Alternative form of Reynold's number

[foo9008]

Homework Statement

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

Homework Equations

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 ?

 

[David Lewis]

What does upper case phi double prime stand for?

Φ'' (Re) = F_D/ρD²V²

 

[foo9008]

What does upper case phi double prime stand for?

Φ'' (Re) = F_D/ρD²V²

I think the author means stand for function...

 

[foo9008]

What does upper case phi double prime stand for?

Φ'' (Re) = F_D/ρD²V²

do u have any idea now ?

 

[foo9008]

anyone know the answer?

 

[David Lewis]

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

 

[foo9008]

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

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 ?

 

[David Lewis]

1/Re = F/ρD²V²

where F = viscous forces

 

[foo9008]

1/Re = F/ρD²V²

where F = viscous forces

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 )

 

[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.

 

[foo9008]

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.

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

 

[David Lewis]

∏₂ = F_D/ρD²V²

What do ∏₁ and ∏₃ equal?