CHAPTER XI 

 DEVELOPMENT OF FORMULA FOR FLOW 



THE first attempts to discover the law by which the velocity 

 of running water depends on the fall and cross-section of the 

 channel is supposed to have been made in 1753 by Brahms, 

 who observed that the acceleration which we should expect 

 in accordance with the law of gravity does not take place in 

 streams, but that the water in them acquires a constant veloc- 

 ity. He points to the friction of the water against the wet 

 perimeter as the force which opposes the acceleration, and 

 assumes that its resistance is proportional to the mean radius, 

 Rj that is, to the area of the cross-section divided by the wet 

 perimeter, or v = CR\H, with C equal to a fraction multi- 

 plied by V^g. 



In 1775 Brahms and Chezy, the latter a celebrated French 

 engineer, whose most famous work was the Burgundy Canal, 

 made the next advance, and altered the relation between the 

 velocity and the mean radius. These engineers are to be 

 regarded as the authors of the well-known formula usually 

 known as the Chezy formula, viz., 



-^S = CVR-S; 



or velocity equals a constant multiplied by the square root 

 of the hydraulic radius and by the square root of the slope. 



Dubuat, 1779, undertook to determine experimentally 

 some of the laws governing flowing water, and for that purpose 

 he made an elaborate series of gagings of some French canals 

 and of artificial channels. His results are summed up in 

 these two laws: 



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