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Imagine opening a water tap in order to have a smooth and cylindrical outflow and then slowly decrease the flow by adjusting the knob. At a certain moment, the side profile of the flow will become uneven, and even if you decrease the scale of the faucet, the water shall start to drip. It is possible to determine, based on the thermodynamic conditions of the system (pressure, temperature, and surface tension of water) the dropping condition?

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The answer is no. Thermodynamical variables like pressure, temperature etc. are not sufficient to determine the flow completely. The reason is, the flow of water is too much chaotic and too much sensitive to its initial conditions. Even a slight change in the initial conditions will make the water flow differently. As each drop leaves the faucet it creates oscillations in the residue of the nozzle which in turn sets the initial condition of the next drop. Since it is almost impossible to know all the details of the system the flow can not be completely predicted. However there are laws by which you can calculate some patterns with much more precision. The whole process comes under the subject of nonlinear dynamics. Follow these links http://www.seas.harvard.edu/softmat/downloads/pre2000-02.pdf http://www.pas.rochester.edu/~AdvLab/10-DrFaucet/DrippFaucet.pdf

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