The discussion revolves around the selection of the characteristic linear dimension for calculating Reynolds' number in the context of a diffusion problem within a rectangular pipe. Participants explore different approaches to defining this dimension based on the geometry of the system and the nature of the flow.
Participants do not reach a consensus on the appropriate characteristic linear dimension to use for calculating Reynolds' number, with multiple competing views and approaches presented throughout the discussion.
Limitations include the dependence on specific definitions and the unresolved nature of the mathematical steps involved in applying the discussed methods. The discussion also highlights the need for further exploration of dimensionless forms of equations in fluid dynamics.
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 said:
Chestermiller said:
The cross sectional area and perimeter of the pipe minus the blue.dRic2 said:
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 said:
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 said:
). I guess I'll go back and study it again. Thank youThere is a general methodology from reducing sets of model equations for a system to dimensionless form. Look up Hellums and Churchill.dRic2 said:I'm not familiar with dimensionless forms of differential equation like Navier-Stockes (actually I skipped that paragraph in my book...
