Whoa! Slow down, everyone. Let's back up.
The most important governing equations here are the incompressible
Navier-Stokes equations. The Bernoulli equation, as noted, is for
frictionless, incompressible fluids (n.b., both liquids and gases are
classified as fluids). The Euler equations are for frictionless,
compressible gases, but air under these conditions is nearly
incompressible, so we can make that simplification (if you want to get
an anser down to the <1% error range, use the full compressible N-S).
As pointed out elsewhere, Boyle's Law is just a simplification of
compressible gas laws, and isn't appropriate here.
Now, the solids in the airstream don't substantially affect the flow.
That means that we can "decouple" the system and calculate how "pure"
air would flow and then throw the wood dust/small chips in and simply
track them through the ducts, using our solution for pure air. (again, a
prefect model would account for the fact that the wood chips can _cause_
turbulence, but this is a secondary effect).
Now, as for the important answer of which is more important for moving
chips: turbulence effects vs. friction effects? I can't say. But if you
work through the calculations, you find that the "recommended" flow
speed usually works out to the transition region between laminar and
turbulent flow. Coincidence? I suspect (and this is pure conjecture)
that some amount of turbulence is necessary to keep dust from sticking
to the sides of the duct. Obviously, though, the bulk motion of the air
is what moves the dust from A to B.
Todd Fatheree wrote:
This didn't seem quite right to me so I took a look at the numbers. IIRC,
recommended duct velocities are 3000 to 4000 fpm.
Reynolds number = Re = (density)(velocity)(diameter)/(viscosity)
At 70 deg F: density = 0.075 lbm/cu ft viscosity = 0.044 lbm/ hr ft
A lower limit could be 3000 ft/min in a 4 inch duct.
Re = (0.075 lbm/ cu ft) (3000 ft/min) (60 min/hr) 4 in) / (0.044 lbm/hr ft)
(12 in/ ft)
Re = 102,273
Since transition from laminar to turbulent flow (in internal duct flow) is
in the range 2,000 to 10,000, this is clearly turbulent. Higher values for
the flow rate and/or duct diameter will yield higher Re numbers.
I would expect you would want to stay away from laminar flow, and certainly
stay away from transition for good performance.
Damn. I'm sure I calculated a much lower Re once, but I can't find my
notes to see where I made the mistake (I assume it was me, but I'll
check yours). Probably got screwed up on the whole lbm/lbf thing...
Bill Leonhardt wrote:
V = 3000 ft./min. X 1 m/3 ft. X 1 min. / 60 sec. = 16.7 m/s
D = (1/3) ft X 1 m / 3 ft. = 0.11 m
nu = 1.46 E-5 m^2/s
Re = VD/nu = 16.7 X 0.11 / (1.46 E-5) = 125,000
A little higher than yours, but I rounded. So, you're correct.
Bill Leonhardt wrote:
I guess it depends on the definition of nationality. I have no idea what
citizenship rules were like then, or if it's relevant. His dad, Johann,
was Swiss and was working in the Netherlands at the time of Daniel's
birth. Were I to move to, say, Sweden and have a child, I would still
consider my child an American. Would it be Swedish? Technically, I suppose.
Let's just say that he was a member of the Axis of Fine Chocolate
Producing Countries (not sure what the third would be)...
I beg to disagree but at the velocities common in dust collection systems
the flow of air is assumed to be incompressible and Boyle doesn't enter
into the calculation. It's not until you have velocities approaching Mach
1 that you start having to consider compressibility.
Maybe so, but Boyle's Law applies to static pressures, not dynamic.
You've got it backwards. Reduce the size of the pipe or duct and you
decrease the pressure and increase the velocity.
That may be _your_ idea but gases don't behave that way in ducts.
I'd like to see a reference to that.
If highways behaved like air ducts then you'd see people going 180 MPH
though construction zones.
Reply to jclarke at ae tee tee global dot net
On 15 Jul 2004 15:19:48 -0700, email@example.com (Joe Emenaker) wrote:
Maybe. It really depends upon distance and the size of your dust
collector. 6" may be *too* good and reduce velocity to the point where
chips settle out. You really need to do the velocity/static pressure
computations to be sure. In my case, 6" was too large, 5" was the ideal
size. Unfortunately, that meant I could not use cheap PVC from the Borg.
Check out the various web sites like
it has an Excel spreadsheet:
http://billpentz.com/woodworking/cyclone/StaticCalc.xls that is invaluable
in sizing your system. Pay attention as well to sizing the ductwork for
I just went through this late last year and have been very satisfied with
the results. I wound up buying metal spiral pipe from a local fabricator
along with Y's, T's and elbows. I can now see plumes of dust being sucked
into the table saw through the insert and the shaper table chips are sucked
into the system with few residuals left behind.
I wouldn't worry. After making the way clear (and, as noted, maintaining
pressure) for dust and chips on the way to the cyclone, it's only air you'll
want to move to the impeller. It's a fluid, not a solid.
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