F+fv+EV/DM*rM
There you go. There's my formula [for denpressure].
F is force.
fv is frequency of vibration
EV is expansion and volume
DM is density and mass
rM is resistance of mass.
Force has dimensions mass * length / time
2, written as
m l t-2Frequency is 1 / time, or
t-1Expansion is dimensionless
Volume is length
3, or
l3Density is mass / volume = mass / length
3, or
m l-3Resistance is, I suppose, friction, which has the same dimensions as Force, so
m l t-2Is that right? When you say "friction
of mass" in that last factor in the last term, do you mean friction
times mass? If the former, it's just force, if the latter, force * mass. I'm going with the latter for the first try since I don't know what "friction
of mass" means[nb]And the units are
a little closer to matching as originally proposed.[/nb], but we'll see later that this may be wrong.
Anyway, your formula
Q = F+fv+EV/DM*rM [Q is "denpressure", I guess]
has dimensions:
? = m l t-2 + t-1 + (l3) (m l-3 m)-1 (m) (m l t-2) = m l t-2 + t-1 + (l3) (m-1 l3 m-1) (m) (m l t-2) = m l t-2 + t-1 + l7 t-2We can see there's a problem here. You can't add terms unless they have the same units, and these are clearly different (thus the '?' on the left, since we can't tell what the dimensions are). In the last term, if you should have multiplied by density instead of dividing, its dimensions would change from
l7 t-2 to
m2 l t-2 (volume divided by mass is simply the inverse of density, and multiplying by density leaves only the dimensionless Expansion factor and friction
of mass factor, which is force times mass - or is it?) Perhaps that friction
of mass factor really doesn't have a distinct mass dimension and is simply friction (force),
m l t-2, so we now have dimensions for the last term, which is the same as the first, which are those of a force. Ta daaa! Maybe squaring the frequency term is needed so all three terms have a common
t-2? That would help, but still isn't a force to match the first or last terms; another possibility is that you're missing a constant with dimensions that supply the missing
m l and possibly
t-1 if fv is, in fact, not squared. Let's conjure up a constant S with dimensions
m l or S' with dimensions
m l t-1. If we do that, then the "denpressure formula" becomes:
Q = F+S*fv
2+EVD/M*rM
or
Q = F+S'*fv+EVD/M*rM
Since V = M/D, then these can be simplified to
Q = F+S*fv
2+E*rM
or
Q = F+S'*fv+E*rM
Hey, at least the units will work now[nb]Many students when introduced to dimensional analysis dread it and think it's dumb. When applied, though, it's actually a very powerful way to tell if there are fundamental errors in your approach; if the units don't work, the answer is
wrong.[/nb]. What say, sceptimatic? It's your formula. If this is correct, what is the value for S or S' as appropriate? Or is this way off track and it's really something completely different?
BTW, what force does 'F' in your original represent? Was that mis-typed and should have been F = fv+EV/DM*rM [making 'F' "denpressure"]?
[Edit] Corrected 'volume' to 'density' in description of suggested correction to formula.