why water flows in a continuous stream down a vertical pipe,where as it breaks into drops when falling freely?

Answer 1

So many reason. Do you really want them all?

Pipes are of course full of water. The surface resistance of the pipes keeps enough back pressure in the pipes to exceed air pressure and this pressure keeps the air out. (But pipes can cavitate if the pressure gets too low -- this means that a stream would break up in a pipe). There is also surface tension at the outlet of the pipe which prevents air from entering and breaking up the water stream (so long as the outlet is small enough)

But that is not the end all, you can have a verticle pipe and have water flow down the outside of the pipe. What holds it together here is the surface tension of the water, the adherance of the water to the pipe, the drag caused by the surface of the pipe and air resistance. (The air reistance will tend to push the water towards the pipe).

What cause water to break into drops on free fall are: (1) Surface tension keeps the water together and if the stream gets too narrow -- and it will get narrower as it speeds up from gravity, the surface tension will 'cut' the narrow stream into droplets. (2) In free fall, the water stream will elongate and get narrower, see 1, above, and (3) air resistance will cause larger drops to break up.

Answer 2

Because the pipe keeps it all together. If you pushed a trickle of water down a vertical pipe, it would break into drops inside the pipe just as it would without the pipe.

Answer 3

Surface tension binds the flow to the pipe walls.