6 INTRODUCTION 



Determination of the depth of flow, with the discharge, roughness, 

 and slope given, is indirect for most types of cross sections. The prob- 

 lem may be solved by assuming values for the depth and computing 

 corresponding values of the discharge, repeating with different values for 

 the depth until the computed value of the discharge agrees with the 

 given value. Extra computation may be avoided if a synthetic rating- 

 curve is drawn, plotting the assumed values of the depth against the 

 corresponding values of the discharge. The use of logarithmic scales 

 will simplify drawing the curve, for when plotted logarithmically the 

 points tend to lie on a straight line. If the Manning formula is to be 

 used, it is sometimes better to plot AR^'^ versus the depth. The desired 

 value of the depth is that for which AR^'^ equals the value of 

 ^w/1.4865^'^ computed from the given discharge, roughness, and slope. 

 This procedure is distinctly advantageous if the given values of S and n 

 are likely to be revised, as often happens in design work. With either 

 method, no more of the curve need be drawn than is necessary to arrive 

 at the required depth. 



y -W/gvA 



^ 



Fig. 102. Overbank Flow. 



The most complicated type of cross section, with regard to the com- 

 putation of uniform flow, is that in which part of the flow is in a deep 

 central channel, and part is in shallow side sections, as shown in Fig. 

 102. Computations based on the hydraulic radius of the entire cross 

 section will be in error. Better results are obtained by computing the 

 flow in the side and central portions separately, considering the areas 

 and wetted perimeters of each to end at an imaginary vertical line above 

 the bank of the submerged main channel. 



Certain simple geometrical shapes are frequently used for canals cind 

 flumes. It is possible to simpHfy the determination of the depth of 

 uniform flow in these sections. Consider first a triangular cross section 

 with side slopes of z horizontal to 1.00 vertical. When the depth of flow 

 is D the area is zD^ and the wetted perimeter is 2DV\ + z^- Thus we 

 may write 



„2/3r)4/3 



1.486^i?2/3 ^ i.486zZ)2 



{2DVi + 2^)2/3 



