Maintaining the same flow rate while subdivding a tube

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Discussion Overview

The discussion revolves around the challenge of maintaining the same flow rate and pressure when subdividing a 5/8" tube into multiple smaller 0.1" tubes and then rejoining them into a single 5/8" tube. Participants explore the implications of fluid dynamics, particularly in relation to pressure gradients and flow rates, while considering the effects of friction.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes that mass conservation dictates the same volume of air must pass through the smaller tubes as through the larger tube.
  • Another participant questions whether maintaining the same flow at the same pressure means keeping the same pressure gradient, suggesting that Poiseuille's equation could be relevant.
  • Calculations based on the area of circles indicate that approximately 40 small 0.1" tubes would be needed to match the flow rate of the single 5/8" tube, although this figure is later challenged.
  • One participant argues that the flow rate through a tube depends on the fourth power of the radius, suggesting that significantly more than 40 tubes—potentially around 6,000—would be required to achieve the same flow rate at the same pressure drop.
  • Concerns are raised about the physical size of the bundle of smaller tubes, which would be much larger than the original tube, due to the high number of tubes needed.
  • Participants discuss the relevance of friction in the context of air flow and consider alternative scenarios, such as using a thin plate with holes instead of tubes, where friction might be less significant.

Areas of Agreement / Disagreement

Participants express varying views on the number of smaller tubes required to maintain flow rate and pressure, with some calculations suggesting a much larger number than initially proposed. There is no consensus on the exact number of tubes needed, and the discussion remains unresolved regarding the implications of friction and flow dynamics.

Contextual Notes

Limitations include the assumptions made about flow conditions (laminar vs turbulent) and the potential impact of friction, which are not fully explored in the calculations presented. The discussion also highlights the complexity of fluid dynamics in practical applications.

Pyper
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I have a 5/8" tube that air is blown through. I want to subdivide the center section using .1" tubes so that the same volume of air can be blown through it. It will start as 5/8", but immediately be divided into the separate .1" tubes, then end as a single 5/8" tube. How many .1" tubes would I need to maintain the flow of the single 5/8" tube?
 
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Ignoring friction with the pipe walls for the moment... mass conservation ensures that the same air that goes through the 5/8" section has to also pass through the tiny follow-on tubes, right?
Is the question instead that you want to maintain the same flow at the same pressure even though you are splitting the tube? If so, don't you want to maintain the same total pipe cross-section, ignoring friction?
 
olivermsun said:
maintain the same flow at the same pressure
What does it mean to maintain the same flow at the same pressure? The same pressure gradient? Then Poiseuille's equation should help.
 
Is the question instead that you want to maintain the same flow at the same pressure even though you are splitting the tube?

yes!
If so, don't you want to maintain the same total pipe cross-section, ignoring friction?

yes!

Basically I want to blow through the tube and it be just as easy to blow through when diverting to smaller tubes as it is with a straight 5/8" tube.

I did these simple calculations just based on area of a circle:

5/8" = 15.875mm = Area of 791.73
.1" = 2.54mm = Area of 20.268
791.73/20.268=39.063
So I would need 40 small .1" tubes to have the same flow rate and pressure of the single larger 5/8" tube.
Does that sound about right?
That seems like a lot!
5/8" is only .625, it seems like 7 smaller tubes would be enough..
My thinking may be flawed here...
 
Last edited:
Pyper said:
Basically I want to blow through the tube and it be just as easy to blow through when diverting to smaller tubes as it is with a straight 5/8" tube.
So the total length is unchanged, but we want a bunch of 1mm capillaries to replace a single 5/8 inch tube and still present the same pressure drop at the same total volumetric flow rate.
I did these simple calculations just based on area of a circle:

5/8" = 15.875mm = Area of 791.73
.1" = 2.54mm = Area of 20.268
791.73/20.268=39.063
So I would need 40 small .1" tubes to have the same flow rate and pressure of the single larger 5/8" tube.
Does that sound about right?
It is far far worse than that. The flow rate through a tube goes as the fourth power of the radial dimension. The ratio of your radial dimensions here is 8.75 to 1. Raise that to the fourth power and you will need a bit under six thousand small tubes to get the same flow rate as that 5/8 inch tube at the same pressure drop.

Edit: corrected my figures to use 0.1 inch small tube rather than 1 mm small tube and added...

There is a reason for this seemingly extreme behavior. In a tube with laminar flow, friction means that the fluid near the tube walls is moving slowly while fluid near the center is moving more rapidly. The closer the walls are to the center, the slower the fluid at the center will move -- for a fixed pressure gradient.

Here is another link to the resulting flow equation: https://www.fxsolver.com/browse/formulas/Hagen-Poiseuille+Equation

The situation is worse yet if the flow is not laminar.
 
Last edited:
jbriggs444 said:
What does it mean to maintain the same flow at the same pressure? The same pressure gradient?]
Yes.
jbriggs444 said:
Then Poiseuille's equation should help.
Yes, I agree that's what the OP should use if this is a practical problem where the pressure gradient is held more or less constant.
 
This is blowing my mind, 6K tubes?
When bundled together they would be MANY times larger than the single 5/8" tube.
All this because of friction, even for air?
 
Pyper said:
This is blowing my mind, 6K tubes?
When bundled together they would be MANY times larger than the single 5/8" tube.
All this because of friction, even for air?
Yes.

[Back of the envelope, since your scale ratio is 8.75 to one you'd need something 8.75 times fatter. A bundle of tubes about six inches in diameter and maybe a bit more by the time you account for wall thickness and the hexagonal packing arrangement]

If you want to change the scenario so that instead of tubes we are talking about a thin plate with holes then friction stops being as relevant. We'd need a real fluid dynamics person to talk about the ins and outs of choked flow in that case.
 
Last edited:
Wow.
No, it is definitely tubes, I can't get around that..
Thank you for the info..
Lots of trial-and-error ahead.
 

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