Crossbar through a variable? (fluid mechanics)

The student I’m tutoring is starting on fluid mechanics, and his textbook sometimes uses a bar through a variable, especially volume (for instance, they write the ideal gas equation as P[del]V[/del] = nkT). I’ve never seen this notation before, and I expect that it probably means something significant, but so far as I can tell, the textbook never actually explains it.

Is anyone here familiar with this notation? Unfortunately, it’s difficult to Google for without knowing what it’s called, and searches involving “bar” tend to get confused by the pressure unit by that same name.

Pretty sure that is “v bar” or the molar volume with bad type setting?

\bar{V} or \bar{v} in the LaTeX form may help with searches these days too.

Search for “V bar” “Van Der Waals” and see if that matches the material, but at that level I expect it is related to the Van Der Waals equation with V bar as molar volume.

The bar is very definitely and consistently through the letters, not above them or below them. And it’s not referring to a specific volume like the molar volume, because they say things like “When [del]V[/del] is very small, the density can vary significantly due to molecules entering and exiting, but when it is large enough, the density remains constant”.

Must be a publishers quirk or some historical convention. \sout or strikeout aren’t even in LaTeX math mode but it still may be negation?.

Typically in intro texts it is:

N = # particles
n = # moles
V = volume
k = Boltzmann constant
T = Temp

pV = NkT
pV = nRT

or the mole-less version.

P = nkT (where n = # particles per volume)

the moles aren’t in the Volume, but even the N above typically involves Avogadro constant and thus still moles…but the last form avoids moles but typically also gets rid of “V”?

Hopefully someone else who remembers this notation comes along, but without more info I would assume they are justifying dumping V since the volume is constant and explaining Charles’ law and Boyle’s law? But not typical of modern texts once again, because LaTeX math mode drives so much.

In quantum physics, plancks constant h , has a h bar version, more formally known as the reduced Planck constant, or the Dirac constant, which is simply h / 2 pi.

I state this not to say that bar means divide by 2 pi, I mean to say that it wouldnt be used for the Dirac Constant if it was confusingly used elsewhere in physics.
I think its clear in words that the V bar is V for Volume, no different to V with no bar for volume.

I wonder if it is trying to indicate whether for the purposes being discussed that volume is fixed (ie incompressible flows) or free, but using otherwise familiar equations and derivations.

Some sort of weird volume integral symbol? I don’t ever remember seeing it in any of my text books.

What is the textbook?

I mean I can only think of volts (V) confusing people but you’re working with basic fluid dynamics and not some weird magneto-hydrodynamic equation and even then…

My bet is on Control Volume - https://en.m.wikipedia.org/wiki/Control_volume

The bar is place so that Control Volume is not confused with velocity.

I just took Fluid Mechanics a few months ago - am77494 is correct. Vbar is just a handy way of not confusing volume with velocity.

OK, so it’s not that the crossbar itself means something, just that [del]V[/del] is a different symbol from V (or v). Got it.

I’ve already noticed that it’s a field that seems to love its Greek alphabet. But hey, what else is nu?

Stop it. :slight_smile:

I eta pi.

Iota, but I can’t.

Oh my, Chron.

Concur.

Also be aware that there are multiple conventions in use that vary between textbooks, countries, or industries in practice. For instance, the ratio of specific heats (or heat capacity ratio or adiabatic index), C[SUB]P[/SUB]/C[SUB]V[/SUB] is identified as γ in aerospace, but as K or κ in other fields. There are other nuances especially when you get into the tensor formulations of the Navier-Stokes equations, which is probably beyond where your tutoring will go (as that is upper division and graduate level coverage) but every textbook and paper should have a parameter glossary (most papers start with it) that explicitly describes what each symbol stands for, and it is often useful to pull that out or print it to keep available for quick refernece. This is particularly true when you get into high temperature plasma thermophysics, where the same symbols can stand for multiple things depending on context, and you are essentially dealing with thermodynamics, highly compressible flows, and electrodynamics all at the same time, and the glossary ran run into more pages than the actual text of a summary paper.

Stranger

Oh, believe me, I know that every textbook or paper should have such a glossary (in relativity, it’s common to see a footnote on the first page "all notational conventions in this paper are those used by Misner, Thorne, and Wheeler [the most popular relativity textbook]), but this one doesn’t. That was the first thing I looked for.

Note \hbar or ħ is through the letter but \veebar is typically ⊻, so if someone can name the publisher it would be awesome, just to capture it.

veebar ⊻
vBar ⫨
Vbar ⫫
vdash ⊢

Hopefully they don’t call it vbar, but if someone knows the publisher or convention name here it would be awesome. Mostly because [del]V[/del] is not in any of the Javascript or TeX math library and it would be a reason to get them added if it was a common convention.

Perhaps ⊻ vs. [del]V[/del] doesn’t matter though?

Note that in Germany, Vdub is commonly used.