I don't have enough reputation to add extra links to my initial answer in response to John's request in comments above, so adding a second answer to do so. Here, I rebuild the same piece, with minor improvements to my first approach:
In response to the request for my workflow in building the last example... I started with two unjoined, Bezier curves (which I converted to Meshes, though you can't see that here):
I joined them:
I deleted the "center" where the T-intersection needs to be built:
I deleted the "extra" bit of center/right-hand-side tubing with L-select:
In top view, I added a few extrusions to limit the amount of intersection I would need to build; also, I rotated after each extrusion, still in top view, to maintain the soft angle of the curve. These were extruded with Shift+Z to keep the tubes of identical height:
I then added all of the "easy" connecting faces by selecting 2-4 verts as needed and tapping the 'F' key a bunch of times. I did this first on the outside, and then in the middle of the top part of the T-intersection:
I then loop-selected the verts in the two spaces that were still not covered by faces, and noticed I needed an extra vertex to get nice quads (although perhaps larger/with more extreme angles than I would ideally like; that could be cured with a bit of moving around loop cuts, or maybe using a third Bezier curve for the right-hand-side tubing, with 2 extra cuts running its length...). To get that, I added a loop cut to the middle-of-T-intersection faces, and filled in the remaining gaps with 4 more taps of the 'F' key:
This is a little bit angular-looking in the T-intersection, so I then:
- turned on Shade Smooth, to see how angular it will actually look at desired render settings
- grabbed everything except the ends of the tubes and used smooth vertices (which I have hotkey'd to Q, not that that's necessary) twice.
In the original image, I also played around with smoothing different subsets of vertices to get the look to about where I wanted it -- more art than science, there.