How is a standard co-relation forumulated?

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In summary: I'll surely look for them...& try to find them out...thanks a lot again for this...In summary, the process of formulating standard correlations involves a combination of theoretical analysis and experimental data. The first step is to establish a theoretical foundation, which often involves non-dimensionalizing terms. This is followed by the verification of these theoretical results through experimentation. However, in some cases where there is a lack of general mathematical models, experimental data is curve fitted to derive correlations. It is recommended to read books that focus on understanding rather than just clearing exams, such as "Fluid Mechanics" by F. White, Young, or Fox, "Thermodynamics" by M.J. Moran and H.N. Shapiro, and "
  • #1
nanunath
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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!...:smile:
 
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  • #2


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


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 want to 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...?...:confused:..:confused:

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

Any views are welcome!..Thanks in advance!...:smile:
 
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  • #4


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.
[tex]
f = aX^mbY^n
[/tex]
Then, numerical analysis is done to find the coefficients by minimizing the error.
 
  • #5


nanunath said:
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!...:smile:

Hi nanunath:smile:

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


Thankssss a lot minger and ank_gl...:smile:

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.

Does that mean...that there's no relation existing which can only be derived from experminentation...only??...:confused:

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 you ank_gl..I've just completed my 6th semester..:shy:
 
  • #7


nanunath said:
Does that mean...that there's no relation existing which can only be derived from experminentation...only??...:confused:

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??

No, that is not what i meant. For example, we don't have very good general mathematical models for turbulent flows(that doesn't mean we don't 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.

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


Thankss ank_gl...:smile:

I think...I atleast have an idea now...about this...thanks to you...

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

and thanks...a lot lot for this.:smile:..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


Any more suggestions...?
or good books for other subjects..?
Do post if an one has any suggestions...:smile:
 
  • #10


nanunath said:
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..

NEVER EVER read filthy books by these writers, they have only copied stuff(important for exams) from other good books.
 
  • #11


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...:smile:
 

FAQ: How is a standard co-relation forumulated?

What is a correlation?

A correlation is a statistical measure that determines the relationship between two variables. It shows how closely these variables are related to each other, and the direction and strength of this relationship.

How is a standard correlation formulated?

A standard correlation, also known as Pearson correlation, is formulated using the covariance between two variables divided by the product of their standard deviations. This formula results in a correlation coefficient, which ranges from -1 to 1, with 0 indicating no correlation, -1 indicating a perfect negative correlation, and 1 indicating a perfect positive correlation.

What is the difference between correlation and causation?

Correlation does not imply causation. While a correlation shows a relationship between two variables, it does not prove that one variable causes the other. There may be other factors or variables at play that influence the relationship between the two variables.

Can a correlation be used to make predictions?

Yes, a correlation can be used to make predictions. If there is a strong correlation between two variables, changes in one variable will likely result in changes in the other variable. However, it is important to keep in mind that correlation does not prove causation, so predictions should be made with caution.

In what situations is correlation analysis useful?

Correlation analysis is useful in many situations, such as determining the strength of relationships between variables, identifying trends and patterns, and making predictions. It is commonly used in fields such as psychology, economics, and social sciences to analyze data and draw conclusions about the relationships between variables.

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