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Hmm... if you have a full duct system to check, you might not want to have to manually select all internal faces and you would have to close the open ends anyways in order for Inventor to give a Volume.
I think you could use a workflow like this maybe:
- Read volume of existing solid
- copy the Solid Body temporarily with an array, as new body
- patch the open ends
- Sculpt the patches to the temporary solid (to fill void)
- Read the volume of this sculpted solid and subtract your original volume for final void volume
At this point you can delete the arrayed solid, pull EOP up above array, or leave it if the extra solid body doesn't bother you
Let me know if you have any questions or if this new workflow is unacceptable, and we can think of something else.