180 HYDRAULICS AND ITS APPLICATIONS 



friction and v is the velocity of the element, 1 then if <o is the angular 

 velocity of the disc in radians per second v = wr, and the moment of this 

 resistance = 2 irf a> n r n + 2 Sr. Then the moment of resistance of the two 

 faces of a disc having a radius of R feet 



= 4 TT/ co" f * r n + ' 2 d r foot Ibs. 



Jo 



. 



n -f 3 



Assuming the resistance of the edge of the disc to follow the same law, 

 and therefore to be given by 2 TT b ,/o> n R n + 2 , where b is the breadth in feet, 

 the total moment of disc resistance, M, will be given by 



M = 2 TT/O)" R + 2 ? -3 + foot Ibs. 

 Effective Radius. Writing the resisting moment as 



l^!. Bl - foot Ibs., 



n -j- o 



where EI is the effective radius of the disc, i.e. the radius of an infinitely 

 thin disc giving the same resistance, then 



+ 3 (H + flftB'*' 



if b is small compared with 2 /2. 



Dr. JF. C. Unwin has carried out a series of experiments on discs 10, 

 15 and 20 inches diameter rotating inside a casing whose side clearance 

 could be varied from 1*5 inches to 6 inches. 2 The maximum speed 

 attained in these experiments was about 470 revolutions per minute. 

 More recent experiments by A. Ryan and the author have extended these 

 speeds up to 2,200 revolutions per minute on discs of 9 and 12 inches 

 diameter. 3 



In the apparatus used in the latter experiments a horizontal, motor- 

 driven shaft carries the disc to be tested. The shaft passes through 

 easily fitting bushes in the sides of a casing surrounding the disc, as 

 shown in Fig. 93. 



\ 



1 The friction per square foot at a velocity v feet per second is, from this definition, 



2 " Proc. Inst. C.B.," vol. 80, 1885, p. 221. 

 8 " Proc. Inst. O.E.," vol. 179, 1909-10, pt. I. 



