open mind. Ask yourself as you go through it if it really is just a handbook filled with equations that give you answers to fluid problems or perhaps you may see the underlying thought and empirical work that went into these correlations and equations. I tend to see the later.

    I also have to question if CFD is good way of understanding the fundamentals of fluid flow. You mentioned:
    A CFD tool such as Fluent does not require the user to understand the basic mathematics behind the NS equations. The entire purpose of CFD is to rid the user of having to resolve innumerable complex equations, and in so doing, one no longer needs to know how to resolve differential equations, tensors, and other higher level math. All the user needs to do is to understand how to apply the tool.

    Please don't misunderstand, I would readily agree that CFD tools are tremendously useful in engineering. Unfortunately, CFD is still a bit too complex for a casual user. I took a class in Fluent, and managed to create a few models with it, but that was 8 years ago. When I went back a month later I found I'd forgotten much of it. Since then, I've never needed to use it sufficiently to become proficient at it and have since dropped using it altogether. Same goes for FEA analysis for example. One really needs to be a regular user, not a casual one in order to become proficient at it. All the folks where I work that can use CFD are very specialized. That's all they do. Similar for FEA folks. There's nothing wrong with that if that's what you want to do, but being a casual user of those tools means you're not going to be effective at using them, and unfortunately, you're not going to be using any of the higher level math skills you learned in college either. If you really want to get into the basic principals and still keep up your higher level mathematical skills, you should consider looking at theoretical studies that allow you to immerse yourself in those equations.
     
  15. Aug 1, 2005 #14

    Clausius2

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    quoting myself, Fred:

    Of course, I am not referring to you. I have been here enough time you are a relatively wisdom man, you know about what you are talking about, and what is the best you never talk about you don't know :smile: (a great quality!).

    Of course, I am not diminishing Crane. Look at my underlined-bolded word "systematically". Abusing of the Crane is the problem. It is an impression I have in my last times over here: rapid short cuts given by someone to studients to short cut and saving time in the process of learning. I am claiming for complementing two stuffs Fred, not for saying only theoretics is God in Fluid Mech.
     
  16. Aug 1, 2005 #15

    Clausius2

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    Ok. I don't think it is in my university library. I will look for it. Surely it is very useful in professional life. Moreover, your recommendation seems to be very sincere. Thanks.

    FALSE!!!!!!!!!! :rofl:

    A good CF dynamicist MUST know what is under all these windows, displays and user functions. To sum up, in order to simulate a problem, choosing a solver method and UNDERSTANDING THE RESULTS the engineer must know what the hell is doing the code just in the depth, looking through the code visual appearance and judging as sharp as possible the results. THESE are the main characteristics that a good CF dynamicist must have.

    A simple guy sat in front of a PC with Fluent could simulate a flow problem, but he surely is unable of interpreting the results because he doesn't know what is employing for solving it, he is unable to find errors carried by the internal method of the CFD code and he is unable to make the best of the code and optimize the time of simulation.

    I have a professor (woman) who is the specialist in numerics in the fluid mech department of my university. I assure to you she knows PERFECTLY the physics and the maths of the flow to be simulated, she knows PERFECTLY what equations are handling the CFD code, and in what way is it going to solve them. She has taught me a lot of times to think as her, in this way of understanding what the hell Fluent is calculating, because it is the only way to actually do it.
     
  17. Aug 2, 2005 #16

    FredGarvin

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    Ahhhh....OK. I do know that I tend to shortcut certain things, especially orifice flows. I'm not usually in the mood to go back through Bernoulli and such to help someone with an orifice flow calc. Anyways, I'm not worried about me. If I shorted an OP's learning then I would expect to be called out for it. Thanks for the compliments!

    The only thing I would add to this discussion then is to echo Q's suggestion to take a look at the book. If not for the brief sections on theorys then for the good amount of empirical data that they have amassed. There is a lot of very useful tabulated data in the pages. There is information on orifices in it that I have only found in one other place (I am sure it is in others though) which would be Miller's Flow Measurement Engineering Handbook.
     
  18. Aug 2, 2005 #17

    brewnog

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    Wow, there's some pretty good discussion going on here chaps!

    I must disagree with this. Any monkey can run a CFD analysis, but it takes a good understanding of the underlying principles not only to interpret the results, but also to know when the outputted results are wrong!

    Many times I have found myself getting lots of pretty pictures from Fluent which look about right, and the numbers seem to make sense, only to have my supervisor point out that I neglected to consider something which would have affected the results drastically. The trouble with CFD is that your results, plots and contours can all look correct, yet be far off the mark, and it takes a very good understanding to be able to do this. This goes for FEA and FDA too.
     
  19. Aug 2, 2005 #18

    Q_Goest

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    Thanks for the comment Brewnog. It seems you and Clausius read that comment in a way not intended. I'm not sure why. I thought it was clear, but perhaps some elaboration is needed.

    Would you say it's the underlying principals that you need to understand (ie: conservation of mass, momentum & energy) or do you actually need to be able to resolve the differential equations that govern those principals yourself? Do you still need to do the math in order to use the program? Do you need to get out pencil and paper, write down differential equations and solve them? Please reread the quote, that's all I'm pointing out here. I'm not suggesting that understanding conservation of mass, momentum and energy, and a handfull of other basic principals aren't necessary. I would of course readily agree that one needs to understand what the computer is doing, and how it is resolving the results from the input. That's something that was brought out in the course I took on it also. The point is that the nuts and bolts of the math itself need not be something one concerns themself with. I hope that clarifies the quote you've referenced.

    Until just 20 or 30 years ago, there was only one way to calculate flow through piping and valves which is what the Crane paper summarizes so effectively. You can't calculate the pressure drop through a piping system by hand without using the equations summarized in the Crane paper, it simply isn't possible. One now has an option, albeit a very cumbersome and limited one. But we can now actually take the differential equations and have a computer perform a numerical analysis on them. This option wasn't even available until relatively recently. So the commentary on NS equations stems from the inference Clausius made here:
    This seems to imply that one needs to use higher level math to understand the basic principals such as Bernoulli's, Darcy, Reynolds number, Compressible fluid flow, choked flow, vena contracta, etc... These are all concepts summerized in basic algebraic equations stemming from fundamental principals too. An engineer doesn't need to use higher level math to determine flow through piping which is what the Crane paper is fundamentally all about. The Crane paper summarizes and provides in a clear and concise format, a large amount of knowledge about internal fluid flow with the exception of those concepts which require higher level math, ie: differential equations stemming most notably from the NS equations.

    I'd highly recommend that students learn the basics of internal fluid flow, and the only way that's done even today is by learning all the fundamental principals that are summarized so well by the Crane paper. Perhaps I really do see these as fundamental principals, though they're not as fundamental as the NS equations and they don't require resolving any differential equations. Does that mean they're not worthy of learning?
     
  20. Aug 2, 2005 #19

    arildno

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    I think I'll side with FredGarvin&QGuest on this issue.
    Although I have a "theoretical" fluid mechanics background,
    (my thesis was about developing an alternative set of shallow water/long wave equations based on Luke's principle of variation), I am as time goes by more impressed by the traditional approach of engineers than I was previously.
    Not denying the value, and indeed necessity, of a solid theoretical understanding of a given problem, so many real-life situations are too complex for theoretical understanding/derivation, so that a hands-on, empirical approach is at least as desirable.
    As I see it, the great revolution with CFD modelling in the latest decades is, in part, our enhanced ability to check more situations than we ever could before, from a financial point of view.
    I am somewhat sceptical whether I would call results gained from CFD analysis THEORETICAL results; rather, they seem to me to be raw data and clues for a theoretical understanding of the problem.
     
    Last edited: Aug 2, 2005
  21. Aug 2, 2005 #20

    Clausius2

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    Ok Qgoest, I have understood your point. Let's try to summarize in order to finish the discussion. Summarizing:

    "The greater the amount of knowledge you have about something the best"

    "The deeper is such knowlegde the best"

    "Each knowledge is divided into two main stages: the principles and pillars, and the practising and applications".

    "The secquence of a correct learning is ALWAYS: i) principles (Batchelor, Spurk, Landau...) and ii) applications (Crane)."

    "The last shown correct learning secquence enhances a good practise in professional life. If some of the two parts are weak, the engineer won't do well his work".

    "Nobody can do anything without passing through and learning the first stage about theoretical principles, no matter how good is the handbook used. If he dares to don't make it so, he will have a lot of errors and misunderstandings in his calculations, no matter Crane or God has said him to do so".

    "If I were a professor I will always begin with books like Landau or Batchelor, because Crane is potentially contained in these books, not being true the contrary. I mean, someone expert in theoretics will spend little time in searching and understanding some topic in the Crane, but someone who don't know the theoretics will find what he was looking for in the Crane, but surely he spend a lot of more time understanding the stuff and probably without success".

    Do you agree with me?.
     
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