The first task is to identify the slope of the line for each port diameter.

Picking any vertical line, ( I chose AR=2 for because there is data for each diameter ) and noting the maximum allowable velocity for each port diameter we get the following points, which are also shown on the above graph as black crosses.

Diameter squared is used as the measure because it is proportional to port area, which is proportional to carrying capacity

Graphing the points and finding the line of best fit which doesn't exceed the allowable velocity .....

Allowable velocities at 30hz for Area Ratio of 2

Maximum Velocity = [3570 + ( port diameter ^ 2 )] /1785 * area ratio

Velocity is in metres per second. Port diameter and flare radius are in millimeters

Rewriting area ratio in terms of diameter and flare radius gives the Full Equation

The second task is to examine the limiting velocity for different port diameters:

Reading the limiting velocities from the graph.....

In reality this relationship would probably be a curve, but for our purposes a segmented line is accurate enough.

Limiting velocities at 30hz

Note: The graph and equations show the solution as chosen for use in version 2.10 of flare-it. This is slightly different to that which was used for ver2.00 See the version notes if more detail is required.

For ports smaller than 103mm in diameter

Limiting velocity = 10 +[ (diameter squared) * (19.5 / 10,000) ]

For ports larger than 103mm in diameter

Limiting velocity = 31 + [(diameter squared - 10,600) * (8.5 / 15,000)]

The next graph shows where the equations fit within the allowable ranges.

Results predicted by equations sit within allowable ranges

Notes:

The results for 51mm ports are a little conservative, which is desirable because it's performance is currently based on measuring a single port.