# Ratio of size of prototype and model

## 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?

## The Attempt at a Solution

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

Simon Bridge
Homework Helper

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=??

• welovephysics

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

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 ?

Simon Bridge
Homework Helper

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?

• welovephysics

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 ,

Simon Bridge
Homework Helper
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!

• welovephysics
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

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

Simon Bridge
Homework Helper
OK: use the same time period to measure Qm and Qp, so Tr=1.

• welovephysics
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.

Simon Bridge
Homework Helper
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?

• welovephysics
... 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 ??