This page derives concentric vent equations that have been simplified by neglecting wall thickness, resulting in an error of approximately 2% or less. This is within the margin that will be encountered when trying to build a port using the range of pipe that is available from plumbing suppliers. These equations are most useful for doing a quick esimate of the sizes involved. When it comes to actual construction, use the full equations.
Calculating tube diameters
Keeping the area presented to the airflow constant;
The middle tube must contain the smallest tube plus the same area again
Thus the middle tube has twice the area of the smallest tube
Thus the diameter of the middle tube is sqr(2) times that of the smallest
Diameter of middle tube = sqr(2) * diameter of smallest tube
The biggest tube must contain the middle tube plus the area of the small one again
Thus the biggest tube has three times the area of the smallest tube
Thus the diameter of the biggest tube is sqr(3) times that of the smallest
Diameter of biggest tube = sqr(3) * diameter of smallest tube
Calculating end gaps
Assume for a moment that you have an inner tube with a hole as shown
The area of the hole will be the length of the arc segment times the height of the hole.
If we increase the arc segment to encompass the entire circumference of the tube, we will define the area presented to the air as it flows around the end of the tube. This area must equal the CSA of our small tube.
CSA=circumference_sml_tube * end-gap_sml_tube
rearranging terms
end-gap_sml_tube=CSA / circumference_sml_tube
substituting for CSA
end-gap_sml_tube=( pi * (dia_sml_tube/ 2) ^ 2 ) / ( pi* dia_sml_tube)
simplifying terms
End gap of small tube = diameter of small tube / 4
The end-gap on the middle tube will be smaller because it has a larger circumference
CSA=circumference_middle_tube * end-gap_middle_tube
rearranging terms
end-gap_middle_tube=CSA / circumference_middle_tube
substituting for CSA
end-gap_middle_tube=( pi * (dia_sml_tube/ 2)^2 ) / ( pi* dia_med_tube)
simplifying terms
end-gap_med_tube=(dia_sml_tube ^ 2 ) / ( 4 * dia_med_tube)
substituting for tube2
end-gap_med_tube=(dia_sml_tube^ 2 ) / ( 4 *dia_sml_ tube * sqr(2))
simplifying
End gap of middle tube = diameter of small tube * sqr(2) / 8
The next page details the full equations
