548 hersey: laws of lubrication 



order to learn just how large — must be in order to thicken up 



the film to any given value we should need to know the complete 

 form of the function 4/ in equation (12); but for all thicknesses 



c 

 greater than ^, the value of /c from (19) may be used for/ with an 



error certainly less than 16 per cent. 



III. AN APPROXIMATE TREATMENT OF THERMAL EFFECTS 



8. Effect of thermal expansion. This can be shown to be 

 negligible compared with other outstanding uncertainties. 



9. Effect of temperature on viscosity. The \dscosity-temperature 

 curves of most lubricating oils can be closely fitted by the empiri- 

 cal equation 



M = ^^f' (20) 



in which 7' denotes t— T,t being the temperature of the oil, and r 

 an empirical constant not greatly different from the solidifying 

 temperature. The subscript designates values at room temper- 

 ature; thus Ti = ti— T and ij. = ijh when t = ti. 



10. Relation of temperature to speed. From (19) and (20) 



Z^^^^^.^^.Ij (21) 



c p 1 



Assume Newton's law of cooling and let h be the heat carried 

 off in unit time b}^ the air, by the jacket water, or otherwise, 

 per unit temperature elevation above room temperature. Then 

 if J denote the mechanical equivalent of heat, equation (4) 

 leads to the condition for equilibrium 



irDnLf 



J 



= h{t-t,) =h(T- T,) (22) 



(xn 



At high enough values of — that /^ may be written /, we may 



p 



solve (22) for the relative temperature T getting 



T= -^{l + ^/l + kn') (23) 



