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Calculating limiting pressure differential across a bearing

Hello all, I am in the process of attempting to put together a list of limiting differential pressure values on a supported bearing. Currently there are values for certain materials listed in an API standard that give this value in a pressure limitation per inch of length. Using the standard shear calculation below:

P = (Shear Strength x Area of Shear Plane) / (Area of Unsupported Cross-section)

P = (Ss x As) / Ap [Assuming a safety factor of 1]

As = Pi x Dm x h

Ap = (Pi / 4) x (Dm^2 - Di^2)

See diagram for the general configuration of the part. The outside component is a cylindrical metal carrier that is secured into a pump bore and the inner element is a cylindrical polymer composite that is secured against the shoulder of the carrier and is the subject of this exercise. Assumptions are no pressure infiltration between the carrier and the insert and there are no moments that exist as a result of the axially pressure loading.

I have not been able to determine a way to derive a value that gives the limiting pressure differential across the bearing as a single number the is defined per inch of length.

Thanks in advance!