# Alternative form of Reynold's number

1. Jun 11, 2016

### foo9008

1. The problem statement, all variables and given/known data
in the third picture , we know that π2 can be written as function of π1 , where π2 is inverse of reynold number , how if i want to change it to π1 = function of π2 , can i write it as (Reynold number ) = F / ρ (D^2)(v^2) ???

p/s : π1 is actually inverse of reynold number

2. Relevant equations

3. The attempt at a solution
IMO , for π1 = function of π2 , it is also (Reynold number ) = f (F / ρ (D^2)(v^2) ) ... we should write it as reynold number instead of inverse of reynold number , am i right ?

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2. Jun 11, 2016

### David Lewis

What does upper case phi double prime stand for?

Φ'' (Re) = FD/ρD2V2

3. Jun 11, 2016

### foo9008

I think the author means stand for function.......

4. Jun 12, 2016

### foo9008

do u have any idea now ?

5. Jun 13, 2016

### foo9008

6. Jun 13, 2016

### David Lewis

OK. If Φ represents a function then double prime would normally indicate the second derivative of that function.

7. Jun 16, 2016

### foo9008

can i write it as (Reynold number ) = F / ρ (D^2)(v^2) ???

or , it should be 1/ reynold number = F / ρ (D^2)(v^2) ???
which one is correct ?

8. Jun 16, 2016

### David Lewis

1/Re = F/ρD2V2

where F = viscous forces

9. Jun 16, 2016

### foo9008

is it wrong to write it as (Reynold number ) = F / ρ (D^2)(v^2) ???
is there a need to change 1/ Re to Re for π1 in this case
P/s : π1 = function of ( π2 , π3 )

10. Jun 17, 2016

### David Lewis

The Reynolds number is dimensionless, so the numerator and denominator will have the same fundamental dimensions (M, L, T).

In aeronautics, the denominator (viscous forces) is smaller than the numerator (inertial forces) -- possibly 5 or 6 orders of magnitude smaller -- which makes Re a large number.

11. Jun 17, 2016

### foo9008

So, no matter pi 1 is Reynold number = ( pi 2 , pi3) or pi 1 is 1/ reynold number d= ( pi2, pi3) are correct??

12. Jun 19, 2016

### David Lewis

2 = FD/ρD2V2

What do ∏1 and ∏3 equal?