have you tried using Revolved Boss?
I've revolved the sketch with thin feature around the construction line.
Please check the attached sketch and section cut of my idea.
I hope it's helpful.
PS if you insist on deleting the face after you've extruded both cylinders maybe you should play around with the Shell or Delete face commands.
Unfortunately neither thing you suggested will work. The revolution will only work if inlet and outlet are centered, which will not always be the case. The shell command will not work because the ends are domed. The radius of the dome dome does not all for the shell to be created. Lastly when I delete face it has the nasty side effect of hollowing my model. Essentially stripping it down from a solid to 2 surfaces.
Thank you for your reply though.
Thank you for the update.
There was no way to know that all info from the original image.
Have you tried using Loft feature instead of the Dome? This way you'll be able to use the Shell command.