LEACH'S DIAGRAM 107 



The correct elevation will be a little higher, try 25.10. For this elevation at 

 section 2, Qn is 25,600, and the corresponding fall in reach 1-2 is 



^ , 6,220 \2 ^^ ^ 

 2 X [— I = 0.118 



\25, 



600/ 



The average fall in the reach, that is, the fall indicated by the average of the 

 falls based upon the computed slopes at each end, is 



ao90 + an_8 = o.io4 



hence the elevation of 25.10 is satisfactory.^ The computations are best 

 arranged in tabular form. Table 901 appears to be unnecessarily repetitious, 

 but this is due to the uniformity of the channel used in the example. For a 

 natural channel, repeating values would occur only by accident. They are 

 included in the table for the sake of completeness, in order to show the proper 

 arrangement for irregular channels. 



Leach's diagram. The trial-and-error step methods for computing 

 backwater curves in irregular channels are awkward and laborious at 

 best. Yet no simpler methods are known that will give results of 

 comparable accuracy. When studies are being made to determine the 

 economical height of a dam or in other problems where the initial ele- 

 vation is indeterminate, a large number of backwater curves may have 

 to be computed for the same discharge. In this case Leach's diagram® 

 may be used to advantage. The diagram may be prepared after a few 

 curves have been computed by the step method. From it the reach 

 elevations for backwater curves between those used in preparing the 

 diagram may be read directly. Figure 905 shows the construction of 

 the diagram. Figure 905 (a) shows the portion of the complete diagram 

 that applies to the first reach. Abscissas are elevations at the lower end 

 of the reach, and ordinates are elevations at the upper end of the reach. 

 After sufficient step computations have been made (at least three) the 

 curve of Fig. 905(a) may be plotted. It shows the elevation at the 

 upper end of the reach for any elevation at the lower end of the reach, 

 within the range of the values plotted. 



The curves for a number of reaches may be combined upon a single 

 diagram, as shown in Fig. 905(6). It is most convenient to alternately 

 reverse the coordinates, so that the entire curve may be traced by 



^ The trial-and-error computations may be avoided by the use of nomographs 

 described by I. H. Steinberg, " The Nomograph as an Aid in Computing Backwater 

 Curves," Civil Engineering, v. 9, p. 365, June, 1939. 



^ " New Methods for the Solution of Backwater Problems," by H. R. Leach, 

 Engineering News-Record, v. 82, p. 768, April 17, 1919. 



