Water flowing through a funnel

[wessholders]

Will water flowing through a funnel be accelerated more by a "curve-walled" funnel rather than a "straight-walled" funnel?

 

[berkeman]

Welcome to PF.

What are your thoughts? What reading have you been doing trying to figure this out? Can you post some links to that reading?

Also, is this for schoolwork?

 

[wessholders]

This is for a project I am working on, not related to school work. So far I have been looking for the optimal funnel to maximize volume and acceleration. I have determined that a "narrower/tall" funnel is better for my purposes that a "wide/short" funnel. I've done this just by playing around with various funnels at the hardware store, nothing super scientific. I just couldn't help but imagine that there has to be some optimal curve, similar to the brachistochrone curve. I have read a few papers discussing flow dynamics of funnels of various angles, but not quite what I am looking for. I can't help but wonder if a simple parabola with a spout would suffice?

-WS

 

[hutchphd]

While I understand the OP question more or less a curvy funnel is a much broader class of objects and so the answer tis almost certainly yes, curvy is better as I think is evident.
But the details are nontrivial and will depend upon a host of factors. For instance how big is the funnel ? Expected flow rates.? Differential pressure?

 

[wessholders]

Thank you hutchphd,
While I wish that I could give you that information, I just don't have it. What made me start thinking about this is a pool toy I saw the other day that is essentially a cone with two handles on the wide end. The wide end is to be submerged and quickly pulled, resulting in a high pressure jet of water being shot out of the narrow end (photo attached). The toy is probably 8" wide at the bottom and 1.5" wide at the top, over a span of 18". Those toys all have straight sides as depicted. I had imagined that a "curvy" funnel would be better, just didn't know if there was an ideal shape.

 

[hutchphd]

Thanks for the description. That looks like an interesting toy. Does the water come out in a relatively collimated jet? I'm sure that turbulent flow is the enemy here. But it may be very subtle. I may cut up some "larger" plastic bottles and hit the pool !

 

[erobz]

It seems like you might try to optimize in such a way that for any fixed nozzle diameter, minimize the time to drain a given volume?

 

[Baluncore]

The aim is to avoid sudden changes in flow direction, which can lead to a "vena contracta" that will reduce the effective diameter of the funnel.
https://en.wikipedia.org/wiki/Vena_contracta
https://en.wikipedia.org/wiki/Borda–Carnot_equation

Potential energy must be smoothly converted to kinetic energy as the fluid falls through the funnel. Cross-section must change by the same ratio per unit travel along the funnel.

I believe the optimum flow will be with an exponential horn, like a reversed loud hailer, so the fluid is accelerating smoothly along the channel, without sudden changes in fluid wall pressure.

 

[wessholders]

The aim is to avoid sudden changes in flow direction, which can lead to a "vena contracta" that will reduce the effective diameter of the funnel.
https://en.wikipedia.org/wiki/Vena_contracta
https://en.wikipedia.org/wiki/Borda–Carnot_equation

Potential energy must be smoothly converted to kinetic energy as the fluid falls through the funnel. Cross-section must change by the same ratio per unit travel along the funnel.

I believe the optimum flow will be with an exponential horn, like a reversed loud hailer, so the fluid is accelerating smoothly along the channel, without sudden changes in fluid wall pressure.

Thanks for the description. That looks like an interesting toy. Does the water come out in a relatively collimated jet? I'm sure that turbulent flow is the enemy here. But it may be very subtle. I may cut up some "larger" plastic bottles and hit the pool !

Here is a short video demonstrating what I am talking about.

 

[wessholders]

Here is a short video demonstrating what I am talking about.

I just took a video and am trying to figure out how to post it, but it does look to be relatively collimated. I am a biologist so not super versed with the vocabulary, but it appears smooth/laminar.