This effect could probably be achieved using booleans, but the method explained here is a good practice.
We will start of by creating a circle. Using the space bar tool menu: mesh-circle. Create it with eight vértices (just for speed of editing later on). We now have a circle centered on the cursor [fig 1].
Now clik the 3d window to the right of the circle to separate the cursor from the circle [fig 2].
Make sure [Numlock] is on for this tutorial, then press [numpad 1] to get this [fig 3].
Our view point has changed to the side view. Go to the editing window [F9] and in the Mesh Tools section press SPIN. We have made a curve based on the shape of the circle [fig 4].
By changing the Degr spinner value (below the SPIN button) to a negative we get a curve in the opposite direction. Press [tab] to exit edit mode. This is the shape we will worque with. Duplicate it once: While in object mode [tab], press [ctrl d] right clik to confirm the copy. Rotate the new copy through 45 degrees in the y axis and reposition it [fig 4]. One shape penetrates the other about half way. This an artistic tutorial not a super scientific technical one, so don't worry about precision. Save your file regularly if you wish. I have pressed [z] to reach wireframe mode for these screenshots, if you are new to blender.
Select one of the tube shapes, hold [shift] then select the other by right clicking it. Pressing [ctrl j] will join the shapes into one editable mesh. Pressing [tab] will reveal the new mesh [fig 5].
Enter edge select mode [ctrl tab 2] and make some cuts in the mesh just to refine it. Right clik this edge [fig 6] then press [crtl r]. Now, left clik twice to make the cut [fig 7].
shows me making another cut where the two objects meet. We need to create two vértices at each point where the surfaces meet, so your cuts may need to be in slightly different positions from mine. You need to make about 4-6 more cuts in the mesh to get enough vértices to merge/weld together [fig 8 y 9].
Now we need to weld. Enter vertex mode [ctrl tab 1]. Select two vértices that are close to each other, one from each tube shape. Select from the vertical tube first, then the horizontal tube [fig 10].
Press [w] then select MERGE from the list. Repeat this process at the boundary of the tube shapes where the vértices meet up. Select vértices in the same first to last order so the surfaces don't warp. If pairs of vértices don't match up, perform more cuts [fig 11].
Go into face select mode [ctrl tab 3], and select the faces of the mesh that are covered or part covered by other faces [fig 12].
Pressing [x] will bring up the erase menu, select faces. This should make quite a mess of the mesh (try saying that after a few pints) [fig 13].
Once again, go bak to vertex mode and begin to repair your mesh by selecting 3-4 connected vértices and hitting [f] to create a face [fig 14].
Repeat until all is well again [fig 15].
Now I will merge these 3 vértices [fig 16],
deleting vértices created during the cutting stage until we have [fig 17].
Select these edges [fig 18],
then enter the script menú. Select Scripts- >Mesh->Bevel center. Press the large Bevel button to create a weld seam of the selected edges [fig 19], which could be uv mapped later.
I hope those who have never used the 3d cursor for modeling before will be exited by its potential for creating arcs and curves as the basis for more complex shapes. I will write another article along these lines in the future, thanks for reading.