The characteristic linear dimension for calculating Reynolds' number and Sherwood number in a diffusion problem within a rectangular pipe is determined by the flow conditions. For short pipes, the axial length (L) is appropriate, while for longer turbulent flows, the characteristic dimension is calculated using the formula 4A/P, where A is the cross-sectional area and P is the perimeter of the pipe. This approach approximates the mass transfer coefficient at the liquid interface and is essential for accurate modeling. For turbulent flows, experimental correlations or Computational Fluid Dynamics (CFD) may be necessary for precise calculations.
PREREQUISITESEngineers, researchers, and students in fluid dynamics, chemical engineering, and environmental science who are involved in modeling diffusion processes and mass transfer in fluid systems.
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...
