Expert: Mark Janus Date: 7/11/2008 Subject: Spool and card demonstration
Question QUESTION: Hi, and thanks for any help you can offer. I'm taking a fluid mechanics class, where the book mentions the demonstration where you blow air through a sewing thread spool, you put a playing card on the other side, and the card sticks to the spool. The explanation they give is that the fast air that flows between the spool and the card has lower pressure than the ambient air due to Bernoulli's equation, therefore the card sticks to the spool, however this makes no sense to me. If the air between the spool and the card has lower pressure than ambient pressure, why doesn’t the air blow in, rather than out? Also I don’t think it’s correct to say that the pressure is lower due to Bernoulli's equation, because in saying that the faster air's pressure is lower than the ambient air’s pressure through Bernoulli, we would be making the unfounded and wrong assumption that the total pressure between the streamlines of the fast air and the stagnant air is equal. It’s wrong to apply Bernoulli’s equation between the two streamlines because they have different total pressures. It makes much more sense to me that the air inside the spool has a higher total pressure and also a higher static pressure; since its static pressure is higher than outside, the air will accelerate until it exits into the ambient, at which point its static pressure reaches exactly ambient pressure but however at that point it has a higher velocity than the surrounding air due to the fact that this flow has a higher total pressure than the surrounding air. But if that is true, then why would the card stick to the spool? Is it due to another effect? Can you help me clear up my confusion? Thank you.
ANSWER: If I understand the demonstration project, the spool is held with its axis (hole) vertical and the card is flat covering the lower hole.... blow across (not down the hole) the top of the spool and let go of the card.... the card stays because the static pressure inside the spool (hole) is lower than the ambient pressure. The pressure on the "other side" of the card is ambient pressure, the pressure inside the hole is lowered similar to the Venturi effect. The flow outside moving over the hole in effect pulls some of the air out of the hole and hence the pressure is lower inside. If you blow to much at an angle (rather than across the hole) this will not be the case, you will actually be blowing air into the hole (and increasing the pressure)...
Hope this helps,
mj
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QUESTION: Hi, thank you for replying. The demonstration is a bit different, you blow air through the hole of the spool as this webpage shows: http://www.exploratorium.edu/snacks/bernoulli_levitator/index.html The webpage gives the same explanation as the book: air accelerates between the spool and the card and it's pressure drops to lower than ambient. I have no doubt that the passing air accelerates and drops its pressure, but I do doubt the pressure drops below that of ambient pressure, since this would lead to the air blowing into the spool and not out. I would think that it rather drops below that of its original pressure (high pressure inside ones mouth), and drops until it reaches ambient pressure just as it exits the spool and card. At this point it has the same pressure as ambient but higher velocity therefore higher total pressure. I think that to say that the pressure drops below ambient pressure would be to assume that the total pressure of both streamlines is equal, which is unfounded. Am I wrong? If I’m right, what would be holding the card attached then? I’m greatly thankful for any help.
Answer Yes, I see this is quite different than what I was envisioning...
In this case, the air (pressure) will be high right in the center of the card yet will rapidly decrease as the air is expelled outward (from the center). The static pressure of a fluid can easily be lower than the surrounding ambient pressure when it comes from a reservoir (in this case your lungs) and is confined. Agreed, the flow must match the ambient pressure at the exit (edge of the spool), but since the area (on the card) over which the pressure is lowered (between the immediate center region and the edge) is greater than the area over which the pressure is higher (right at the center) the card would be supported. Consider the path the flow must take and the cross-sectional area over which the fluid is flowing when considering Bernoulli's. The cross section (perpendicular to the flow) gets larger as you move away from the center (think of the surface area of a cylinder as the diameter of the cylinder gets larger) so the velocity will decrease (due to conservation of mass V1A1 = V2A2) and hence the pressure will increase. So the fluid pressure is lower (than ambient) in the region between the card and the edge of the spool (where it must be ambient). The fluids momentum is what enables the flow the continue flowing "out" instead of flowing back in (like you surmised due to the pressure difference).
