This is difficult to answer without more info on the carousel content, as others have said. I also agree with the comment on using reading time as a rule of thumb, if text is involved.
One additional answer could be to do a usability study (potentially with eye tracking data if you have access to those tools). You could set all transitions to be manually initiated then ask test participants to "click next" (however that fits into your carousel design) when they feel they have seen and absorbed the contents of the image. Average those times over some number of users, and add something like 50% to account for various reading/viewing speeds and other biases, and use that number.
This could be done pretty quickly and informally in a "hallway test" fashion. All you need is a few people roaming your halls, a stopwatch, and a build of your carousel with automatic transitions disabled. Change up the imagery in this test version if everyone you've got available is already familiar with your carousel, to further help with accounting for bias.