4 INTRODUCTION 



Steady uniform flow. The Manning and Kutter formulas, which are 

 the open channel velocity or " friction " formulas most frequently used 

 in the United States, apply only to steady, uniform flow. The channel 

 should be uniform, and the slope of the water surface should be constant 

 and the same as 'that of the bottom of the channel. The requirement of 

 parallelism of water surface and channel bottom is the more important. 

 The effect of channel irregularities may be taken into account, to a 

 certain extent, in estimating the roughness, but lack of parallelism of 

 the water surface and the general grade line of the bottom of the channel 

 may cause direct application of the friction formulas to give grossly 

 inaccurate results. Reasons for this, and methods for computing non- 

 uniform flow, will be explained in later chapters. 



The Manning formula is 



^=li?5 2^2/3^1/2 [101] 



n 



The Ganguillet-Kutter formula, usually known as the Kutter formula, 

 gives the value of the coefficient C in Chezy's formula 



[102] 



0.00281 1.811 

 41.65 -\ 1 



C = z T [103] 



n / 0.00281\ ^ ^ 



A discussion of these formulas, and the older formulas that they have 

 supplanted, is given in Part IV of the Technical Reports of the Miami 

 Conservancy District, also in H. W. King, Handbook of Hydraulics, and 

 in many other sources. Recent studies of turbulence in open channel 

 flow have suggested newer types of formulas, but for the present volume 

 it will be assumed that the Manning and Kutter formulas are 

 satisfactory. 



Both formulas give the average velocity in terms of the hydraulic 

 radius, the slope, and a roughness coefficient. In problems on uniform 

 flow in a given channel, the quantities that need to be solved for may be 

 (1) the velocity or the discharge, (2) the roughness coefficient, (3) the 

 slope, or (4) the depth of flow. The shape of the cross section of the 

 channel is assumed to be known. 



Solution of the first three types of problems is straightforward, involv- 

 ing no especial difficulty except selection of the proper value of the rough- 

 ness coefficient. Table 101 may be used as a guide. A detailed discus- 

 sion of the values of the roughness coefficient to be used over a wide 



