48 



Professor Osborne Bepiolds 



[March 28, 



mouth-piece ; or when the motion is reversed, diverging. Moreover, 

 the streams may be straight or curved. 



All these circumstances have their influence on stability in a 

 manner which is indicated in the accompanying diagram : — 



Circumstances conducive to 



Direct or Steady Motion. 



1. Viscosity or fluid friction which 



continually destroys disturb- 

 ances. 

 (Treacle is steadier than water.) 



2. A free surface. 



3. Converging solid boundaries. 



4. Curvature with the velocity 



greatest on the outside. 



Sinuous or Unsteady/ Motion. 



5. Particular variation of velocity 



across the stream, as when a 

 stream flows through still 

 water. 



6. Solid bounding walls. 



7. Diverging solid boundaries. 



8. Curvature with tlie velocity 



greatest on the inside. 



It has for a long time been noticed that a stream of fluid through 

 fluid otherwise at rest is in an unstable condition. It is this insta- 

 bility which gives rise to the talking-flame and sensitive-jet with 

 which you have been long familiar in this room. I have here a glass 

 vessel of clear water in front of the lantern, so that any colour-bands 

 will be projected on the screen. 



You see the ends of two vertical tubes one above the other. 

 Nothing is flowing through these tubes, and the water in the vessel 

 is at rest. I now open two taps, so as to allow a steady stream of 

 coloured water to enter at the lower pipe, water flowing out at the 

 upper. The water enters quite steadily, forms a sort of vortex ring 

 at the end which proceeds across the vessel, and passes out at the 

 lower tube. Now the coloured stream extends straight across the 

 vessel, and fills both pipes. You see no motion ; it looks like a glass 

 rod. The water is, however, flowing slowly along it. The motion 

 is so slow, that the viscosity is paramount, and hence the stream is 

 steady. 



I increase the speed, you see a certain wriggling sinuous action 

 in the column ; faster, the column breaks up into beautiful and well- 

 defined eddies, and spreads out into the surrounding water, which, 

 becoming opaque with colour, gradually draws a veil over the 

 experiment. 



The same is true of all streams bounded by standing water. If 

 the motion is sufficiently slow, according to the size of the stream 

 and the viscosity of the fluid, it is steady and stable. At a certain 

 critical velocity, the which is determined by the ratio of the viscosity 

 to the diameter of the stream, the stream becomes unstable. Under 

 any conditions, then, which involve a stream flowing through sur- 

 rounding water, the motion will be unstable if the velocity is sufficient. 



Now, one of the most marked facts relating to experimental 

 hydrodynamics is the difference in the way in which water flows along 

 contracting and expanding channels ; these include an enormously 

 large class of the motions of water, but the typical phenomenon is 

 shown by the simple conical tubes. Such a tube is now projected on 



