How do water molecules know to change direction as the stream narrows?

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A common misconception is that Coandă effect is demonstrated when a stream of tap water flows over the back of a spoon held lightly in the stream and the spoon is pulled into the stream. While the flow looks very similar to the air flow over the ping pong ball above (if one could see the air flow), the cause is not really the Coandă effect. Here, because it is a flow of water into air, there is little entrainment of the surrounding fluid (the air) into the jet (the stream of water). This particular demonstration is dominated by surface tension.
http://en.wikipedia.org/wiki/Coandă_effect

Klimatos said:
I suggest using waxed paper to avoid any chance of using surface tension to explain the movement. Wax and water repel one another, not attract.
Do you have any waxed paper at your disposal? I suggest you get some and actually experiment with it. Waxed paper might not have as much adhesion as other materials, but it does not repel water. You can clearly demonstrate this by wetting it and then flipping it upside-down. Some small droplets of water will cling to it, even when upside-down.
 
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klimatos said:
Case One - Vacuum: The water molecules vaporize almost instantly. At 25°, one square meter of water surface will vaporize some 3.41 kilograms of water per second in the absence of any surrounding gas. That is equivalent to a column erosion of some 3.42 millimeters per second, and a numerical vaporization rate of some 1.14 x 1026 molecules per square meter per second.

Case Two - Air at Equilibrium Vapor Pressure: Firstly, let us replace your intermolecular ropes with fairly rigid springs. The angles at which water molecules form their intermolecular hydrogen bonds have preferred values. Any deviations from these values require the application of force. Secondly, water—being a fluid—has no rigid structure. The molecules cannot and will not keep their relative positions. Thirdly, hydrogen bonding is ephemeral. At 25°C, the average liquid water molecule breaks all of its hydrogen bonds with its neighboring molecules and forms new bonds with new neighbors many billions of times each second. Even a surface water molecule making up part of the surface tension network will vaporize and be replaced some ninety billion times a second. At equilibrium vapor pressure, the number of new arrivals and the number of escapees roughly balance. Fourthly, molecules are in random movement. At rest there are just as many water molecules moving in anyone direction as in any other direction.

As the water falls, more molecules will have a downward component of motion than in any other direction. Since pressure is the simple product of number of impacts per unit area and time and the mean impulse per impact, this reduction in lateral motions is reflected in the diminution of lateral water pressure (the Bernoulli Effect). Meanwhile, the air pressure remains the same. The consequence is increased relative lateral pressure on the water column and a diminished diameter.

Arashmh, did I give you the molecular explanation you were looking for?

You are very detailed in your explanation. I appreciate it. Ok, we know that if the stream of water has enough path to fall freely , after some time , it will break down to some branches and finally into a spray. how this ball-spring model explains this in molecular level . by the way, feel free to call me Arash :)