# Characteristic linear dimension (Reynolds' number)

#### 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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#### Chestermiller

Mentor
What is the precise problem you are trying to solve?

#### dRic2

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...

#### Chestermiller

Mentor
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.

#### dRic2

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?

#### Chestermiller

Mentor
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.

#### dRic2

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...

#### Chestermiller

Mentor
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.

#### dRic2

is it sort of a definition? I know it is an approximation, but i don't get why it has been defined this way

#### Chestermiller

Mentor
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.

#### dRic2

I'm not familiar with dimensionless forms of differential equation like Navier-Stockes (actually I skipped that paragraph in my book... ). I guess I'll go back and study it again. Thank you

#### Chestermiller

Mentor
I'm not familiar with dimensionless forms of differential equation like Navier-Stockes (actually I skipped that paragraph in my book... ). 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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