How to start a siphon with a tube filled with liquid? If I have a tube filled with water, whose one end I dip into a container filled with water. If I release the other end will it start a siphon ?
 A: Yes. Valve B doesn't need to be closed (it doesn't need to exist). Open A, and water will flow out. I have tested this experimentally.
A: When both valves A and B are open, then it will start to siphon if both openings are below the level of the surface of the water in the container. It does not matter how deep opening B is.  It does matter how far below the surface opening A is. The further down you go the faster the flow will be.
Essentially what is happening is that you have extended the container to point A via a convoluted upside-down U-shaped path.  If you put a hole in the side of the container at the same height at point A, water would leak out. The same thing happens at point A but there is some flow resistance because of the tube. 
Now, there are some caveats:  (1) If valve B is closed, you might get a few drops from internal pressures adjusting but it will not siphon. (2) The fact that the tube rises above the surface of the water doesn't prevent siphoning because the water rising in one side of the upside-down U is balanced by the water descending in the other side.  However, there is a limit to how high it can go and this is based on the air pressure experienced at the surface of the water. A taller U will have a slower flow and at some point (about 33 feet at sea level) all flow will stop.
