# How is a standard co-relation forumulated?

1. Jul 16, 2009

### nanunath

How is a standard co-relation forumulated???

I always wandered ... how are standard relations [Like famous non - dimensional results for a heat exchanger..like relational between Nusselt,Re number,etc developed and standardised...
I mean I want to know the detailed steps behind this...[which technique]
eg: modelling,CFD,results,Interpretation,Validation by experiments,develpoing a co-relation

I want a more full detailed explanation of how to develop[using what..and all such steps]...a co-relation between various parameters for any good result observed for a certain analysis...

As always:Any help is appreciated!
Thanksssss!....

2. Jul 16, 2009

### FredGarvin

Re: How is a standard co-relation forumulated???

I guess I don't quite understand what you are pressing for here. Anything starts with basic theory. Once you reach either the limit of your abilities or those of the theory, you rely on experimentation. Most relations we take for granted are the result of a fair amount of theory and a large amount of experimental results.

3. Aug 3, 2009

### nanunath

Re: How is a standard co-relation forumulated???

Ok...
Thanks a lot FredGarvin

I want to know about experimental part..
I mean its quite a lot possible that a particular correlation is derived only from experimental data...
So I wanna know...
If I have a large amount of experimental data..and I want to find the correlation between some of these parameters...so
I think ..1 possible way is : I plot them...find an approximate curve fit for the results..and there I have a new correlation....
so what are the techniques used for curve fitting...????.....

and also what other ways can be used to get a relationship out of this experimental data...and in cases in which they cant be derived theoretically..only experimentation is the way out??.....
I think that was clear enough...
Sorry if it wasn't....

Any views are welcome!..Thanks in advance!...

Last edited: Aug 3, 2009
4. Aug 3, 2009

### minger

Re: How is a standard co-relation forumulated???

Many times you predict what you think the data should look like and draw an appropriate curve through it. If my data sets are velocity, displacements and time, then perhaps I think there should be a linear relationship.

Often times we just do a power and say that the variable we're looking for is the product of coefficients times our variables raised to the x power, e.g.
$$f = aX^mbY^n$$
Then, numerical analysis is done to find the coefficients by minimizing the error.

5. Aug 3, 2009

### ank_gl

Re: How is a standard co-relation forumulated???

Hi nanunath

Seeing your other questions, I assume you are in 5th or 6th semester.
All the standard relation you talked about are derived by writing equations of law of mass conservation, application of second law of motion and the law of energy conservation & then non dimensional-izing them. The non dimensional terms thus obtained are given names like Nusselt Number, Biot number, Grashof number & many more.

This is not something which can be explained in 1 or 2 days, you need to have thorough understanding of calculus, fluid mechanics & thermodynamics to be able to understand & derive the physics behind it.

6. Aug 4, 2009

### nanunath

Re: How is a standard co-relation forumulated???

Thankssss a lot minger and ank_gl....

Does that mean...that theres no relation existing which can only be derived from experminentation...only??...

That should mean..that the very first step in establishment of these correlations is:
Killing theoretical analysis...and then one possible outcome of it is non-dimensional-ising terms...and a relation between them...and then comes the experimental part...whose sole purpose is mere verifying the theoretically established results..right??

and ya ank_gl..I've just completed my 6th semester..:shy:

7. Aug 4, 2009

### ank_gl

Re: How is a standard co-relation forumulated???

No, that is not what i meant. For example, we dont have very good general mathematical models for turbulent flows(that doesnt mean we dont have them at all, we do), in such cases, experimental results are curve fitted & a co relation is derived. Examples are calculation of nusselt number in convection problem, friction factor in turbulent flows.
But the bottom line is that they all have a theoretical background to them.

I suggest you start reading good books(books not meant to clear the exams, but books meant to understand). Search your local library. Here are some good books
Fluid Mechanics - F white or Young or Fox(all 3 are very good)
Thermodynamics - Michael J. Moran, Howard N. Shapiro
Heat Transfer - Frank P. Incropera

8. Aug 4, 2009

### nanunath

Re: How is a standard co-relation forumulated???

Thankss ank_gl...

and thanks...a lot lot for this...because I was in need of this at this point of time...
Even I realized that I'm not studying the right way...and started studying some of the important subjects again...I've started with Thermodynamics[from Engg. Thermodynamics by PK Nag] 1st...followed by Heat transfer...and so was in need of that list of good books..

9. Aug 4, 2009

### nanunath

Re: How is a standard co-relation forumulated???

Any more suggestions....???
or good books for other subjects..???
Do post if an one has any suggestions...

10. Aug 4, 2009

### ank_gl

Re: How is a standard co-relation forumulated???

NEVER EVER read filthy books by these writers, they have only copied stuff(important for exams) from other good books.

11. Aug 6, 2009

### nanunath

Re: How is a standard co-relation forumulated???

Ya..
even I did notice that..lately...
they copy from other good books...leaving some imp points...and sometimes even giving abrupt explanations[especially in derivations]...
anyways.....Thanks a lot...