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Correct way to write pi buckingham theorem

  • Thread starter foo9008
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  • #1
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Homework Statement


in this problem , the author make π1 = D(dp/ dx) / ρ( V^2) , and make π3 as μ/ ρVD , how if i want to make μ/ ρVD (reciprocal of reynold number ) as π1 and make D(dp/ dx) / ρ( V^2) as π3 ?



Homework Equations




The Attempt at a Solution


since we know that π1 is function of ( π2 , π3 )
is it necessary to change μ/ ρVD (reciprocal of reynold number ) to reynold number (ρVD / μ ) ?
which is correct ? Re = f ( D(dp/ dx) / ρ( V^2) , Ks/ D ) or μ/ ρVD = f ( D(dp/ dx) / ρ( V^2) , Ks/ D ) ? which is correct ?
 

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Answers and Replies

  • #2
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wow , thi is considered as advanced physics question ?
 
  • #3
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I don't see any difference between taking the reciprocal of Reynold's number and taking actually Reynold's number as ##\pi_1##.
 
  • #4
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I don't see any difference between taking the reciprocal of Reynold's number and taking actually Reynold's number as ##\pi_1##.
Why?
 
  • #5
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If you take ##\pi_1 =f (\pi_2 , \pi_3)## for some function ##f## of ##\pi_2 , \pi_3## in which case you can find a function ##g## such that ##\pi_1^{-1} = g(\pi_2 , \pi_3)##; so it doesn't matter which one you choose your ##\pi_1## to be, your function will of course be different for different cases, but you don't seem to know what is your function ##f##, right?

You didn't state what is your precise problem here?
 
  • #6
678
4
If you take ##\pi_1 =f (\pi_2 , \pi_3)## for some function ##f## of ##\pi_2 , \pi_3## in which case you can find a function ##g## such that ##\pi_1^{-1} = g(\pi_2 , \pi_3)##; so it doesn't matter which one you choose your ##\pi_1## to be, your
function will of course be different for different cases, but you don't seem to know what is your function ##f##, right?
It's pi Buckingham theorem, can I still do so???
You didn't state what is your precise problem here?
 
  • #7
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Re = f ( D(dp/ dx) / ρ( V^2) , Ks/ D ) or μ/ ρVD which is 1 / Re = f ( D(dp/ dx) / ρ( V^2) , Ks/ D ) ? which is correct ?
 
  • #8
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Do you know what is f here?
 
  • #9
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  • #10
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I mean is f given explicitly?
 
  • #11
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  • #12
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I mean do you know how is f given? I mean do you know what is f(\pi_2, \pi_3) what is this function of \pi_2 and \pi_3?
 
  • #13
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I mean do you know how is f given? I mean do you know what is f(\pi_2, \pi_3) what is this function of \pi_2 and \pi_3?
Dun know
 
  • #14
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As it mentioned in one of the pics you rearrange only for convenience, i.e. it doesn't matter if you take Reynold's number or the reciprocal of Reynold's number as a function of the other dimensionless variables since you can always take the reciprocal of the function if you have ##Re = f(\pi_2 , \pi_3)## then you can take ##1/Re = 1/f = g(\pi_2,\pi_3)##.

If on the other hand ##f## were given then you'd know how to rearrange the equation.
 

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