As @ScottWorld mentioned, there is currently no native Airtable functionality that would allow you to dynamically filter linked record fields based on another value in the record. This feature is often referred to as “dependent dropdowns”.
As previously noted, one way to accomplish what you’re after would be to utilize a front end that facilitates the user input. In its simplest form this can be a script. You could also utilize a tool like MiniExtensions. In order for this to work you may need to do a little more data modeling up front.
Specifically, you would add a linked field relationship between your Measurement & Department tables. Be sure to leave the default option selected that allows for many links on each side of the relationship. On the Measurement table, this new field would allow you to link each measurement with which Departments you want it to be selectable for. Conversely, on the Department table it would allow you to indicate which measurements would apply to each department.
You could then create a view in the Measurement table for each Department, & for each one, use the filter function to only show measurements that include that department in the new linked field created above. Obviously these views are statically created but since I don’t imagine departments changing often this is probably fine.
At this point, you could also create a lookup field on the Inventory table that shows the Measurement value of the Department field based on the mappings created above. Then, when you select a department, this lookup field will automatically show the measurements that are valid. This lookup field could be used as a source of valid selectable options for your front end.
Once you’ve done that, you can then configure your front end to utilize the views or lookup field value as described above in order to filter the selection of measurements based on department. In the case of a script, you could dynamically retrieve these values & present them as selectable button options using the
I know this wasn’t the answer you were hoping for, but hope it helps in some small way!