Hydrodynamics. — "On the resistaiice experienced by a fluid in 

 turhii/ent motion". By J. M. Bukgers. (Communicated by 

 Prof. P. Ehrenfest). 



(Communicated at the meeting of May 26, 1923). 



^ J . Introductory remarks. 



The problem which is discussed in the following lines is to search 

 for a metliod to calculate the resistance experienced by a fluid in 

 turbulent motion. A definite solution has not lieen ari'ived at; a 

 (irst attempt only is given. 



As is generally known, in most cases the motion of a fluid through 

 a straight cylindrical tube or channel is not in parallel lines with 

 a constant velocity along each line. On the contrary it is usually 

 very irregular: the velocity of a particle changes its value and its 

 direction continually, and particles situated very near to each other 

 have very different velocities, whereas there seems to be no definite 

 law governing these deviations. This type of motion is called ^wiuotts 

 or turbulent, as distinguished from the streamline or laminar motion, 

 which occurs at low velocities only. In studying turbulent flow the 

 conception of the mean motion or principal motion h&s, h^en \n\ro(\u(^QA 

 by various authors. This mean motion is obtained if in every point 

 of the space occupied by the fluid the mean value of the true 

 velocity with respect to time is determined, and then the steady 

 motion is imagined the velocities of which are equal to these mean 

 values. The true motion may be described as the resultant of the 

 mean motion and of a fluctuating relative motion. The mean velocity 

 of the latter is zero '). 



A turbulent flow usually experiences a high resistance, which is 

 approximately proportional to the second power of the velocity of 

 the mean motion. If the law of resistance is written : 



loss of pressure per unit of length J =^ ~j"' 



^) In connection with tlie distinction between mean motion and relative motion 

 the reader is referred to: H. A. Lokentz. Turbulente Fliissigkeitsbewegung und 

 Strömung durch Röhren. -Abhandl. iiber theoretische Pliysik \ (1907), p. 58 — 60. 



