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#261
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lift, wings, and Bernuolli
The distinction is that a compressible fluid (commonly called gas)
undergoes a volume change proportionate to the pressure change Well, when an object passes through the air, does it not compress the air in front of it (and rarefy the air behind it)? This is how speakers work. Those are all pressure changes. Jose -- Money: what you need when you run out of brains. for Email, make the obvious change in the address. |
#262
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lift, wings, and Bernuolli
In open air the volume of air moving around the fan is larger,
but moving at a lower speed than the air moving through the fan so that the momenta of the flow in either direction is equal magnitude and opposite in direction to the flow in the other direction. Seems to me "almost equal" would make more sense, otherwise an airplane propeller would not work. A propeller throws air backwards (alabeit imperfectly); the airplane moves forwards in response. Jose -- Money: what you need when you run out of brains. for Email, make the obvious change in the address. |
#263
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lift, wings, and Bernuolli
Jose wrote:
The hovering spacecraft has zero horizontal and vertical momentum. It has weight, directed downwards. The engine accelerates mass downward producing an upward force equal in magnitude and opposite in direction to the weight of the spacecraft. This imparts an acceleration to the spacecraft equal in magnitude and opposite in direction from the local acceleration due to gravity. The flying wing has some horizontal momentum which is secondary here, How much? and zero vertical momentum. It also has weight, directed downwards. The wing accelerates mass downward (mass it finds in the air molecules) producing an upward force equal in magnitude and opposite in direction to the weight of the wing (and its presumably attached aircraft. It does so by finding air in front of it, flinging it downwards and forwards (which causes the air in front to try to get out of the way by rising). In the steady state, one can measure high pressure below and low pressure above, but this is just the macroscopic manifestation of the greater number of molecular collisions below, and the lesser number of collisions above. That's what pressure is - we have both agreed on this. The greater number of collisions below imparts an acceleration to the aircraft equal in magnitude and opposite in direction from the local acceleration due to gravity. I agree that lift is a force, exerted on the aircraft by the air, which in steady level flight is equal in magnitude and opposite in direction to the weight of the aircraft. Energy is 'pumped' into the air by the plane. There is no need for a net momentum exchange between the airplane and the air in order for energy to be exchanged or for forces to be applied. Indeed, in those last two paragraphs above, you make no mention of momentum. BTW, I was wrong to invoke conservation of momentum. Momentum is conserved in elastic collisions, like the collision between a cue ball and the eight ball. Momentum is not conserved in inelastic collisions, like the collision between a cue ball and a nerf ball. Roll the airplane into a 90 degree bank. The weight is now orthogonal to the lift. As teh airplane falls, it banks even though there is no Earth 'under' the belly. Why? -- FF |
#264
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lift, wings, and Bernuolli
Jose wrote: In open air the volume of air moving around the fan is larger, but moving at a lower speed than the air moving through the fan so that the momenta of the flow in either direction is equal magnitude and opposite in direction to the flow in the other direction. Seems to me "almost equal" would make more sense, otherwise an airplane propeller would not work. A propeller throws air backwards (alabeit imperfectly); the airplane moves forwards in response. For the stationary fan if it were only _almost equal_ then you would eventually run out of air on one side of the fan. Air molecules flowing through the propellor cetainly experience momentum changes. But you can have a net flow of energy without a net exchange of momentum because momentum is a vector, energy is a scaler. If the airplane is in level flight at constant speed it does not NEED to gain any momentum from the propellor because the momentum of the airplane is not changing. It needs force to counter the force of drag. Consider your example of the person who 'hovers' by dribbling a basektball. His momentum is zero, the momentum of the Earth is zero and the momentum of the ball is constantly changing and reverses twice each dribble. The dribbler is pumping energy into the Earth yet there is no net exchange of momentum. -- FF |
#265
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lift, wings, and Bernuolli
The flying wing has some horizontal momentum which is secondary here,
How much? mv The air thrown forward (or, if you will, the higher pressure ahead) tries to reduce that, the engine presumably makes up for it. Energy is 'pumped' into the air by the plane. Yes, and what form does that energy take? I maintain that it takes the form of a net increase in mv^2/2 over all the air molecules. Since m doesn't change, and 2 only changes in a pentium, that leaves v to change. This changes mv, thus momentum. We agree that there is (microsocopic) momentum transfer at each collision. We disagree as to whether the net is zero, and I think that part of that disagreement has to do with just how much of the system we are looking at. The wing throws air down. If that causes other air to be squeezed up, so be it - the wing will grab that air and throw it down again. The air piles up in front of and below the wing, and ultimately pushes on the earth. New (undisturbed) air keeps appearing in front of the wing (where it is pushed up, and then back down). But if, instead of feeding this system fresh air, we instead feed it the same air, say, by flying around in circles, there will be a net movement of air. Air will be sucked from the (infinite amount of) air above, and pushed down into the (infinite volume of) air below. The next time the wing encounters this area, there will already be downward movement of air from the first passage... etc. etc. and so forth. Momentum is conserved in elastic collisions Low speed collisions between air molecules and aluminum sheets are to first order elastic (although some energy goes into making molecules wiggle and spin, and I suppose an electron is knocked out every now and again). Roll the airplane into a 90 degree bank. The weight is now orthogonal to the lift. As teh airplane falls, it banks even though there is no Earth 'under' the belly. Why? I'm not sure I understand the question. But if you put an airplane in a knife edge and let it dive as it will, and maintain a lift-producing AOA, the wing will push air in the belly direction, as it pushes itself against that air in the antibelly direction. Some of that air will swirl around the wing, but enough of it will dissipate the momentum that the wing imparted to it over the entire atmosphere, and there will be a (very) slight breeze blowing in the belly direction. Jose -- Money: what you need when you run out of brains. for Email, make the obvious change in the address. |
#266
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lift, wings, and Bernuolli
For the stationary fan if it were only _almost equal_ then
you would eventually run out of air on one side of the fan. No, the pressure would build up on one side of the fan, and that pressure would push against the wall and against the other air that is being pushed by the fan. When the pressure on that side is sufficiently high, no more (net) air will be able to be smooshed together on that side, and the air will all be going around. But a pressure difference will be maintained until the fan is turned off. Consider your example of the person who 'hovers' by dribbling a basektball. His momentum is zero, the momentum of the Earth is zero and the momentum of the ball is constantly changing and reverses twice each dribble. The dribbler is pumping energy into the Earth yet there is no net exchange of momentum. I agree. Overall, no net change. Microscopically (at each impact) there is a momentum change. Inbetween dribbles, the earth and the dribbler experience momentum changes which each dribble then counteracts. Now look at the same situation with a "basketball transparant" earth, and an endless supply of basketballs being tossed at the dribbler (who is backed up against a frictionless wall, so for now we don't need to consider horizontal forces). The dribbler keeps on deflecting basketballs downwards, but they don't bounce back up - they pass through the earth. The dribbler (who admittedly is no longer really dribbling) is imparting momentum to basketballs, and once he stops doing that, he will himself experience a momentum change. In both cases, as far as the putative dribbler is concerned, he is throwing basketballs down. He imparts momentum to basketballs, and really doesn't care what happens to that momentum afterwards. Jose -- Money: what you need when you run out of brains. for Email, make the obvious change in the address. |
#267
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lift, wings, and Bernuolli
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#268
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lift, wings, and Bernuolli
Air is pressurized behind the speaker, just as well as the air in front of
it. That is how bass reflex speakers work. Yes, but out of phase. Air is pressurized in the direction the speaker cone is moving. It goes back and forth. Jose -- Money: what you need when you run out of brains. for Email, make the obvious change in the address. |
#269
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lift, wings, and Bernuolli
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#270
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lift, wings, and Bernuolli
F = m/t * v/t; the force is equal to the rate of mass per unit time,
multiplied by the distance per unit time. I assume a typo: F = m/t * d/t (since v=d/t) Jose -- Money: what you need when you run out of brains. for Email, make the obvious change in the address. |
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