Parry. — Resistance to Flow of Water through Pipes. 47 



pipes. According to Professor Lees,* the mean curve can be expressed 

 in the form 



rs 



n 



+ =a \x) +b (5) 



the values, the coefficients, and the index being as follows : — 



a = 0-00801 ; b = 0000028 ; n = 0-35 



all the quantities being in foot-pound units. 



More recently Landert carried out an extensive series of experiments 

 upon the flow of water and steam at speeds varying from 191 ft. per 

 second to 11*55 ft. per second through ordinary commercial drawn-steel 



pipe of 0*423 in. diameter, and upon plotting the values of — against log. 



he finds than an equation of the form (5) satisfies the relation between 

 them. He, however, obtains different values of the coefficient and of the 

 indices, the values being 



a = 00202 ; b = 0*0000622 ; n = 0*44 



all values being in foot-pound units. 



It is evident on contemplating the two sets of experiments that an 

 equation of the form given in (5) correctly expresses the relation between 

 the quantities near enough for all practical purposes, and it remains to 

 be seen how far the principle is applicable to larger diameters and 

 rougher surfaces, and it is the purpose of this paper to test its ap- 

 plicability to cast-iron, riveted steel, and wood-stave pipes of such sizes 

 and characteristics as are in common use in the arts. 



Before proceeding further in the direction indicated it may be useful 

 and interesting to compare the form of equation (5) with Chezy's formula, 

 viz. : — 



v = c </rs (6) 



where o is a coefficient and r the hyraulic mean depth. It will be seen 

 that c can be expressed in the form 



1 



c = 



v-(£)"+» p> 



Comparing this with other well-known formulae for c, we have Prony's 

 equation, viz. : — ■ 



1 



-^•G) 



+ b 



whilst Darcy and Bazm's formula may be expressed as follows : — 



1 



= V"(i) + > 



Evidently the influence and value of v predominate in Prony's experi- 

 ments, whilst the value of d predominated in Darcy's experiments ; and 



* C. H. Leks, On the Fiow of Viscous Fluids through Smooth Circular Pipes, 

 Proc. R>>y. Soc, A, vol. 91, pp. 46-53, 1914. 



f C. H. Lander, Surface Friction : Experiments with Steam and Water in Pipes , 

 Proc. Boy. Soc, A, vol. 92, pp. 337-53, 1916. 



