# Confused about Reynolds Number- Fluid Mechanics

• Qais Hassan
In summary, the conversation discusses the calculation of the Reynolds number for a laminar flow in a nozzle. The initial calculation resulted in a Re greater than 120,000, which raised questions about the validity of the result. The possibility of laminar flow in open channels with Re in the millions was mentioned, but further information about the system configuration and definition of Reynolds number is needed. The speaker also shares their efforts in creating a laminar flow fountain and asks for assistance and clarification on the concept of Reynolds number. The conversation also touches on the potential use of air instead of water for the flow and the impact of viscosity on the Reynolds number. Overall, the conversation highlights the complexities of calculating and defining Reynolds number for different flow scenarios.

#### Qais Hassan

Hi, I am working on the laminar flow and during my calculation at the outlet of my nozzle my Re was even greater than 120,000 however my other calculations seemed legit to me.
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

I strongly doubt it. How much research have you done to answer your question? I have a reference, but I'm not going to reveal it until I see significant effort on your part.

You haven't described anything about your system configuration, so it would be difficult to determine how realistic that number is. You also haven't told us how you are defining the Reynolds number in this case. There are plenty of instances where laminar flows can exist well into the millions or even tens of millions, but it all depends on how you define ##Re## and the system in question, and you've given us essentially no information there.

@Chestermiller
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 Re 120,000, this can be a laminar flow if I treat it like an open flow as the limiting value of open flow stream flowing down the hill is 5 exp 5 for laminar...But the stream is not in contact with any surface I can't consider it like that
Kindly provide some help sir I'm struck
P.S: I am trying to create a laminar flow fountain

You haven't described anything about your system configuration, so it would be difficult to determine how realistic that number is. You also haven't told us how you are defining the Reynolds number in this case. There are plenty of instances where laminar flows can exist well into the millions or even tens of millions, but it all depends on how you define ##Re## and the system in question, and you've given us essentially no information there.
Let me tell you the whole working of my jet which I am going to use to produce the laminar stream...
Water is pumped into 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

It would be really helpful if you could provide a schematic diagram of the system.

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?

@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?

Chestermiller said:
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?

Go to YouTube and search for "laminar jet fountain." They are actually really neat, and a turbulent jet would definitely not reproduce the effect.

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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)

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

Qais Hassan said:
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)

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.

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.
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.
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?

Well with those numbers (which indicate that your water is at 70°C?), then your Reynolds number seems to actually be that high. Laminar-turbulent transition in jets is a well-studied phenomenon, so if I were you I would search through journals to see what you turn up.

## 1. What is Reynolds Number in Fluid Mechanics?

Reynolds number is a dimensionless number used in fluid mechanics to characterize the relative importance of inertial forces and viscous forces in a flow. It is named after Osborne Reynolds, a British scientist who first studied its significance in fluid flow.

## 2. How is Reynolds Number calculated?

Reynolds number is calculated by multiplying the fluid velocity by the characteristic length of the flow and dividing it by the kinematic viscosity of the fluid. It is represented by the equation Re = (ρ * V * L) / μ, where ρ is the density of the fluid, V is the velocity, L is the characteristic length, and μ is the dynamic viscosity of the fluid.

## 3. What is the significance of Reynolds Number in fluid flow?

Reynolds number helps determine the type of flow that a fluid will exhibit, whether it is laminar or turbulent. It also helps predict the behavior and stability of a flow, as well as the pressure drop and heat transfer in a system. It is an important parameter for understanding and analyzing fluid dynamics.

## 4. What is the difference between laminar and turbulent flow?

In laminar flow, the fluid particles move in smooth, parallel layers with no mixing between them. This type of flow is characterized by low Reynolds numbers. In turbulent flow, the fluid particles mix and move in an irregular and chaotic manner, resulting in a higher Reynolds number. This type of flow is more common in real-world applications.

## 5. What is the ideal Reynolds Number for a specific flow?

The ideal Reynolds number for a specific flow depends on various factors such as the geometry of the flow, the fluid properties, and the boundary conditions. Generally, a Reynolds number below 2300 indicates laminar flow, while a number above 4000 indicates turbulent flow. In between these values, the flow may exhibit characteristics of both laminar and turbulent flow.