hersey: laws of lubrication 547 



be termed dynamically similar. The power dissipated in either 

 of them may be calculated from a test made on the others, for 

 by (4) 



^=5..!L.^ (16) 



P' D' n' L' ^ ^ 



Moreover by (13) and (15) it follows that ^o = ^o, hence by (14) 



(17) 



Thus if the safe load and therefore the carrying power of one 

 bearing has been established experimentally, the carrying power 

 of the other can at once be calculated. 



7. Relation of friction to film thickness. This is as far as the 

 problem can be carried by the foregoing general type of reason- 

 ing. Further information must be obtained by experiment or 

 by making some assumption as to the geometrical form of the 

 oil film. In the particular limiting case of a perfectly cylindrical 

 bearing free from end-effects and cavitation (i.e., completely 

 lubricated) it is a simple matter to deduce the relation 



D^fxn 



T 



/= ,' ' (18, 



>/7(^-f) 



Equation (18) merits careful scrutiny. It is an expression for 

 the coefficient of friction of a bearing constrained to run with a 

 given film thickness. While the coefficient of friction for any 



u n 

 given value of — is excessively high at very small film thick- 

 nesses, it will have fallen to within 16 per cent of its minimum 

 value when the film thickness has become as large as half the 

 clearance. Hence the relation 



/^ = /-:5.^ (19) 



c p 



to which (18) reduces when x = c, may conveniently be used as 

 an approximate expression for the coefficient of friction, /. In 



