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Using formula without knowing it. 7
- Thread starter 19652022
- Start date
I’d disagree.
Take for example Manning‘s Equation for flow in pipes. It is an emphatical formula so you cannot derive it.
You don’t need to understand how he came up with that formula only that it works.
You do need to know the limitations and constraints on the formula and when and more importantly when not to use it, but you don’t have to be able to develop it from experimental evidence.
Rick Kitson MBA P.Eng
Construction Project Management
From conception to completion
Take for example Manning‘s Equation for flow in pipes. It is an emphatical formula so you cannot derive it.
You don’t need to understand how he came up with that formula only that it works.
You do need to know the limitations and constraints on the formula and when and more importantly when not to use it, but you don’t have to be able to develop it from experimental evidence.
Rick Kitson MBA P.Eng
Construction Project Management
From conception to completion
I agree with Rick. Sometimes the necessity use a complicated formula greatly outweighs the need to understand it's derivation.
Reiterating Rick's 2nd point. It is VERY important, to understand when and where a formula applies. Otherwise, GIGO...
Wes C.
Reiterating Rick's 2nd point. It is VERY important, to understand when and where a formula applies. Otherwise, GIGO...
Wes C.
Emphatical = empirical?
Anyway, most formulae have a derivation or proof available either in a textbook or on the net. Someone who has a reasonable standard of maths should be able to follow most of them. Are there any in particular you can think of?
I use Laplace transforms now and then, and I'm damned if I can remember how they're derived. I've a book of standard transforms, and I've never considered proving them from first principles. These days I would probably experience a brain meltdown if I tried!
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One day my ship will come in.
But with my luck, I'll be at the airport!
Anyway, most formulae have a derivation or proof available either in a textbook or on the net. Someone who has a reasonable standard of maths should be able to follow most of them. Are there any in particular you can think of?
I use Laplace transforms now and then, and I'm damned if I can remember how they're derived. I've a book of standard transforms, and I've never considered proving them from first principles. These days I would probably experience a brain meltdown if I tried!
----------------------------------
One day my ship will come in.
But with my luck, I'll be at the airport!
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- #5
The statement
Is elitist BS foisted upon generation after generation of unsuspecting college students. No one has ever found a closed-form solution to Navier-Stokes. The Euler Equation made some extremely limiting assumptions (such as incompressible flow and zero friction) to solve part of it. Bernoulli added some of his own fantasy's to Euler to come up with the famous "Bernoulli Equation". Most people who can "derive" the Bernoulli Equation forget the assumptions that Euler and Bernoulli were very careful to explicitly state.
Self-important berks who say "if you can't derive it, you shouldn't use it" do a significant disservice to their students.
Having completed that rant, it makes me very sad to see someone taking an empirical equation from a book and applying it without first asking "where does this apply?" I talk to Oil & Gas engineers every day about multi-phase flow in a vertical conduit. The most common correlation is called "Turner". Mr. Turner did his research at elevated pressures and in his landmark paper said that it is not appropriate to extrapolate his work outside of the pressure/temperature ranges where he did his experiments. Engineers feel like they're doing good work when they apply his equation 1,000 psi lower than his experiment.
I would restate the basic premise of this thread with: "If you haven't verified that the assumptions and universe of an equation, don't use it."
David
Is elitist BS foisted upon generation after generation of unsuspecting college students. No one has ever found a closed-form solution to Navier-Stokes. The Euler Equation made some extremely limiting assumptions (such as incompressible flow and zero friction) to solve part of it. Bernoulli added some of his own fantasy's to Euler to come up with the famous "Bernoulli Equation". Most people who can "derive" the Bernoulli Equation forget the assumptions that Euler and Bernoulli were very careful to explicitly state.
Self-important berks who say "if you can't derive it, you shouldn't use it" do a significant disservice to their students.
Having completed that rant, it makes me very sad to see someone taking an empirical equation from a book and applying it without first asking "where does this apply?" I talk to Oil & Gas engineers every day about multi-phase flow in a vertical conduit. The most common correlation is called "Turner". Mr. Turner did his research at elevated pressures and in his landmark paper said that it is not appropriate to extrapolate his work outside of the pressure/temperature ranges where he did his experiments. Engineers feel like they're doing good work when they apply his equation 1,000 psi lower than his experiment.
I would restate the basic premise of this thread with: "If you haven't verified that the assumptions and universe of an equation, don't use it."
David
I would say anybody who is not familiar with the concepts behind Bernoulli's equation would quickly get lost in head losses due to friction. Laminar or turbulent flow (Reynold's number) or kinematic and absolute viscosity are concepts that a person using the formula must understand. The derivation of the horsepower in the pump/motor gains and losses is also something that must be understood. Tell someone that all the entities are in feet or meters and watch a puzzled look come over their face.
Someone using complex formulas must have an understanding of the subject.
Someone using complex formulas must have an understanding of the subject.
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- #8
EnglishMuffin
Mechanical
Consider what happened in the Columbia tragedy. NASA knew that a large chunk of foam had come off and hit the wing at 400 mph, and they knew how roughly how large and how heavy the piece was. While the shuttle was in orbit, they decided to check and see whether the foam strike was likely to have done serious damage, so they got hold of an engineer at Lockheed and asked him to run some calculations, which were reportedly executed on an Excel spreadsheet. He used an empirical formula developed many years before by others, which he was apparently unfamiliar with, and which was intended to apply only to very small objects (such as micro-meteorites) hitting the foam. This gave a completely erroneous (and highly optimistic) answer, presumably because the mass of an object increases as the cube of the leading dimension, but the projected area increases as the square. Now I am not saying that it would have made any difference if this guy had found the correct answer, and it's easy to be wise after the event, but I think some would agree that it is food for thought.
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- #9
A mathematical equation is nothing more that a model that gives approximate quantities to a situation between limits. As an engineer you 'must' be able to 'reason' with the result and situation to which it is applied.
I disagree with the view that you must be able to derive each equation in order to use it. An understanding is enough and let reference books do their job when more is needed
The golden rule 'If in doubt ask'.
I disagree with the view that you must be able to derive each equation in order to use it. An understanding is enough and let reference books do their job when more is needed
The golden rule 'If in doubt ask'.
SomptingGuy
Automotive
In some cases it can be better to remember where formulae come from rather than try to remember the formulae themselves. Two examples from acoustics/DSP:
1) The relationship between frequency, wavelength and the speed of sound. It's a simple relationship best derived each time you need it.
2) How to calculate the frequencies associated with data points following a DFT.
In both cases the formulae are trivial, but I often see people trying to look them up in books rather than understand them.
1) The relationship between frequency, wavelength and the speed of sound. It's a simple relationship best derived each time you need it.
2) How to calculate the frequencies associated with data points following a DFT.
In both cases the formulae are trivial, but I often see people trying to look them up in books rather than understand them.
You really need to know the underlying assumptions and the intended applications of formulas, equations and even codes before you use them. Many times the assumptions are not clearly stated when the formulas are presented. Think about the TV commercial when the customer comes back with a car exhaust system that doesn't fit. The parts counter states "Book says it fits". Exactly what we don't want to do as engineers.
DrillerNic
Petroleum
I don't think you have to know what the formula is or how to derive it, but you do have to know when it is applicable, and what assumptions are included in teh use of that formula: English Muffin's example above shows what happens when you just plug numbers into a formula without knowing it's limits.
The best ocurse I ever did on multiphase flow in pipes was one given by a software manufacturer on their vertical lift programme for the oil & gas industry. The software came with a whole host of different correlations& the guy gave a sheet isting the applicability of each correlation: 'limited to small diameter pipes', 'limited to GOR below 500', and so on. So now I know to use the Fancher & Brown correlation as this usually gives the lowest pressure loss, and Duns & Ross as this usually gives the highest pressure loss as a check on the data, and then to start actually loking a the results instead of picking the first correlation on the drop down list and designing off those results....
The best ocurse I ever did on multiphase flow in pipes was one given by a software manufacturer on their vertical lift programme for the oil & gas industry. The software came with a whole host of different correlations& the guy gave a sheet isting the applicability of each correlation: 'limited to small diameter pipes', 'limited to GOR below 500', and so on. So now I know to use the Fancher & Brown correlation as this usually gives the lowest pressure loss, and Duns & Ross as this usually gives the highest pressure loss as a check on the data, and then to start actually loking a the results instead of picking the first correlation on the drop down list and designing off those results....
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- #13
moltenmetal
Chemical
Elitist argument like this is what forces unnecessary, obsolete analytical mathematics on generations of new engineers while important, useful subjects go untaught for lack of available course time! We spend so many lectures getting people to the state of the art of mathematics in the early 18th century, and then we sell this as a rite of passage to new engineers and a means to teach them to "think". Hogwash!
Clearly, an engineer has a responsibility when using someone else's work (whether that be equations, correlations, experimental data, drawings, specifications etc. etc. is irrelevant) to make themselves aware of the limits of applicability of the work in question. Being able to derive the equations yourself is going above and beyond the call of duty in most cases.
Clearly, an engineer has a responsibility when using someone else's work (whether that be equations, correlations, experimental data, drawings, specifications etc. etc. is irrelevant) to make themselves aware of the limits of applicability of the work in question. Being able to derive the equations yourself is going above and beyond the call of duty in most cases.
Pythagorus is credited with the proof that the square on the hypotenuse is the some of the squares on the other two sides.
He provided the proof but the relationship was known and used for centuries before that.
I doubt if every user was able to derive the relationship and until Pythagporus, no one could prove it which, importantly, presumably meant that no one could say for sure if there were situations when it didn't apply.
Perhaps we should recognise that deriving somthing is very much more difficult than re-creating it and perhaps this would be a better way to consider some equations. That is, you don't need to have the same creative genius to develop the equation in the first place but might, perhaps, be expected to be familiar enough with recreating the equation or its shape, without all the proofs that go with it. I should also hope to have sufficient familiarity with any equation I use regularly to develop a "feel" for the conditions where it can be used and the results I would expect. One trick taught to me was to do approximations to develop that feel i.e. to use easily calculated order of magnitude values to arrive at a "ball-park-figure" then do the actual calculation and make sure the result obtained was within the expected range of values.
JMW
He provided the proof but the relationship was known and used for centuries before that.
I doubt if every user was able to derive the relationship and until Pythagporus, no one could prove it which, importantly, presumably meant that no one could say for sure if there were situations when it didn't apply.
Perhaps we should recognise that deriving somthing is very much more difficult than re-creating it and perhaps this would be a better way to consider some equations. That is, you don't need to have the same creative genius to develop the equation in the first place but might, perhaps, be expected to be familiar enough with recreating the equation or its shape, without all the proofs that go with it. I should also hope to have sufficient familiarity with any equation I use regularly to develop a "feel" for the conditions where it can be used and the results I would expect. One trick taught to me was to do approximations to develop that feel i.e. to use easily calculated order of magnitude values to arrive at a "ball-park-figure" then do the actual calculation and make sure the result obtained was within the expected range of values.
JMW
Perfect example.
How many here have ever used the Pythagorus’s Theorem and how many can derive/prove it?
I have and I can’t.
Rick Kitson MBA P.Eng
Construction Project Management
From conception to completion
How many here have ever used the Pythagorus’s Theorem and how many can derive/prove it?
I have and I can’t.
Rick Kitson MBA P.Eng
Construction Project Management
From conception to completion
I've heard similar and I'm sure the person had good intentions.
Isn't the saying similar to "If you can't design a structural member size by hand, do not use a computer program." For this instance, I would agree with the statement.
It is also similar to "If you can't calculate by hand, do not use a calculator." I would partially disagree. I wouldn't dare hand calculate a square root of any number to the hundredths.
I agree strongly with wes616 about GIGO. It is important to understand where and how a particular formula should be applied.
Time is more of the essense than it was in the past. Computers definitely can reduce the design time. It would be wrong as engineers to rely on input-output without fully realizing the capabilities and limitations of any software.
I believe the person who said the above statement had good intentions and wouldn't take it too literally...
Isn't the saying similar to "If you can't design a structural member size by hand, do not use a computer program." For this instance, I would agree with the statement.
It is also similar to "If you can't calculate by hand, do not use a calculator." I would partially disagree. I wouldn't dare hand calculate a square root of any number to the hundredths.
I agree strongly with wes616 about GIGO. It is important to understand where and how a particular formula should be applied.
Time is more of the essense than it was in the past. Computers definitely can reduce the design time. It would be wrong as engineers to rely on input-output without fully realizing the capabilities and limitations of any software.
I believe the person who said the above statement had good intentions and wouldn't take it too literally...
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- #17
BitTwiddler
Electrical
The theorem of Pythagoras is only correct for plane geometry. The postulates which are needed to prove it are not correct for other types of geometry, such as spherical geometry. A surveyor who assumes that the world is flat will discover that his measurments don't add up over long distances.
It *is* necessary for engineers to understand enough about any mathematical theory to know the conditions which are necessary for that theory to be valid. Both space shuttle catastrophes were caused in part by engineers who blindly applied formulas or software without understanding the limitations of the models they represented.
It *is* necessary for engineers to understand enough about any mathematical theory to know the conditions which are necessary for that theory to be valid. Both space shuttle catastrophes were caused in part by engineers who blindly applied formulas or software without understanding the limitations of the models they represented.
EnglishMuffin
Mechanical
Although slightly off topic, here is another classic example of a disaster caused by engineers blindly applying and relying upon "state of the art computer analysis" which they do not seem to have fully understood.
These guys apparently did not realize (or ignored) the fact that the analysis package did not consider buckling.
Of course it could, and maybe will, happen to any of us - but usually it doesn't have this sort of consequence.
These guys apparently did not realize (or ignored) the fact that the analysis package did not consider buckling.
Of course it could, and maybe will, happen to any of us - but usually it doesn't have this sort of consequence.
GregLocock
Automotive
Coo. My final year project was (partly) on torsional instability of truss members!
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Greg Locock
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