488 



Transactions. 



term on tlie right-hand, side of the equations. By modification of the 

 diagrams these may be made to apply to open conduits and canals, and as 

 the cross-sections, generally speaking, are very much larger compared with 

 the largest pipe in use, the value of the expression which would correspond 

 to log vd/v is large, and in consequence the variation of 1/C^ is small, and 

 tends to become nearly constant, and will vary roughly wath the surface 

 and very little with the viscosity and consequently with temperature. 



It should be noted that whilst the fluid under discussion has been water, 

 the curves, and therefore the equations, are quite general and apply to 

 any fluid, the link being the kinematic viscosity v. For convenience of 

 reference two curves are shown in fig. 4, showing the viscosity and kinematic 

 viscosity of water and its variation with temperature, which enables the 

 value of the function vd/v to be obtained for any given temperature, whilst 

 the value of log vd/v can be obtained for any value of v and d, and any 

 temperature between 0° centigrade and 30° centigrade, by reference to the 

 curves in fig. 5. 



Fig. 5. 



The following is a summary of the foregoing and of the present state 

 of knowledge in respect to the friction of fluids in pipes : — 



1. The resistance ofiered to the flow of fluids through round pipes with 

 smooth surface is represented by curve a, fig. 1, which may be expressed, 

 according to Professor Lees, by the equation 



d I / V \ 0'35 



i^/v^ = -00801 (-^1 + -000028. 



2. The value of 1/C^ in Chezy's modified formula v = G\/ri is approxi- 

 mately expressed for smooth pipe by 



•00801 



\vd) 



+ -000028. 



