Froude Number Equations

[Mike4chemic]

Dear Colleagues,
I found in a literature the different form of the Froude No. equation: Fr= V^2/g*D, instead of the well-known form: Fr= V/SQRT(g*D).
At the same velocity the equations gave the different Froude numbers.
Which of the equations is more correct?

Thank you,
Mike

 

[3DDave]

Which one is dimensionless?

Ha - trick question. They both are. However:

https://en.wikipedia.org/wiki/Froude_number#Definition_and_main_application

suggests the second one is the correct one.

 

[Latexman]

The derivation of the Froude Number equation is dependent on geometry and the application. It can take several forms. Be careful you pick the right one.

Good Luck,
Latexman

 

[LittleInch]

Where have you found the first equation - all other definitions I can find have the second equation.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

 

[EdStainless]

All that I know of are forms of the second one.
That isn't to say that one of them doesn't reduce to the first one, but I don't know of it.


= = = = = = = = = = = = = = = = = = = =
P.E. Metallurgy, consulting work welcomed

 

[Mike4chemic]

Thank you All.
I found the 1st equation in the "Beggs-Brill Two--phase flow in pipes" book. Please see the attached. In the equation Vm is 2-ph mixture velocity.
For which applications the 1st and 2nd forms are applicable?

Thanks, Mike

 

[3DDave]

You missed actually attaching the file - this forum software uses a separate upload and then attach function. No, I have no idea why.

 

[Mike4chemic]

The file attached

 

[3DDave]

All I can figure is that it may not matter; The Foude number = 1 is a transition point and squaring the term doesn't cause a value to move from one side to the other. Numbers less than one, squared, are still less than one. Similarly those greater than one, squared, remain greater than one.

Squaring is normally done to eliminate negative values; if somehow a negative velocity crept in, that would be taken care of.

I see the same construction in

https://www.sciencedirect.com/topics/engineering/froude-number

as used in a number of articles.

 

[Latexman]

That correlation is 50 years old (1972). That was way back, before hand-held scientific calculators, when it was a lot easier to square a number with pencil and paper, than to find the square root of a number using a slide rule. I am speculating that Brill and Beggs took the easy way out and used the square of the dimensionless Froude number for their works in that book, so they would not have to find (gd)[sup]1/2[/sup] time and time again. Again, that's me speculating.

If you are using the correlations, charts, graphs, etc. in their book, use their definition.

If you are not using the resources in their book, use v/(gd)[sup]1/2[/sup].

Or, it's an error in their book. Try to search for errata for the book, or contact the authors, if they are still alive.

My $0.02.

Good Luck,
Latexman

 

[3DDave]

Having used a slide rule, squaring and square roots were just as easy. There was typically a cube root scale as well. 5th roots was where trouble would begin.