NOTES ON THE FLOW OF WATER IN 

 IRRIGATION DITCHES 



By Clement C. Williams 



A complete and entirely satisfactory method of determining the 

 flow of water in irrigation ditches has not yet been devised. Galileo 

 once declared that he "found less difficulty in the discovery of the motion 

 of the planets, in spite of their amazing distances, than in investigations 

 of the flow of water in rivers which takes place before my very eyes." He 

 maintained that the laws of falling bodies applied to the flow of streams, 

 and hence the velocity was dependent upon the fall regardless of the 

 length of the channel. Torricelli was the first to discover that the inclina- 

 tion of the stream bed governed the velocity of flow. In the first half of 

 the eighteenth century, Pitot and Bernoulli showed that the rate of 

 flow of streams was dependent upon the cross-section of the channel. 

 About fifty years later, Chezy, a French engineer, developed the familiar 

 formula which bears his name based on the fact that in uniformly flowing 

 streams the accelerating forces are equal to the retarding forces. His 

 formula is 



v=cVrJs 

 where 



V = velocity in feet per second 



i?= hydraulic radius or mean depth 



5= slope 



C=a coefficient, which he assumed to be constant. 



Hydraulic engineers since that time have accepted Chezy's formula 

 and have devoted their efforts mainly to finding a value of the coefficient 

 C based on the slope, the cross-section and the roughness of the 

 stream bed. Dubuat, Venturi, Coulomb, DeProny, Eytelwein and 

 others have contributed various additions to the science along this line. 

 Darcey in 1857 published the first definite formula, which Bazin, 

 Ganguillet and Kutter modified and gave to the world in the following 

 form, commonly known as Kutter's formula: 



237 



