Parry. — Resistance to Flow of Water through Pipes. 45 



Art. II. — The Resistance to the Flow of Water through Pipes. 



By B. Parry, B.Sc, Public Works Department, New Zealand. 



[Read before the Technological Section of the Wellington Philosophical Society, 7th 

 July, 1917 ; received by Editors, 31st December, 1917 ; issued sepaiatrly, 24>ih May, 

 1918.] 



Introductory. 



In a previous contribution to this subject communicated to the Philo- 

 sophical Society, and printed in the Transactions ot the Neiu Zealand 

 Institute,^' an attempt was made to determine the limits between which 

 the resistance to the flow of water in a turbulent state is found to 

 vary, first, for riveted steel pipes, and, secondly, for wood-stave pipes. 

 This was done by plotting all the experimental determinations of loss 

 of head which are on record and afterwards enveloping the observations 

 as a whole by curves, the form of which was deduced from analogy with 

 the ascertained law of resistance to flow through smooth pipes. In 

 the present contribution an attempt is made to analyse the effect of 

 different surfaces more in detail and to extend the study of the subject. 

 The principle herein employed has been applied by the author to the 

 observations upon the resistance to the flow of water in open channels, 

 and the results communicated to the New Zealand Society of Civil 

 Engineers.! 



It is well known that the flow of water or any fluid assumes two 

 different modes, the one in which the flow is linear and known as stream- 

 line or viscous motion, and the other in which the flow is non-linear 

 or sinuous, the flow being otherwise described as eddying or turbulent. 

 The two terms "linear" and "sinuous" describe the two states very 

 well, and are used herein in the sense defined. Between the two states 

 there is an unstable region below which the flow is linear and above 

 which it is sinuous. 



In the linear stage the relationship between the elements affecting the 

 resistance to motion is simple in character, and in consequence the nature 

 of the relationship was discovered by experiment at an early date and 

 subsequently rationalized, and is expressed as follows : — 



" = a (Z.) 



v 2 \vd) 



(1) 



where s is the hydraulic gradient, r the hydraulic mean depth, d the 

 diameter of the pipe, v the mean velocity, v the kinematic viscosity 

 (i.e., the viscosity divided by the density of the fluid), and a a constant. 

 Here the resistance is expressed as a loss of head per unit length of pipe, 

 as is customary in engineering practice, whilst the customary notation has 

 also been adopted — viz., r and s for the hydraulic mean depth and 

 hydraulic gradient respectively. 



In the sinuous or eddying stage, on the other hand, the relation 

 between the elements of resistance is evidently complex, and as a 



*E. Parry, Resistance to the Plow of Fluids through Pipes, Trans. N.Z. Inst.., 

 vol. 48, pp. 481-89, 1916. 



t E. Parry, A Critical Discussion of the Subject of the Fiow of Water in Pip^s 

 and Channels, wi h Special Reference to the Latter, Proc. N.Z. Soc. Civil Engineers, 

 vol. 3, pp. 116-32, 1917. 



