FLOW OF WATER IN CLEAN PIPES 249 



call the depth or thickness of the disturbance or resistance. In the begin- 

 ning we can observe that m remains finite for any real channel with real 

 flow. In the case of a pipe flowing under pressure the maximum value 

 which m can attain is the value 0.5 and this occurs when the length of 

 the pipe is equal to three diameters for a flush fitted pipe. For such a 

 pipe m remains practically constant and equal to 0.5 for different veloci- 

 ties and diamet'ers. As the length of the pipe increases the value of m 

 diminishes, rapidly at first and then more slowly imtil the length of the 

 pipe is about 500 diameters when m assumes the value expressed in (8) 

 for long pipes. This variation in m due to the disturbance at entry dies 

 away in about the length of 500 diameters. If we indicate by M the com- 

 plete coefficient of resistance for a pipe of length L measured from the 

 end of the first three diameters of length, then 



The second term which represents the loss due to entry amounts to 

 1 in the fourth decimal place for L/D about 1200, but the errors of experi- 

 ment amount on the whole to 3 or 4 per cent for ordinary pipes, so that 

 pipes from 3 to 500 diameter in length are called short pipes, those greater 

 long pipes. 



4. We consider now the depth of the disturbance AR. This from 

 consideration of the stream lines as above varies inversely as the velocity 

 it cannot exceed in an open chaimel the depth of the water, or at most 

 a certain mean value of the distances of all points in the cross section from 

 the central axis of flow, and in the case of pipes under pressure running 

 full Ai? cannot exceed the radius of the pipe. We assume tentatively 

 the form of the function representing the second term in the parenthesis 

 of (8) to be 



— = ^ , m 



2r rV^-q ' 



in which p and g are constants, the maximum value p/g being some proper 

 fraction or unity. 



5. The slope of the resistance Ai2/AL depends directly on the mean 

 slope of the rigid roughness of the material boundary, and it diminishes 

 as the velocity and mean radius increase. Its greatest value occurs when 

 the velocity and mean radius are least when it approximates the mean 

 slope of the topography of the rigid material boundary. As the velocity 

 and radius increase Ai2/AL diminishes, but not indefinitely. As the 



