Reynold Number: ρvD/μ or ρvR/μ?

[fonseh]

Homework Statement

https://en.wikipedia.org/wiki/Reynolds_number#Flow_in_a_pipe

In this link , i was told that Reynold number = ρvD / μ ,

However in the notes below , i was told that Reynold number = ρvR / μ .

Homework Equations

The Attempt at a Solution

I think Reynold number = ρvR / μ is wrong , because i learned that Reynold number = ρvD / μ in fluid mechanics , however , in the hydraulics notes , i was told that that Reynold number = ρvR / μ . I'm very confused now

 

[BvU]

I agree. The characteristic length is the hydraulic diameter and it is confusing to use the term "hydraulic radius".

 

[Chestermiller]

Homework Statement

https://en.wikipedia.org/wiki/Reynolds_number#Flow_in_a_pipe

In this link , i was told that Reynold number = ρvD / μ ,

However in the notes below , i was told that Reynold number = ρvR / μ .

Homework Equations

The Attempt at a Solution

I think Reynold number = ρvR / μ is wrong , because i learned that Reynold number = ρvD / μ in fluid mechanics , however , in the hydraulics notes , i was told that that Reynold number = ρvR / μ . I'm very confused now

It doesn't really matter, as long as the meaning is established within the context of the system being analyzed. Anyway, it's Reynolds number, not Reynold number.

 

[fonseh]

I agree. The characteristic length is the hydraulic diameter and it is confusing to use the term "hydraulic radius".

So , which is correct ? ρvD / μ or ρvR / μ ??

 

[fonseh]

I agree. The characteristic length is the hydraulic diameter and it is confusing to use the term "hydraulic radius".

So , do you mean ρvD / μ is correct ? and ρvR / μ is wrong ?

 

[Chestermiller]

So , do you mean ρvD / μ is correct ? and ρvR / μ is wrong ?

Both are correct, depending on how it is used.

 

[fonseh]

Both are correct, depending on how it is used.

Can you explain further when we need to use ρvD / μ or ρvR / μ ?

 

[Chestermiller]

Can you explain further when we need to use ρvD / μ or ρvR / μ ?

In a given problem, you just need to specify which definition is being used. For example, the laminar-turbulent transition occurs at $\rho v D/\mu=2100$ for flow in a pipe, but it also occurs at $\rho v R/\mu=1050$. So you have to tell which definition of the Re you are using.