Characteristic linear dimension (Reynolds' number)

In summary, the characteristic linear dimension for a diffusion problem in a rectangular pipe can be calculated using either the length of the pipe or 4A/P, depending on the length of the pipe compared to the entrance length. The cross sectional area and perimeter of the pipe are used to calculate A and P, as it is an approximation for the mass transfer coefficient at the liquid interface. This method is determined based on the system at hand and can be further refined using dimensionless forms of the differential equations.
  • #1
dRic2
How can I choose the characteristic linear dimension? For example in pipe it is its diameter, but on a surface is the length, on a flat plane it can be measured as 4A/P. I was having problems determining the characteristic linear dimension for a diffusion problem in a "rectangular" pipe. I don't know if I have to use the length L or 4A/P.

Here's the picture of the problem
 

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  • #2
What is the precise problem you are trying to solve?
 
  • #3
Looking at the picture I've uploaded the blue part is an organic compound. Air is forced to flow stationary into the system (like a pipe). The aim is to erase the organic compound by forced convection. When I try to calculate Reynlods' number and then Sherwood I'm not sure about the characteristic dimension...
 
  • #4
dRic2 said:
Looking at the picture I've uploaded the blue part is an organic compound. Air is forced to flow stationary into the system (like a pipe). The aim is to erase the organic compound by forced convection. When I try to calculate Reynlods' number and then Sherwood I'm not sure about the characteristic dimension...
If the pipe is fairly short, then the velocity- and concentration profiles within the pipe are going to be developing over the length of the pipe, and this approximates boundary layer development over a flat plate, so you would use the axial distance in conjunction with the solution for a flat plate. If the pipe is long compared to the entrance length required to develop the velocity- and concentration profiles (and the flow is turbulent), I would use 4A/P in calculating the pressure drop, the concentration change, and the mass transfer coefficient at the liquid interface.
 
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  • #5
Chestermiller said:
I would use 4A/P

But what surface are you referring to when you calculate A and P? The "blue" one or the section of the pipe?
 
  • #6
dRic2 said:
But what surface are you referring to when you calculate A and P? The "blue" one or the section of the pipe?
The cross sectional area and perimeter of the pipe minus the blue.
 
  • #7
Can I ask you why? Because the diffusion takes place along the internal area of the pipe thus I don't get the meaning of considering the cross sectional area...
 
  • #8
dRic2 said:
Can I ask you why? Because the diffusion takes place along the internal area of the pipe thus I don't get the meaning of considering the cross sectional area...
This is how the take into account the gas flow to get the mass transfer coefficient at the liquid interface. It is only an approximation, but is about the best you you are going to do without using CFD.
 
  • #9
is it sort of a definition? I know it is an approximation, but i don't get why it has been defined this way
 
  • #10
dRic2 said:
is it sort of a definition? I know it is an approximation, but i don't get why it has been defined this way
It is specified in whatever way seems appropriate to the system at hand. If you have the actual partial differential equations that apply to your system, you can reduce the equations to dimensionless form and determine all the dimensionless groups that apply, including Reynolds number. Then you can solve the equations in dimensionless form. However, if the flow is turbulent, you need to determine the dimensionless behavior experimentally (or use CFD, with turbulent flow capabilities), or find appropriate experimental correlations for your particular situation (or a similar system) in the literature.
 
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  • #11
I'm not familiar with dimensionless forms of differential equation like Navier-Stockes (actually I skipped that paragraph in my book... :frown:). I guess I'll go back and study it again. Thank you
 
  • #12
dRic2 said:
I'm not familiar with dimensionless forms of differential equation like Navier-Stockes (actually I skipped that paragraph in my book... :frown:). I guess I'll go back and study it again. Thank you
There is a general methodology from reducing sets of model equations for a system to dimensionless form. Look up Hellums and Churchill.
 
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What is the characteristic linear dimension in the Reynolds' number equation?

The characteristic linear dimension in the Reynolds' number equation is a measure of the size of the object or flow relative to the fluid it is moving through. It is often represented by the letter "L" and can refer to different dimensions depending on the specific application.

How is the characteristic linear dimension determined?

The characteristic linear dimension can be determined by measuring the length, diameter, or other relevant dimension of the object or flow. In some cases, it may be an average of multiple dimensions.

Why is the characteristic linear dimension important in the Reynolds' number equation?

The characteristic linear dimension is important because it helps to scale the Reynolds' number and determine the type of flow that will occur. It also allows for comparisons between different objects or flows of varying sizes.

What is the relationship between the characteristic linear dimension and the Reynolds' number?

The characteristic linear dimension is directly related to the Reynolds' number. As the characteristic linear dimension increases, the Reynolds' number also increases, indicating a transition from laminar to turbulent flow.

How do changes in the characteristic linear dimension affect the Reynolds' number?

Changes in the characteristic linear dimension can significantly impact the Reynolds' number. As the characteristic linear dimension decreases, the Reynolds' number also decreases, resulting in a lower tendency for turbulence. Conversely, an increase in the characteristic linear dimension leads to a higher Reynolds' number and a greater likelihood of turbulent flow.

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