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Using formula without knowing it. 7
- Thread starter 19652022
- Start date
EnglishMuffin
Mechanical
Greg Locock : I am going to get hammered if I keep replying to these off topic things, which I always find more interesting than the original questions. I think I see what you are getting at. It presumably all comes down to the problem the Pythagoreans had with irrational numbers. I don't see an issue with the area of a specific square associated with a line of length L1 being L1^2. I think the problem comes when you define another line of irrational length relative to the first, and try to prove that the relative areas associated with the two lines are in the ratio L1^2/L2^2. I think all this has been rigorously figured out by mathematicians, but as I (sort of) suggested before, you do have to be careful about mixing geometry and algebra if you want a rigorous Euclidean style proof.
- Thread starter
- #42
Surely we must recognise a difference between mathematical theorems like the cosine rule, trig identities, roots of a quadratic equation etc. which can be derived logially from basic axioms and engineering formulae which are approximate mathematical models of physical systems. In the latter case it is essential to know what assumptions were made in the derivation of the formula even if you don't actually know how to derive it.
If I wanted to know how much tip force is required to deflect a cantilever box beam (length 1m and cross section 0.2 x 0.2 m made of 2mm thick steel) by 0.1 m, I could plug the numbers into a formula derived from Euler beam theory and get an answer. It would be a very wrong answer however (because of assumptions about small displacements, linearity of stress-strain relationships - Hooke's law, Neglecting 2nd order terms in strain-displacement relationships - Love's elasticity postulates, omission of shear deformation effects etc. etc.).
OK, this is an extreme example, but I can think of plenty of others.
M
--
Dr Michael F Platten
If I wanted to know how much tip force is required to deflect a cantilever box beam (length 1m and cross section 0.2 x 0.2 m made of 2mm thick steel) by 0.1 m, I could plug the numbers into a formula derived from Euler beam theory and get an answer. It would be a very wrong answer however (because of assumptions about small displacements, linearity of stress-strain relationships - Hooke's law, Neglecting 2nd order terms in strain-displacement relationships - Love's elasticity postulates, omission of shear deformation effects etc. etc.).
OK, this is an extreme example, but I can think of plenty of others.
M
--
Dr Michael F Platten
casseopeia
Structural
speaking of off-topic, 19652022, is your handle a partial phone number or did your cat walk across your keyboard as you typed in your profile? I've been wondering ever since your original post.
ps, as someone who recently went back to school, and had to re-learn formulas and concepts, I find I enjoy learning where something comes from and how a formula was derived. I'm no longer satisfied to learn just enough to get the grade I need if it means compromising a real understanding.
"If you are going to walk on thin ice, you might as well dance!"
ps, as someone who recently went back to school, and had to re-learn formulas and concepts, I find I enjoy learning where something comes from and how a formula was derived. I'm no longer satisfied to learn just enough to get the grade I need if it means compromising a real understanding.
"If you are going to walk on thin ice, you might as well dance!"
I, like Cass, am going to school to get the ABET degree. I have worked in the engineering, surveying field for 30+ years and have worked both inside (designing) and out (making the design work). The problem to me with school is with the example, problems, etc. being so otherworldly with their intended content. It has actually hurt me that I have the real world experience. I will work the problem and the answer will be ‘the flywheel turns 90 billion RPM.’ I know in my heart that this cannot be right, so I will try reworking the problem and again…. The problems that bug me are working out everything on the computer when the back of an envelope will do (knowing how to work the numbers correctly but not knowing what they mean) and not knowing what the builder need from the design people. Example – designing the CL of a manhole down to a eighth of an inch not knowing that they are normally put in to the nearest 6 inches or so.
John
John
GregLocock
Automotive
Those who can, do.
Those who can't, teach.
Those who can't teach, lecture
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
Those who can't, teach.
Those who can't teach, lecture
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
ColourfulFigsnDiags
Chemical
There seems to be a lot of egos floating around in this thread ... "Why do I need to know where it came from to be able to use it?"
Fair question ...
Of course you can use equations / formulae without knowing where they come from, or how they are derived ... but only a poor engineer would do so.
For example, I look up a text book, it says that the average velocity of a fluid flowing in a pipe Vave=0.5* Vmax.
That formula is true.
But if you didn't know where it came from, you wouldn't know that it is only applicable for laminar flow.
It is IMHO VERY important for students to learn the fundamentals. From the fundamentals you can derive what you need. They give you a better physical understanding of what is actually happening, in this case momentum transfer between the walls of the pipe and the fluid, and viscous transport of momentum within the fluid.
In my mind, universities / teaching institutions teach people how to teach themselves - they are not in the buisniness of mass producing people who will enter the workforce and immediately able to do the same job as someone there for 20 years. Therefore AFAIC, universities SHOULD teach the fundamentals, and engineers SHOULD make it their buisiness to know, at least in general, where the equation came from.
Comments like "Those who can't, teach." are very tiresome and juvinille. They imply a certain amount of arrogant snobery ... get off your high horse.
By the way, I'm a process engineer, not a teacher.
Read the Eng-Tips Site Policies at FAQ731-376
Fair question ...
Of course you can use equations / formulae without knowing where they come from, or how they are derived ... but only a poor engineer would do so.
For example, I look up a text book, it says that the average velocity of a fluid flowing in a pipe Vave=0.5* Vmax.
That formula is true.
But if you didn't know where it came from, you wouldn't know that it is only applicable for laminar flow.
It is IMHO VERY important for students to learn the fundamentals. From the fundamentals you can derive what you need. They give you a better physical understanding of what is actually happening, in this case momentum transfer between the walls of the pipe and the fluid, and viscous transport of momentum within the fluid.
In my mind, universities / teaching institutions teach people how to teach themselves - they are not in the buisniness of mass producing people who will enter the workforce and immediately able to do the same job as someone there for 20 years. Therefore AFAIC, universities SHOULD teach the fundamentals, and engineers SHOULD make it their buisiness to know, at least in general, where the equation came from.
Comments like "Those who can't, teach." are very tiresome and juvinille. They imply a certain amount of arrogant snobery ... get off your high horse.
By the way, I'm a process engineer, not a teacher.
Read the Eng-Tips Site Policies at FAQ731-376
SomptingGuy
Automotive
I'd say that those who can't, make bad teachers.
I'm married to a teacher: I'm allowed to say it!
In honesty I couldn't do her job any more than I could fly. I've got neither the patience nor the self control to get through a day trying to educate disinterested kids. I'd end being arrested before the first day finished. Good teachers are worth their weight in gold. Bad teachers can kill a kid's interest in a subject so easily.
There is an element of truth in the "Those who can't, teach" comment because teaching pays less than industry, and the most able will be attracted to the higher paid positions. Those that are left are either the also-rans or those who just really want to teach. My wife is the latter - devoted to her job.
----------------------------------
One day my ship will come in.
But with my luck, I'll be at the airport!
In honesty I couldn't do her job any more than I could fly. I've got neither the patience nor the self control to get through a day trying to educate disinterested kids. I'd end being arrested before the first day finished. Good teachers are worth their weight in gold. Bad teachers can kill a kid's interest in a subject so easily.
There is an element of truth in the "Those who can't, teach" comment because teaching pays less than industry, and the most able will be attracted to the higher paid positions. Those that are left are either the also-rans or those who just really want to teach. My wife is the latter - devoted to her job.
----------------------------------
One day my ship will come in.
But with my luck, I'll be at the airport!
ScottyUK,
My spouse is not a teacher but I know of many colleagues' wives that are. I was led to believe in the past that teachers (K-12) make low salaries. However, when considering their salary at an hourly rate, it is not bad at all (Factor in three months summer vacation, one month winter vacation, a week of spring break and most national holidays).
Many engineering professors have double income being a teacher and consulting in their field outside the university. Not a bad deal.
For an engineering career, the job gets progressively more challenging as one becomes more experienced, teaching career appears to get easier.
My spouse is not a teacher but I know of many colleagues' wives that are. I was led to believe in the past that teachers (K-12) make low salaries. However, when considering their salary at an hourly rate, it is not bad at all (Factor in three months summer vacation, one month winter vacation, a week of spring break and most national holidays).
Many engineering professors have double income being a teacher and consulting in their field outside the university. Not a bad deal.
For an engineering career, the job gets progressively more challenging as one becomes more experienced, teaching career appears to get easier.
- Thread starter
- #57
Casseiopapea,
This is just my Id i prefer.
Whiyun,
I think you should understand the formula you are using whether you can derive it yourself or somebody has derived it.
Thaanks a lot for all participants. Thanks a lot for ENG-TIPS Forum for such a live and interesting discussion.
This is just my Id i prefer.
Whiyun,
I think you should understand the formula you are using whether you can derive it yourself or somebody has derived it.
Thaanks a lot for all participants. Thanks a lot for ENG-TIPS Forum for such a live and interesting discussion.
GregLocock
Automotive
Einstein said
We can't solve problems by using the same kind of thinking we used when we created them.
Excellent
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
We can't solve problems by using the same kind of thinking we used when we created them.
Excellent
Cheers
Greg Locock
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.
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