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Ratio of size of prototype and model

  • #1

Homework Statement


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?

Homework Equations




The Attempt at a Solution



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


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 ????
 

Answers and Replies

  • #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=??
 
  • #3
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=??
no , i use Q= (L^3) / T , so Qr = (Lr^3) / Tr , am i right ?
where Lr= Lp / Lm , Tr = Tp/ Tm
 
  • #4
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=??
i am not sure Lp / Lm or Lm / Lp = 10 ..... can you explain ?
 
  • #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?
 
  • #6
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?
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 ,
 
  • #7
Simon Bridge
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i want to find the Qm thru the relationship of Qp / Qm = (Lr^3) / Tr ,
where Tr = Tp / Tm , Lr = Lp / Lm
If you do not tell me what these letters mean I cannot help you.
Don't make me guess!
 
  • #8
If you do not tell me what these letters mean I cannot help you.
Don't make me guess!
Q = flow rate , T = time , L = length
 
  • #9
If you do not tell me what these letters mean I cannot help you.
Don't make me guess!
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
 
  • #10
Simon Bridge
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OK: use the same time period to measure Qm and Qp, so Tr=1.
 
  • #11
OK: use the same time period to measure Qm and Qp, so Tr=1.
ya , i know that . for the scale ratio 10; 1 , it means Lp / Lm = 10 ?
or Lm / Lp = 10 ? i am confused.
 
  • #12
Simon Bridge
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for the scale ratio 10; 1 , it means Lp / Lm = 10 or Lm / Lp = 10 ? i am confused.
... 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?
 
  • #13
... 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?
so , the prototype must be bigger than the model ??
 

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