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#32
03-14-2005, 02:26 AM
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Re: Faucet Physics Question
[ QUOTE ]
And how much the stream narrows is a function of the viscosity of the liquid, [/ QUOTE ] no it isn't... not to any significant degree [ QUOTE ] So to focus on the conservation of mass aspect of the equation is not particularly helpful. [/ QUOTE ] sure it is, if you think of it in the right way. call it conservation of mass, conservation of matter, or whatever. the change in velocity is what is important. 
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#33
03-14-2005, 02:30 AM
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Re: Faucet Physics Question
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#34
03-14-2005, 02:31 AM
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Re: Faucet Physics Question
[ QUOTE ]
[ QUOTE ] And how much the stream narrows is a function of the viscosity of the liquid, [/ QUOTE ] no it isn't... not to any significant degree [ QUOTE ] So to focus on the conservation of mass aspect of the equation is not particularly helpful. [/ QUOTE ] sure it is, if you think of it in the right way. call it conservation of mass, conservation of matter, or whatever. the change in velocity is what is important. [/ QUOTE ] We might be talking about two ways of explaining the same thing. Nevertheless, I am not convinced of your explanation. Answer this question: If there were a liquid which had absolutely no attraction to istelf, what force would cause a molecule of that liquid which starts on the edge of the faucet to move inwards?
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#35
03-14-2005, 02:35 AM
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Re: Faucet Physics Question
[ QUOTE ]
Of course it must obey conservation of mass, but the most important part of the equation is the cohesion. Theoretically, if the water molecules were not attracted to each other at all, the stream would not narrow at all. And how much the stream narrows is a function of the viscosity of the liquid, which is a function of how much the molecules are attracted to each other. So to focus on the conservation of mass aspect of the equation is not particularly helpful. [/ QUOTE ] A stream of something non-polar like methanol would behave the exact same way as water, the cohesiveness of water is not why the stream becomes narrow. The narrowing of the water is basically Bernoulli's principle. I believe what is happening is that as the fluid velocity increases the pressure of the stream decreases and therefore the force exerted on the stream by air pressure increases narrowing the stream.
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#36
03-14-2005, 02:38 AM
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Re: Faucet Physics Question
[ QUOTE ]
The narrowing of the water is basically Bernoulli's principle. I believe what is happening is that as the fluid velocity increases the pressure of the stream decreases and therefore the force exerted on the stream by air pressure increases narrowing the stream. [/ QUOTE ] That is what I am looking for. So if this happened in a vaccuum, the stream would not narrow?
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#38
03-14-2005, 04:08 AM
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Re: Faucet Physics Question
the pressure terms in bernoulli's equation cancel so it doesn't matter if it's in a vacuum or not. bernoulli's equation just shows that the velocity increases as the water moves down. then mass conservation shows that because the water is moving faster the diameter must decrease.
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#39
03-14-2005, 04:09 AM
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Re: Faucet Physics Question
straight.
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#40
03-14-2005, 05:21 AM
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Re: Faucet Physics Question
This has essentially already been said, but I'll take a shot at explaining this...
Everyone agrees that for a steady stream of water or sand or anything else, the mass / unit time passing through any plane of the stream (the flux) has to be equal - this is the conservation of mass part, and is essential. The flux for any cross-section of the stream is equal to Area x Velocity x Density. Since the velocity increases further down the stream, the area and/or the density must decrease to compensate. Since the stream is a unbroken column of water, the density cannot decrease (because its a liquid) and so the cross-sectional area must decrease. In the sand case, the individual grains of sand act sort of like a gas, so the density of sand grains will go down and the stream will not narrow. So the part about water molecules being attracted to each other is just saying that the bonds are strong enough to make it a liquid, not a gas.
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