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Ratio of size of prototype and model

  1. May 25, 2016 #1
    1. The problem statement, all variables and given/known data
    a gemoetrical similar open chanel model is constructed with 10: 1 , if the model discharged 7m^3 /s , what is the corresponding discharge in prototype?

    2. Relevant equations


    3. The attempt at a solution

    Q = (L^3) / T ,
    [ (Lp^3)/ (Tp) ] / [ (Lm^3) / Tm ] = (Lr^3) / Tr



    but , i assume (Lr^3 ) = (Lp^3) / (Lm^3)

    so , Qp = (5^3) x 7 = 875 m^3 /s , is it correct ?
    or it should be (1/125 ) x 7 = 7/725 m^3 /s ????
     
  2. jcsd
  3. May 25, 2016 #2

    Simon Bridge

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    Please explain your reasoning... I am not following your notation.

    If we say that the flow rate in the model is q = kr^3/T (here k is a constant of proportionality, r is a characteristic length, and T is time) and the flow rate in the prototype is Q=kR^3/T ... then Q/q=?? and R/r=??
     
  4. May 25, 2016 #3
    no , i use Q= (L^3) / T , so Qr = (Lr^3) / Tr , am i right ?
    where Lr= Lp / Lm , Tr = Tp/ Tm
     
  5. May 25, 2016 #4
    i am not sure Lp / Lm or Lm / Lp = 10 ..... can you explain ?
     
  6. May 25, 2016 #5

    Simon Bridge

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    I don't know what your variables mean: you have to tell me. If you do not answer questions I cannot help you.

    Guessing: Q=L^3/T where Q is the flow rate, L is some characteristic length, and T is time.
    Is this correct?

    Are you using two-letter variable names (this is bad practise)?
    So that Qm is the flow rate through the model?

    Thus Qm = Lm^3/T and Qp=Lp^3/T for the model and the prototype respectively.
    Thus: complete the following: Qp/Qm =?? and Lp/Lm=??

    Consider: which is usually smaller - the scale model or the prototype?
     
  7. May 25, 2016 #6
    scale model

    i want to find the Qm thru the relationship of Qp / Qm = (Lr^3) / Tr ,
    where Tr = Tp / Tm , Lr = Lp / Lm

    so , Qp = (5^3) x 7 = 875 m^3 /s ,
     
  8. May 25, 2016 #7

    Simon Bridge

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    If you do not tell me what these letters mean I cannot help you.
    Don't make me guess!
     
  9. May 25, 2016 #8
    Q = flow rate , T = time , L = length
     
  10. May 25, 2016 #9
    Tr = ratio of time of prototype to model , Lr = ratio of length of prototype to model , Qr = ratio of flow rate of prototype to model
     
  11. May 26, 2016 #10

    Simon Bridge

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    OK: use the same time period to measure Qm and Qp, so Tr=1.
     
  12. May 26, 2016 #11
    ya , i know that . for the scale ratio 10; 1 , it means Lp / Lm = 10 ?
    or Lm / Lp = 10 ? i am confused.
     
  13. May 26, 2016 #12

    Simon Bridge

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    ... you can work it out: you have already said that the prototype has to be bigger than the model.
    This means that Lp > Lm
    Lp/Lm = 10 means Lp=10*Lm
    Lm/Lp = 10 means Lm=10*Lp
    ... so which is right? Which one means that Lp > Lm?
     
  14. May 26, 2016 #13
    so , the prototype must be bigger than the model ??
     
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