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Well, I wouldn't say a misconception, Al, converting
kinetic energy to static pressure is exactly what happens. Besides, if I
am screwed up in my logic then by presenting it fully, someone can catch and
correct it and that will enhance my understanding
Part of what causes some confusion (I believe) is
whether you are using an absolute or differential/gauge pressure
instrument to measure pressure. IF using an absolute pressure gage
then the static pressure measured in the tube (or duct) would be indeed be
ambient + dynamic. But, using a differential pressure gauge( a
manometer for example ) only measures the localized static pressure inside your
"pitot" measuring tube which is the dynamic pressure component above
ambient.
In other words, air velocity is only potentially static
pressure. It does not increase the localized ambient pressure until the
kinetic energy is converted to pressure. This can be done by the air being
slowed or impacting a non-moving object.
Now the 84% is straight out of K&W for the
streamline duct. Attached is the graph showing (upper left hand
corner of lower graph) an equation (PB1 - Pi)/(1/2pVi^2) =
0.84. The denominator of the equation is our old friend
dynamic pressure 1/2pVi^2. So re-arranging the equation
slightly we have PB1-Pi = 0.84 * 1/2pVi^2.
Vi is the velocity of the air entering the inlet of the duct.
p is the air density.
PB1 is the duct localized static pressure
(above ambient) right before the core and Pi is the
ambient pressure at the entrance of the duct. So the difference shown
is the increase in static pressure (NOT ambient + Dynamic, but Dynamic
increase over ambient, with ambient being the reference or zero point) from the
duct entrance to the core - or your pressure increase due to converting the
moving air's kinetic energy to a local static pressure increase.
IF PB1 = Pi then that says there is either no air flow OR there
is no conversion of kinetic energy to static pressure increase. If
PB1>Pi then some dynamic potential is being converted to
static, so that leads back to my taking of your
9.5" H20 at the entrance and since that is the amount of
dynamic pressure available at the entrance Pi and you measure
3.25" at the core (PB1). I would have expected with the
perfect streamline duct that you would have measure PB1 = 0.84 * 9.5 =
7.98 " H20 vice 3.25". Now, the tube was not pointed directly
into the flow from the best I can tell, but that would imply that the 9.5" H20
was less than that available in the free flow (12.0") which could mean you
actually have more dynamic potential at the entrance than the 9.5"
reflects. But, if true then that only reinforces my speculation that
something evil is going on in your duct. You are recovering 9.5" localized
static pressure in your measuring tube at the entrance but by the time you
measure it next to the core if has decreased considerably.
But, I'll stop here, before I confuse myself.
K&W makes good go-to-bed reading {:>)
Good luck on your modification. I will be very
interested in seeing what a van does for you.
Best Regards
Ed
----- Original Message -----
Sent: Monday, July 16, 2007 9:16 PM
Subject: [FlyRotary] Re: FW: Oil cooler
air flow
Ed;
I appreciate your
thorough presentation. I guess you could have been brief; and said “Yep;
you have a misconception” J In any case I was
not aware of the 0.84 maximum.
Even though I guess
I knew at some level it wasn’t correct; somewhere along the way I had gotten
it into my head that in converting the ‘dynamic’ to ‘static’ the static
pressure could be greater – something about conservation of energy; or who
knows what; but clearly that was a ‘misconception’ (having one of those is
much better than being completely screwed up)J.
Al
-----Original
Message-----
From: Rotary
motors in aircraft [mailto:flyrotary@lancaironline.net] On Behalf Of Ed Anderson
Sent: Monday, July 16, 2007 3:38
PM
To: Rotary motors in
aircraft
Subject: [FlyRotary]
Re: FW: Oil cooler air flow
OK, Al, let me restate in a more
comprehensive manner and see if that helps.
We know that "dynamic pressure" is
actually measured by the increase it causes in localized static
pressure. So the term "dynamic pressure" is actually just
referring to the energy potential (Kinetic) of the moving air to cause a
localized increase in static pressure - if that air movement were
brought to a stop.
In other words, if we had a
flow of air with a specific velocity and specific density, that air would have
a ambient static pressure (say at sea level of 29.92" HG). The moving
air would also have a static pressure potential (Dynamic pressure) based
on its velocity and density. So that if a tube were used to measure this
"Dynamic Pressure" it must first bring that part being measured to a
stop the action of which converts the dynamic pressure potential of
the moving air to a localized static pressure increase in the
tube.
So the total static pressure
at the measuring point would be the static pressure of the ambient air
(29.92"HG) plus whatever increase was caused by stopping the moving air or
converting its dynamic potential to static pressure. So Pt = Pa +
Pd with Dynamic Pressure component, Pd = p*1/2V^2.
So in case of a duct there is, of
course, only ambient static pressure in the duct if there is no air flow
through the duct. Once there is airflow then you also have potential
pressure in the form of the kinetic energy of the moving air. So that Pt
= Pa + p1/2V^2. p being air density, V being the
velocity.
The streamline duct
(theoretically) can convert 84% of the moving air potential dynamic pressure
to static pressure increase. So that at the widest part of the duct just
before the core you would have a total static pressure Pt = Pa +
0.84*p1/2V^2.
But, using differential pressure
gauges with tubes pointed into the moving air, we are not measuring total
pressure, but the pressure increase due solely to the moving air. In
other words, if you were measuring 5" H20 and then the air stopped moving ,
the gauge would read zero.
So with the manometer you
are measuring the pressure above ambient pressure or that resulting solely
from the dynamic pressure potential of the moving air being converted from
kinetic energy to static pressure. Yes, the ambient pressure is present
but you are not measuring it. With no moving air the water levels in you
manometer would all be exactly at the same level..
The fact is that you are measuring
static pressure at both locations - the 9.5" before the duct was a static
pressure increase in your measuring tube - cause by stopping the moving
air so its refer to as dynamic pressure. The fact is that you were also
measuring static pressure 3.25" at the location in the duct - but both
resulted from the transformation of the air's kinetic energy into a local
static pressure increase. Therefore, the fact that you were measuring
considerably more pressure before the duct than inside it indicates that the
air stream's velocity is not being efficiently transformed into static
pressure in the duct.
This implies that perhaps there is
less air velocity entering the duct than your measurement a couple inches in
front suggests OR there is sufficient eddies and adverse flow
situation inside the duct that precludes the efficient transformation
into a static pressure increase.
I do not have an aerodynamic or
gas dynamics background, so I could certainly be wrong. But, that is my
understanding based on the somewhat extensive reading I have
done.
----- Original Message -----
Sent: Monday,
July 16, 2007 5:48 PM
Subject:
[FlyRotary] Re: FW: Oil cooler air flow
if the free air velocity (160)
converts to 12"H20 and you had a streamline duct inlet actual had that
coming in then theoretically you could get approx 12 * .84 = 10.8" inside
the duct. Since you measured 3.25" static in front of the core, that
would indicate a significant lack of pressure recovery inside your duct
(what ever the reason). There are several reasons this
might be happening.
I
think the confusion here is whether we’re talking “dynamic” pressure or
“static” pressure. Are you saying that the maximum static pressure in
the duct is 0.84 of the dynamic pressure at the entrance to the duct? If
that is true, I have been under a misconception. I measured 9.5”
dynamic pressure out in front of the scoop; and 3.25” static pressure near
the face of the core – just below the midpoint.
1. The air flow and
velocity is considerably reduced from what you are expecting (too small
opening/exit - which I don't believe to be the case)
2. The boundary layer is a
significant part of your duct total air flow and as a
consequence its lesser velocity has less dynamic pressure
potential.
3. A significant part of
your duct flow is chaotic with eddies which does not provide recoverable
pressure - or it is much reduced. (The boundary layer could be
contributing to this)
4. Some combination of the
above.
Right, now I
would suspect that the boundary layer could be the culprit in that it can
contribute to 2 and 3 above. But, as you know, this is speculation
on my part
I’m sure you’re
right; a combination of 2 and 3. Yesterday I measured the static pressure
near the upper surface of the duct; an inch or so in front of the core –
less than 0.25” H2O. That confirmed to me that the
“flow is
chaotic with eddies”, as you
say. I think the addition of a
vane is worth a try.
Al
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