# 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

## 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 ?

#### Attachments

What does upper case phi double prime stand for?

Φ'' (Re) = FD/ρD2V2

What does upper case phi double prime stand for?

Φ'' (Re) = FD/ρD2V2
I think the author means stand for function...

What does upper case phi double prime stand for?

Φ'' (Re) = FD/ρD2V2
do u have any idea now ?

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

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 ?

1/Re = F/ρD2V2

where F = viscous forces

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 )

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??

2 = FD/ρD2V2

What do ∏1 and ∏3 equal?