THE VOKTEX PROBLEM 



[Scientific American, XIII, 308, 1865] 



Messrs. Editors: In a late number of your paper an inquiry was 

 made why a vortex was formed over the orifice of an outlet 1 pipe; as, 

 for instance, in a bath tub, when the water is running out. If the 

 water be first started, the explanation will be on the same principle 

 that a ball and string will, if started, wind itself up upon the hand; the 

 ball being attached to the string will, as the string winds up, get nearer 

 the hand, and, consequently, will have less far to go to make one revo- 

 lution, and thus the momentum, though perhaps not great enough to 

 carry it around in the great circle, is still sufficient to make it revolve 

 in the smaller one. 



Therefore, as the string is continually winding up, and the ball con- 

 tinually nearing the hand, it will, if the resistance of the air is not too 

 great, continue to revolve until the string is wound up. Now, in the 

 case of the water, each particle of it will represent the ball, the force 

 of the water rushing toward the outlet will be the string, and, the water 

 running out, and thus causing the particles to come nearer the center 

 at every revolution, will represent the winding-up process. Thus, we 

 see this case is analogous to the preceding, and the same reason that 

 will apply to one will apply to the other. I suppose that some slight 

 motion existing among the particles of the water, united to the motion 

 produced by the outlet, causes the vortex to begin, and, once begun, it 

 will continue until the water is exhausted. 



Such motion could either previously exist, or might be produced by 

 the form * of the vessel, which would cause the water, in running to 

 the outlet, to assume a certain direction. 



H. A. R. 



Troy, N. T., October, 1865. 



'[In the original article this reads "outlet of an orifice," an obvious misprint.] 

 MIn the original article this word is "power," an obvious misprint.] 



