Parry. — Resistance to Flow of Fluids through Pipes. 



483 



In order to comprehend the whole range satisfactorily both below and 



above the critical velocity it is necessary to take logs of both sides, and 



4v- 

 the standard curve is set out again m fig. 2, curye a, with log —^ as 



ordiiiates and log vd/v as abscissae. 



The diagram fig. 2 shows the first of stream-line stage as a straight line, 

 and as the index x is equal to unity in this region the line is inclined at an 

 angle of 45°. The equation of the line is 



.d 

 'I. 



h=^i^ 



where a has the value 8, an experimental value obtained from an exami- 

 nation of Stanton's experiments already referred to. Thus straight portion 

 of the characteristic in fig. 2 intercepts the abscissa at log 8. 



Fig. 1. 



The curved portion of the characteristic marked a is Professor Lees's 

 equation already referred to, which represents the behaviour of fluids in 

 smooth pipes above the critical velocity in the eddy state of motion. 



Inasmuch as the change is abrupt from one state to the other, the exact 

 nature of the connection cannot be determined, but the two portions are 

 joined together on the principle that it requires a higher force to change 

 a state of motion than to maintain either the previous or subsequent stage. 

 This phenomenon was observed by Reynolds, and is similar in its behaviour 

 to elastic and magnetic phenomena. 



Having obtained a standard of reference in this way, the next step is 

 to plot to the same scale all the observations available on some one class 

 of pipe and see how they stand in reference to the standard. Comparing 

 first riveted pipes in general, the dots on the sheet represent 129 observa- 

 tions made on riveted pipes, varying from 12 in. in diameter to 102 in. in 

 diameter recorded by Messrs. Marx, Wing, and Hoskins in the '' Trans- 

 actions of the American Society of Civil Engineers," vol. 40. This is a 



16* 



