MB. C. W. SIEMENS ON UNIFORM EOTATION. 669 



The normal speed of a cup of these dimensions is, according to our formula, 



_^I9600 X 200(1 + ^^^,_^^;3 ^ ^^, ) _ ^_^ 



n=— i luu-^Jdx^o/^g.g]^ revolutions per second. 



200t ^ 



The height to which the liquid is raised by rotation increases in the square ratio of the 

 speed of rotation, the increase of height due to 1 per cent, increase of speed would 

 therefore result from the following proportion, 



100 V : 101 v=y/h : y/hJ, 



or the height due to the increased speed, 



^'=204 millims., 



that is to say, the liquid would be raised 4 millims. above the brim of the cup, which, 

 being an unbalanced column, will produce an upward flow of the liquid in the cup, as 

 expressed by the well-known formula, 



v=\/2gh; 



or h being in this case =4 mUlims., we have 



«=*280 metre flow per second, 



which, if multiplied by the least sectional area at the entrance into the cup = -0057 

 square metre, gives the quantity of liquid 



•280 metre X "0057 square metre ='0016 cubic metre, 



or 1"6 litre of liquid raised 204 millims. high and projected with a velocity of 



j^3-31x2rff=2-l metres per second 



over the brim of the cup, to be stopped by the stationary wings and once more accele- 

 rated by the rotating wings, which, being one-fifth more in diameter than the cup itself, 

 impart to the liquid a velocity of 



f 2*1 =2*5 metres per second. 



These accelerations represent a power which, according to the formula 



is equal to the same liquid being lifted 



for v=2-l metres . to -225 metre height, 

 and for v=2-5 . . to -320 metre height. 

 In the cup it was lifted to -200 metre height, 

 making a total lift . . to -745 metre height. 



If the liquid employed is water, the 1-6 litre represents 1-6 kilogram., and the resist- 

 ance produced by 1 per cent, increase of velocity is 



l"6x'745=:l-2 kilogrammetres per second. 



