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And someone told me that I am calculating the Reynolds number of an open channel and for that flow can remain in laminar condition even it's Re is in millions..

Is this true? can anyone provide me some reference material as well

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- Thread starter Qais Hassan
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- #1

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And someone told me that I am calculating the Reynolds number of an open channel and for that flow can remain in laminar condition even it's Re is in millions..

Is this true? can anyone provide me some reference material as well

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Chestermiller

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I have spent my hours on this problem but since this is a field of science and any research in this field is not much so pardon me if I am wrong

I know that Reynolds Number is proportional the ratio of inertial forces and viscosity of any flowing fluid and this was going very good for me when the flow was in the pipe as it was offering much resistance to it to flow in a laminar stream for which the limiting value of Re is 2300 in a pipe. But when I am considering the flow just right after the outlet I am confused that how should I define the Reynold's number as the flow has no interaction with any solid surface it's just flowing like a free stream like when the water is flowing out from a tap and at that outlet I'm getting a

Kindly provide some help sir I'm struck

P.S: I am trying to create a laminar flow fountain

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Let me tell you the whole working of my jet which I am going to use to produce the laminar stream...

Water is pumped in to the jet through the tangential inlet attached at the bottom of the Jet, this tangential inlet creates a rotational flow and passes through a filter (foam) to decrease the initial turbulence and make the velocity profile bit uniform then the flow is divided to pass through the capillaries having a very small diameter which creates a shear stress and decreases the velocity of the flow and this is the portion where "Laminar Flow" is created.

After passing through the capillaries flow is passed through the outlet, velocity has to be low at this point as well to avoid the turbulent transition but the velocity is getting high around 5.6 m/sec which is producing a Re of 120,000 using reynold's number for pipe flow

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Chestermiller

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Also, for this application, why is it necessary for the flow to be laminar? What is it about a turbulent version of the application that would not provide the desired functionality or aesthetics?

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@Qais Hassan

Why do you think you need to have some kind of interaction with a solid surface in order to have a Reynolds number? Also, what definition of Reynolds number are you using?

Just doing quick back of the envelope calculations, it seems to me that your jet would have to be roughly 22 mm in diameter to have a Reynolds number as high as you are quoting. This makes it seem plausible that your Reynolds number is ##O(10^5)## if your orifice really is that size. Is this the case?

Why do you think you need to have some kind of interaction with a solid surface in order to have a Reynolds number? Also, what definition of Reynolds number are you using?

Just doing quick back of the envelope calculations, it seems to me that your jet would have to be roughly 22 mm in diameter to have a Reynolds number as high as you are quoting. This makes it seem plausible that your Reynolds number is ##O(10^5)## if your orifice really is that size. Is this the case?

Go to YouTube and search for "laminar jet fountain." They are actually really neat, and a turbulent jet would definitely not reproduce the effect.Also, for this application, why is it necessary for the flow to be laminar? What is it about a turbulent version of the application that would not provide the desired functionality or aesthetics?

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No my orifice diameter is 8mm.

To create inertial effects, solid interaction is important I guess as the viscosity of air is nearly zero.

And Reynolds number is simply the ratio of inertial effects and viscosity

Re = (density)(velocity)(diameter)/(dynamic viscosity)

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@Chestermiller here are the schematics Sir and it would be really helpful if you can watch some videos related to laminar fountains on youtube

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Ah, you are using air. I was using water in my previous post. You don't need for air to interact with a surface for the concept of Reynolds number to make sense. The inertial (upper) part of the Reynolds number has nothing to do with viscosity, so I am not sure why you think the low viscosity of air would affect that. Further, jets do have a mechanism for generating viscosity (much as a wall does). Your jet emerges from an orifice into a body of still fluid, meaning there will be velocity shear at the edges of the jet. Look up the Kelvin-Helmholtz instability.

No my orifice diameter is 8mm.

To create inertial effects, solid interaction is important I guess as the viscosity of air is nearly zero.

And Reynolds number is simply the ratio of inertial effects and viscosity

Re = (density)(velocity)(diameter)/(dynamic viscosity)

Also, I am well aware of the generic definition of the Reynolds number. I am asking you what you used for the quantities in the definition. You used diameter as your length scale. Was that the diameter of the exit of your nozzle? What values did you use for density and viscosity? I am coming up with an answer that is two orders of magnitude smaller than yours if I do it for air. Why don't you show your work here to show us exactly how you came up with 120,000, because I can't reproduce it.

Finally, a note on the minimum critical Reynolds number:

For something like the flow in a pipe, where there is a well-defined critical Reynolds number that leads to turbulence, this doesn't mean that as soon as you reach that number, the pipe suddenly becomes turbulent. What it really means is that once you reach that number, the flow is now unstable to minute disturbances and will transition at some point. However, pipes are unusual in that they have a very well-defined critical Reynolds number that leads to transition. This is not generally the case in all fluid flows. Like I mentioned before, it is not uncommon for the Reynolds number (based on length) to reach well into the millions on something like an airplane wing before transition occurs. In short, be careful when drawing parallels between pipe flows and other situations.

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OK I got the concept that shear forces will act in an open stream as well Thanks for that. I am using water in my jet the thing which I said above was for the interaction between water and air, which is now clear.Ah, you are using air. I was using water in my previous post. You don't need for air to interact with a surface for the concept of Reynolds number to make sense. The inertial (upper) part of the Reynolds number has nothing to do with viscosity, so I am not sure why you think the low viscosity of air would affect that. Further, jets do have a mechanism for generating viscosity (much as a wall does). Your jet emerges from an orifice into a body of still fluid, meaning there will be velocity shear at the edges of the jet. Look up the Kelvin-Helmholtz instability.

Also, I am well aware of the generic definition of the Reynolds number. I am asking you what you used for the quantities in the definition. You used diameter as your length scale. Was that the diameter of the exit of your nozzle? What values did you use for density and viscosity? I am coming up with an answer that is two orders of magnitude smaller than yours if I do it for air. Why don't you show your work here to show us exactly how you came up with 120,000, because I can't reproduce it.

Finally, a note on the minimum critical Reynolds number:

For something like the flow in a pipe, where there is a well-defined critical Reynolds number that leads to turbulence, this doesn't mean that as soon as you reach that number, the pipe suddenly becomes turbulent. What it really means is that once you reach that number, the flow is now unstable to minute disturbances and will transition at some point. However, pipes are unusual in that they have a very well-defined critical Reynolds number that leads to transition. This is not generally the case in all fluid flows. Like I mentioned before, it is not uncommon for the Reynolds number (based on length) to reach well into the millions on something like an airplane wing before transition occurs. In short, be careful when drawing parallels between pipe flows and other situations.

In order to get the height of 6 feet I got my velocity of 6.06 m/sec using Bernoulli's equation (V= sq. root 2gh as the Gage pressure is zero and at max height velocity is zero), now for the Reynolds number at the orifice, diameter is 8 mm, density of water 1000 kg/m^3, dynamic viscosity of water is 0.000404 kg/(m.s) which will lead to Re of 120,000

Yes that's what I'mm stuck in it,I know that Reynolds number can get into millions for different situations but I'm not getting any reference for this type of flow which is occurring in the laminar stream right after the nozzle. can you please provide me a reference so that I can mention it in my research papers?

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