funnel

[chiddler]

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Suppose a liquid is going down a funnel. When is velocity the highest?

Answer is at the thin part of the funnel.

I'm trying to figure out how the velocity changes in the thin part vs after it leaves the funnel completely and free-falls in air. How do they compare? Why is thin-funnel velocity higher than free falling?

 

[Morsetlis]

Conservation of mass: Bernoulli's.

Same mass : more flow with lower radius. Imagine open-air as having an infinite amount of radius (not really, but yeah).

 

[chiddler]

oh.

thank you.

 

[EnginrTheFuture]

The velocity after the funnel is the same as right before it leaves the funnel... conservation of energy.

If there is no air resistance, and there is gravity (which there must be) the velocity after the pipe will always be greater than before leaving the pipe. But that is never going to be tested because the velocity after it leaves the pipe is worthless to think about if they are trying to test fluid dynamics.

Just don't want you thinking that somehow the radius is magically infinite and it still follows bernoulli's. If that was the case the infinite radius would mean a velocity of 0 which is clearly not the case.

 

[chiddler]

The velocity after the funnel is the same as right before it leaves the funnel... conservation of energy.

If there is no air resistance, and there is gravity (which there must be) the velocity after the pipe will always be greater than before leaving the pipe. But that is never going to be tested because the velocity after it leaves the pipe is worthless to think about if they are trying to test fluid dynamics.

Just don't want you thinking that somehow the radius is magically infinite and it still follows bernoulli's. If that was the case the infinite radius would mean a velocity of 0 which is clearly not the case.

Then why is the answer in the question I solved "velocity highest inside the thin part of the funnel"?

 

[SaintJude]

Maybe they didn't really think through it and just wanted to design a question that tested if you knew the inverse A * velocity relationship

 

[Morsetlis]

The velocity after the funnel is the same as right before it leaves the funnel... conservation of energy.

If there is no air resistance, and there is gravity (which there must be) the velocity after the pipe will always be greater than before leaving the pipe. But that is never going to be tested because the velocity after it leaves the pipe is worthless to think about if they are trying to test fluid dynamics.

Just don't want you thinking that somehow the radius is magically infinite and it still follows bernoulli's. If that was the case the infinite radius would mean a velocity of 0 which is clearly not the case.

I don't observe this with a hose.

Streams of water expand IRL.

 

[chiddler]

I don't observe this with a hose.

Streams of water expand IRL.

well hold on. what about how a faucet's tap water shrinks as it drops?

this is due to pressure velocity relationship of bernoulli's, yes. but i don't think your approach is entirely accurate.

 

[milski]

Once the horse is out of the barn, I mean the fluid out of the pipe it gets really complicated, really fast. I'll be perfectly happy that I don't have to deal with that. 🙂


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[chiddler]

alright well if milski says it is complicated, screw it. probably a rogue question.

thanks for the responses.

 

[milski]

I think they're asking only about where inside the funnel.

Outside of the funnel it starts to matter what holds the fluid together, will it split in droplets and other "interesting" things.


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[chiddler]

the question was like, from top to bottom of my image,

I


II


III


IV

at which point is fluid velocity the highest. III being inside the thin part, IV being outside the funnel. were it only the funnel, this would be a lot easier for sure.