S292 HYDRAULICS AND ITS APPLICATIONS 



This form of equation is in common use in France, and has given good 

 results with velocities not exceeding 4 feet per second. 

 and Kutter deduced the coefficient 



41 c 



C = - in foot units< 



Vm 



the equation being identical with that used for pipe flow. N depends on 

 the character of the surface, and has values given on p. 293. 



The complication of this formula is largely due to an attempt to make 

 it conform to the results of experiments made on the Mississippi. In 

 certain of these, however, the results should have been corrected for the 

 error introduced by the use of double floats, while in others the slope of 

 the water surface was too slight to be measured with any degree of 

 accuracy. 



More recent investigations render it extremely doubtful whether the 

 value of C does depend on i as this formula indicates, and the simpler 

 formula of Bazin would appear to give results at least as accurate, except 

 possibly in the case of very large channels. The formula is, however, of 

 very general application in Great Britain, India, Germany and the 

 United States, and the inconveniences due to its complication are removed 

 by the use of hydraulic tables which have been prepared giving the values 

 of C for practically all values of i and of N. 



By altering the value of i in this formula from '001 to '01, the value of 

 C is altered by less than 1 per cent. For streams of fairly rapid slope 

 the value of i may then be taken as sensibly equal to '001, in which case 

 the value of C simplifies to 



44-4 + 



c = _ 



1 + 44-4 N 



Vm 



In very large rivers the flow is sensibly independent of the character of 

 the bed, and for such a case Manning 1 gives C the value 



C = 62Jl + ^-^L}in foot units. 

 7 Vm J 



C = 34 1 + - - in metre units. 



4 Vm ' 



From the nature of the case it would appear hopeless to obtain any 



1 Inst. Civil Engineers of Ireland, December 4, 1889. 



