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Like I said... Bernoulli's theory is a subset of Newtonian theory, which is a subset of Einsteinian theory When you experience the downwash behind say a 747 on final, if you can get to where it passes overhead, and close, a LOT of air is being moved! Newton does a better job of explaining the overall response of the atmosphere to the disturbance of the airplane.
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LouW wrote:
quote:
Actually the Bernoulli equation is a mass balance (conservation of mass). It simply states that within the confines of a stream tube , the mass passing through each section must be equal.
Bernoullis equation is NOT a mass balance equation. Bernoullis equation is about conservation of energy. It simply states that the sum of potential energy and kinetic energy (measured per unit of volume) is constant.
/Red B.
< Message edited by Red B. -- 2/18/2004 8:00:17 AM >
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Please go back and examine the derivation of the Bernoulli equation. It is derived from the fact that within the confines of a stream tube the mass in equals the mass out. Thus the mass flowing by any section must be constant. From this is derived the velocity/pressure relationship defined in the equation.
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Tall Paul, you have got it pegged. Let’s see how it happens.
First, the air doesn’t flow, the wing moves through a basically stationary air mass. If the wing is also stationary, the pressure of the air is the same all around the section. If it moves through the air. There is a point near the leading edge where the air is split, with some going above and some below (the stagnation point). Before it splits, the air sort of piles up there causing the pressure to rise (dynamic pressure). If the wing is moving at some angle of attack (relative to the zero lift angle), the air going beneath is squeezed toward the under surface and the local static pressure is increased. The air going above is first pushed up sharply, then due to inertia tries to pull away from the upper surface and the local static pressure is decreased. The sum of all these changes to the local static pressure results in a net force on the wing. The vertical component is called lift and the horizontal component is called drag.
The resulting pressure changes not only act on the wing, but also act on the air surrounding this pressure field. The air a little more distant from the wing, flows toward negative pressure on top of the wing, and below the wing it is pushed a little further away. The overall effect of the passage of the wing and its surrounding pressure field is to accelerate a mass of air downward, and forward. The reaction to the downward acceleration of the mass is called lift and the reaction to the forward acceleration is called drag.
The pressure distribution around the wing is the proximate cause of lift (the Bernoulli side), but the ultimate source of lift is the acceleration of a mass of air (the Newton side).
Now here is the dirty little secret. The pressure field surrounding a moving wing can be easily measured and the results compared to the theory, and the results can be used to design the shapes for maximum utility. Engineers love it. On the other hand, engineers hate things they can’t measure. Both the quantity of mass accelerated by the wing’s passage and the resulting velocity can’t be easily measured. In fact since there are three variables and two unknowns and only one equation, the problem is unsolvable. Therefore in the endless discussions of lift that keep popping up on this forum, you tend to find engineers arguing passionately for Bernoulli, while pilots usually vote for Newton.
In fact both are right.
< Message edited by LouW -- 2/18/2004 12:54:13 PM >
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Lou W wrote:
quote:
Please go back and examine the derivation of the Bernoulli equation. It is derived from the fact that within the confines of a stream tube the mass in equals the mass out.
Ditto! It is correct that one assumption when deriving Bernoulli's equation is that "within the confines of a stream tube the mass in equals the mass out" but your original statement was that Bernoulli's equation "is a mass balance ...", which is simply wrong!
Conservation of mass (flow) can simply be vritten as: density * velocity = constant. No need for Bernoulli's equation whatsoever!
What Bernoulli did was to use this assumption, together with the assumptions that the fluid is incompressible and that there is no internal friction (inviscid fluid) involved, to study the relationship between potential and kinetic energy of the fluid flow.
An example: Let's have a look at any term of the equation, e.g. the dynamic pressure term, density * velocity^2 / 2, and find out what the units of this expression are. Density has the units kg/m3 (or as I prefer to write it, kg*m^-3). Velocity has the units m/s (in my way of writing things, m*s^-1) and the units of the expression thus are:
kg * m^-3 * (m * s^-1)^2 = kg * m * s^-2 * m * m^-3 = N * m * m^-3= J * m^-3
As you can see the dynamic pressure term is about energy (Joules) per unit volume (cubic meters) and not mass balance! With some further manipulation of the units one obtains:
J * m^-3 = N * m * m^-3= N * m^-2= Pa
i.e. another unit for the dynamic pressure term is Pascal (the SI unit normally used for pressure).
/Red B.
< Message edited by Red B. -- 2/18/2004 4:00:52 PM >
There is no dirty little secret here. Engineers whose job is to design or improve airfoils or wings DO love the fact that they have a predictive (but not perfect) tool for their work. They use "Bernoulli" not only because it involves quantities that can be measured, but because it is more closely related to the thing they must refine: the shape of the wing. Even if one could measure the downward momentum caused by the passage of a wing, it would give no insight to suggest how to modify the shape of the wing. A tool that tells the engineer about the pressure distribution on the wing DOES give this insight. An engineer uses whatever tools are effective and available. In the early days of an industry or discipline, the tools tend to be a limited understanding of the underlying physical phenomena and a lot of trial and error. As an industry matures, the understanding of the phenomena improves, and predictive tools are developed. This is what we've seen in the area of airfoils and wings.
A debate between "Bernoulli" and "Newton" is ridiculous. The Bernoulli equation is a direct result of Newton's Laws. To claim that one is correct and the other is not is nonsensical. As you point out, one person may find that the pressure on the surface of the wing is of more interest than the downward momentum resulting from a wings passage, but that doesn't mean that he needs to claim that the other is wrong. It is not differing perspectives that fuels the debate here, it is a lack of understanding, along with some incorrect statements (like, "the air that goes over the wing must reach the trailing edge at the same time as the air that goes under the wing" .
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Paul,
The numbers I picked for dynamic pressure were very high, and I chose to use PSI instead of inches of mercury becuase I was trying to talk to the non engineers. Engineer to Engineer, I know that local static pressure can not be reduced below the ambient static pressure, but If you look at just the local change in dynamic pressure as air speeds up to get around the wing instead of the dynamic pressure of the flow field ahead of the airplane you'll see that this makes perfect sence.. there is no way that the local increase in dynamic pressure would reach such a high value that it would require local static pressure to drop below ambient pressure. If the dynamic pressure measured by the pitot static system is 2 PSI, then the local dynamic pressure on top of the wing would have to increase by yet another 2 PSI before it would be asking the static pressure to drop lower then ambient. And if the local velocity over the wing did get so high, relative to the free stream velocity, it woud be subject to a lot more then Bernoulli, you'd have to account for compressibility, and possibly even shock waves.
I teach my flight students Pressure lift, and Mass lift (Downwash)... I actually think that focusing on the downwash behind the wing helps understand the interaction between the wing and the tail much better then just focusing on pressure differences on the wing. If you just teach pressure students think that the nose pitches down during a stall because the airplane lost all of its lift and began to free fall. If you teach downwash students understand that the downwash angle behind the wing changes dramatically during a stall and therefore the relative wind to the tail changes causing the tail to rise, or the nose to drop, depending on your frame of reference. The same interaction causes the nose to pitch up when they put flaps down ect.... for the most part downwash provides a better understanding of lift for pilots. But, In the wind tunnel I have never been able to measure the downwash angle, flow rate, density ect.. I can't even imagine the equipment that would accomplish it. I have measured static pressure, dynamic pressure ect... and calculated numbers that match the numbers from the force ballance that the wing was mounted to, which in my mind is proof that pressure can be used to calculate lift more effectively then mass (downwash).
Ty
< Message edited by acropilot_ty -- 2/18/2004 5:14:30 PM >
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I couldn't agree more. As an Aeronautical engineer with 40+ years in the field, I appreciate the predictive tools. As pilot and flight instructor, like acropilot_ty in the following post, I find the deflection of air a more usefull concept in teaching pilots to fly. The point of all my posts is that both viewpoints are valid and are usefull in their respective spheres. If you look up last years rubarb starting with "wingtip Vortices" you will see some of the engineers passion on this subject.
< Message edited by LouW -- 2/18/2004 7:35:45 PM >
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Ty, I have to admit I do not understand what you are saying about air pressures. 2 psi of dynamic pressure isn't "very high". It's a lot more than a model will see, but its magnitude depends on the airspeed, everything else the same. Whatever that may be, though, 2 psi represents a specific change in indicated airspeed regardless of altitude. If as you mentioned somehow a total pressure of 17 psi became 1 psi more than the 2 you said, that change represents a LARGE change in indicated airspeed, regardless of how it is achieved. It's worth about 50 knots, indicated. That is not seen. The most pressure a plane experiences is the total pressure, which when subtracted from the static pressure, yields dynamic pressure, which is airspeed, and which doesn't vary wildly around the airplane. It can only go lower as the energy dissipates around the airplane. As a thought problem an increase in q can be postulated OK, but it probably would only be encountered in a explosion in the real world. The attached chart* shows how Indicated Airspeed relates to pressures, at 1,000 feet and 50,000 feet. The indicator in the cockpit would show the -same- value for the same dynamic pressure at these widely differing altitudes. It's the reason people are told "planes stall at the same airspeed, at any altitude". However, the TRUE airspeed IS affected with altitude changes. 265 KIAS at 1,000 feet is still 265 KIAS at 50,000 feet, but the Mach number is > by far, as is the True Airspeed. These change from M= .41 at 1,000 feet to M=1.09 at 50,000 feet, the corresponding TAS's being 273 knots and 585 knots. Same q!
A plane which stalls at 102 knots at 1,000 feet will stall at the same 102 knots at 50,000 feet and although it will be going a lot faster it will still stall! And the indication in the cockpit won't be a sharp increase in airspeed, which an increase in dynamic pressure over that the plane is actually experiencing demands. There might be erratic indications in the instrument, but those would be due solely to erratic flow at the pitot head or static port, and not represent any major aerodynamic event to the airplane. The static pressure after all surrounds the airplane, regardless of flight conditions. Only q varies, and it can't increase unless the speed increases. Flopping around in the air isn't going to make q go up in any meaningful manner. . My boss at Instrumentation in Flight Test was incensed, for example, finding out the SR-71 flight profiles were scheduled using Equivalent Airspeed, which is IAS without the instrument corrections. For a Mach 3 airplane, it had a P-38 "steam gauge" to tell the pilot how fast it was going! A true airspeed indicator was added late in its life. I guess knowing the structural restriction on the plane would be important, but that's what a g-meter does, better. Particularly in a plane with a 2-g limit! . *"Computers for Sea and Sky", by Rogowski, 1982; Creative Computing Press, ISBN 0-916688-38-0 presents all the math any flier might need, in equation formats quite amenable to spreadsheet use.
< Message edited by Tall Paul -- 2/18/2004 4:38:15 PM >
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Paul, We are talking about two completely different things. I'm talking about the local pressure at any given point on a wing, and you are talking about free stream pressure ahead of the aircraft.
Lets say your at an EAA flyin and you see a homebuilt with a pitot tube mounted on top of the wing right at the high point of the airfoil... and along side of that pitot tube there is a static port also on the high point of the airfoil. What do you think the airspeed indicator and altimeter would read? What would the pressure be at the pitot, what would the pressure be at the static port... what is the total pressure at that position on the wing? That is what I am talking about... The slight increase in velocity as the flow speeds up to get around the wing, the corresponding changes to the dynamic and static pressure, and the fact that the two still add up to equal total pressure (which hasn't changed). In my wind tunnel class in College the first experiment used a NACA 0012 airfoil with static pressure ports spaced along the chord from leading edge to trailing edge. Each of these static ports was attached to the top of a long tube filled part way with water. The other side of the tube was open to atmospheric pressure... at zero degrees angle of attack the water went up in the tube slightly due to the decrease in static pressure over the wing... at 10 degrees angle of attack the water went way up in the tube, again due to the decrease in static pressure. At negative angles of attack the exact opposite happened, but to a lesser extent. High static pressure would cause the water level to go down in the tubes, but the high pressure accounted for less then 10 percent of the pressure differential. Since this was a symetrical airfoil pressure ports could be used on only one side and measurements taken from -15 degrees to +15 degrees could be used to determine the pressure on the upper and lower surfaces from 0 degrees to +15 degrees. Basically I'm saying that static pressure is deffinately not constant around the entire airplane otherwise they wouldn't fly. Look at any picture taken from a CFD program and you'll see all the different colors representing local static pressure.
My Stinson used to have a venturi powered gyro... that venturi would pull 6 to 8 inches of mercury vacuum... or a static pressure inside of the venturi that is 20% lower then atmospheric pressure, which of course means that the dynamic pressure inside of the venturi is much greater in order to conserve total pressure.
Ty
< Message edited by acropilot_ty -- 2/19/2004 8:13:34 PM >
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I understand it. I even used water manometers doing the same experiments many years ago. I think todays students use some sort of transducers, or even just simulate it with a "program". LOL
< Message edited by LouW -- 2/19/2004 9:29:30 PM >
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It is incorrect to refer to the change in pressure on the upper surface of an airfoil as a change in "static pressure" without considering the change on the bottom surface of the airfoil which occurs at the same time. This pressure is greater than the change on the top side for lift. Yet neither by themselves are "static pressure". It is the difference between the pressures on the surfaces which generates lift. And drag. The diminished pressure on the upper surface is NOT the pressure the airplane's static port reads. That is independent of the existence of the airplane. The velocity of the airplane thru the air, or the wind past the model in the tunnel generates the total pressure the object experiences. The difference between the total pressure and the static pressure is the dynamic pressure. There are NO other correct definitions for these terms. The plane responds to v^2*rho/2 only... as modified by the angle of attack which generates the Cl and Cd multipliers which make lift and drag and moment. Lift can be zero; upper and lower pressures identical, but the dynamic pressure still remains, as long as there's airflow. Change the plane's attitude to where it generates lift at the same airspeed, the static pressure doesn't change, and the dynamic pressure remains the same.
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quote:
I think todays students use some sort of transducers, or even just simulate it with a "program". LOL
Not true ... I'm in 4th year aerospace engineering in Ottawa, and in 3rd year, we have one course where we get to do lots of different wind tunnel labs.... And I did indeed have to stand in front of ~50 manometers with a ruler calling out numbers to the guy with the log book over the noise of the wind tunnel :P
It's only in 4th year that they tell you that you could get a pretty good estimate of the lift produced by a wing using stuff like computers.
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