[ 513 ] 



LVI. The Variation of Disk Resistance icith Temperature in 

 Water. By Professor A. H. Gibson, D.Sc, University 

 College, Dundee *. 



A POSSIBLE law of the variation o£ disk resistance with 

 temperature may be deduced from purely theoretical 

 considerations, the only assumptions made being that resist- 

 ance of each element of the rotating surface is proportional 

 to the same power * n ' of its velocity, and to some power of 

 the viscosity /x, and of the density co of the fluid, both of 

 which vary with temperature j*. 



On these assumptions it may be shown that the resistance, 

 other things being equal, is probably proportional to y?~ n . co"" 1 : 

 and to test the validity of the reasoning a series of expe- 

 riments has recently been carried out by the author on disks 

 12 inches in diameter rotating in a closed casing, with 

 different values of n 9 and with a range of temperatures from 

 60° F. to 160° F. The values of n were determined in each 

 case from a preliminary series of experiments carried out at 

 as nearly as possible uniform temperature, all these results 

 being corrected to 65° F. by an application of the foregoing 

 hypothetical formula. This involves the method of successive 

 approximations for finding the true value of ' n '• but as the 

 temperature corrections were always small (usually much less 

 than 2 per cent.), the first approximation was in general 

 sufficiently accurate. In this way the following values were 

 obtained. 



Series A. n 



12-inch brass disk in smooth casing with | inch side clearance . . 1'785 



Series B. 

 12-inch brass disk in rough cast iron „ | „ , .. 1-800 



Series C. 

 12-inch brass disk with radial vanes „ £ „ „ . . 1-950 



The results of the temperature variation experiments are 

 given in the following tables. 



* Communicated by the Author. 



t By the theory of dimensions. The method is applied to pipe-flow bv 

 the author in a paper in the Phil. Mag. ser. 6, vol. xvii. p. 389 (1909). 

 ft is calculated from Poiseuille's formula, t being in ° Fahr. 



371 6x10-8 lb ft 



** 0-4712+0-01435 *+0-0000682 1 2 ' per Sq ' 

 Phil Mag. S. 6. Vol. 19. No. 112. April 1910. 2 L 



