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Formula of forces

  1. Jun 16, 2016 #1
    1. The problem statement, all variables and given/known data
    from the notes , the author stated that force has the formula of ρ(L^2)(v^2) and also = ρ(L^3)
    i think there's something wrong with the ρ(L^3)
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    BDZcGcq.jpg
    2. Relevant equations


    3. The attempt at a solution
    IMO , ρ(L^2)(v^2) can also be written as ρ(L^4)(T^2) , so Force is proportional to L^4 , am i right . ? IMO, the prototype force should be [ (100^4) ] x 0.12 N

    correct me if i am wrong ...
     
  2. jcsd
  3. Jun 16, 2016 #2
    I'm not sure, but in your picture, one is ##\rho## and the other is ##\rho_r.## Maybe there is detailed definitions in the problem?
     
  4. Jun 16, 2016 #3
    rho r is actually r , it's the pi buckingham theorem
     
  5. Jun 17, 2016 #4

    haruspex

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    I guess you mean ρ(L^4)(T^-2), but either way it does not follow. The whole point of figuring out these dimensionless expressions is that you cannot change the scale of L and assume T fixed, etc. There are physical constants in the system, like viscosity, which impose a relationship between the fundamental dimensions. Changing L keeping T etc. fixed will therefore change the viscosity.
    Similarly, density fixes a relationship between M and L.
     
  6. Jun 17, 2016 #5
    Then, what is the correct formula of force in this question?
     
  7. Jun 17, 2016 #6
    so , the author is correct ? it is (rho)(L^2)(L ) , where (v^2) = L ??
     
  8. Jun 17, 2016 #7

    haruspex

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    I'm hampered by not knowing what Fr stands for in the first line.
    I presume F=ρL2V2 comes from some earlier work.
    If we accept both of those equations, the rest follows.
     
  9. Jun 17, 2016 #8
    So, the authors working is correct??
     
  10. Jun 17, 2016 #9

    haruspex

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    I'm not sure. I don't know where the first line of equations comes from, or what Fr represents. I'm surprised to see any reference to g here. How is gravity relevant? If gravity were to increase but the densities, masses, and lengths stay the same, those equations seem to say the velocity would increase. Why?
     
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