Faucet Physics Question

[MrOnizuka]

Just wanted to say that 7A at Berkeley sucks.

Between that class and CS61A I'm thinking of switching to something useless like geography.

bleh, thanks for reminding me I didnt do any homework this weekend. [img]/images/graemlins/smirk.gif[/img]

[Piz0wn0reD!!!!!!]

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hmm i did take fluid mechanics. i know we talked about this too. i think it has to do with conservation of mass laws.

picture it like this, the water falls faster near the bottom of the stream than near the top. the same amount of mass has to pass through certain areas of the stream in the same amount of time, so it has to narrow as it goes faster.

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if you poured balls out of a big tube, the stream of balls would not narrow as it picked up speed. Its because the water is attracted to itself.

[styleish]

balls are not fluid.

[Lazymeatball]

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balls are not fluid.

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and that is the reason why they were a useful example.

[Matt Flynn]

Did someone give the equation? Assuming no air enters the water after leaving the faucet (which is close enough), it is velocity x area through which water flows. In other words, mass is conserved.

v1 x A1 = v2 x A2.

A = pi x (r x r) so drop out pi:

v1 x r1 x r1 = v2 x r2 x r2 (can't get it to read r sqaured correctly)

Or: v2/v1 = r1 x r1 / r2 x r2

Chapter 1 in any intro physics book. Can't believe one of the MIT boys didn't get here first.

Matt

[theBruiser500]

Matt Flynn RULEZ!!

[TimM]

This does not tell us anything about the diameter from the stream at a given distance from the faucet.

http://ist-socrates.berkeley.edu/~phyh7a/hw10.pdf

Top of page 7.

But I'm not sure this is correct. Shouldn't the viscosity resist the acceleration due to gravity somewhat? Maybe this is negligible for water.

http://xtronics.com/reference/viscosity.htm

[daryn]

</font><blockquote><font class="small">In risposta di:</font><hr />
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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</font><blockquote><font class="small">In risposta di:</font><hr />
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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i just want to take this opportunity to say damn i'm good. patrick, don't let your employer see this!

[Philuva]

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This does not tell us anything about the diameter from the stream at a given distance from the faucet.


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Matt's equation tells us that since the water must be moving faster further away from the faucet because of gravity (v2 &gt; v1) then in order for the ration to work r1&gt; r2.

[The Goober]

So after posting this, I looked at an actual smooth stream of water from my faucet and noticed something - at the very bottom of the stream, the stream stopped narowing, and instead it broke up and started mixing with air. Clearly, there is some point (before reaching terminal velocity) where the surface tension is not enough to keep the stream as a solid column of water and instead the density does go down as the water breaks into smaller droplets. So, the viscosity / surface tension does play a pretty big part here. I imagine that if one poured out a nice big stream of syrup from a very high distance, you would see the stream get pretty damn narrow before it starts to break up (and it may not break up at all if its still a stream when it reaches terminal velocity). I think this is the only reason that it would change things if you did this in a vacuum - without air, there is no terminal velocity and even the most viscous liquid stream would eventually break up into smaller droplets.