﻿14 Unsteady Motion in a Rotating Cylinder of Water. 



sufficient to account for the effects, except for small values 

 of c and Q, i. e. for long, narrow cylinders and slow speeds. 

 A little dye introduced into the rotating water shows no 

 signs of any minute eddying or micro-turbulence ; and so 

 we must look for currents in the water as the cause, of the 

 discrepancy, which is obviously the case in the " stopping " 

 experiments. The formation of large eddies in large bodies 

 of fluid seems to be due chiefly to the interaction of two 

 local currents, or to low pressure caused by an obstacle or a 

 sink, and not to the slower processes of viscosity. 



If we attribute the deviation from theory to an ignored 

 increase in the kinetic viscosity v, we find that when the 

 large cylinder is stopped at the high speed, the increase 

 would have to be represented by a factor exceeding 10 in 

 value nearly everywhere, while the value would lie between 

 50 and 100 on r/c = 0'3 shortly after stopping. With the 

 middle cylinder, stopped at the high speed, the factor has 

 about half these values ; and with the small cylinder, stopped 

 at the same speed, the factor ranges from 1*3 to 3*0. In 

 the starting experiments the factors are nearly unity, but 

 they are meaningless here as the motion is not turbulent. 



Some earlier experiments illustrate the instability of the 

 stopping experiments. In these an inner cylinder was 

 rotated coaxially with a fixed outer one. As is well known, 

 it was found that at no speed of rotation of the inner cylinder 

 was it possible to set the water moving in circular paths, o wing- 

 to the eddies which were continually thrown off. The slower 

 the speed of rotation the more conspicuous were the eddies, 

 especially on the borders of the outer, more slowly-moving 

 water. Measurements of the angular velocity showed a large 

 departure from theory, the inner parts rotating more slowly 

 and the outer parts more rapidly than the theory indicates. 

 The effect o£ the travelling eddies is thus to make the angular 

 velocity more like that of a rigid body. When the speed was 

 very great (2500 r.p.m.) the kinetic energy seemed to give 

 stability to the water. A whirlpool formed next the inner 

 cylinder, and a large oscillation was presently set up in the 

 form of a wave with its crest along a radius of the outer 

 cylinder and its trough on the other half of the same diameter. 



Some thick, very viscous oil residues, when rotated in a 

 cylindrical tin about 15 cm. in diameter, acquired the full 

 velocity on starting (36 r.p.m.) in something less than 

 4 seconds, and came to rest in the same time when the 

 cylinder was stopped. Only a slight displacement of the oil 

 occurred, the surface being momentarily roughened with fine 

 lines like cracks. 



