Liquid stream dispersal

[tony1941]

In the scenario of a stream of liquid emerging from a pipe and then falling freely under gravity, does anyone have an elegant method of calculating the point at which the stream thins and breaks up into droplets? The rate of acceleration is probably g for longer than expected as there should be no air resistance initially. (By the way, this problem came out of a bunch of railway engineers discussing whether it was safe to relieve oneself from a bridge over the 25kV overhead lines!)

[Mortartube]

I would imagine that much depends on the design of the "Nozzle" that the liquid exits from, as well as the suface tension of the liquid. In this case a high percentage of water. At 25kv the chance of a flashover between liquid droplets would be great

[Cathyhuns]

Any railway engineers daft enough to even ask this question should not be working on the railway and are a danger to other people as well as themselves. As well as relieving themselves being dirty and unhygenic the 22kV is not to be messed with. Anyone who has seen someone who has been in touch with the 22kV power will never go near it again. It doesn't always kill you but you are generally so disabled that you might well wish that it had.

[ugly_bob]

and you certainly wouldn't want that part of you to be first in contact with a shock like that

[newtron]

You can probably come up with some type of dimensionless number (if one does not already exist) that may help to determine when a stream will break into droplets. For example, the Reynolds number is the ratio of inertial forces to viscous forces and is used to determine if a certain fluid flow is laminar or turbulent. In your case, it is necessary to determine why the stream breaks up into droplets. The more I think about it, the Reynolds number might work.

The Mythbusters did an experiment where they simulated a dummy peeing on a subway rail. The dummy was connected to a volt meter. The breaking up of the stream into droplets was very effective at creating discontinuity and preventing the dummy from receiving a shock. They had to get the source of the stream very close to the rail to before the dummy felt anything.