102 



STEP METHODS FOR BACKWATER CURVES 



(905) are all functions of the elevation of the water surface at the 

 section. Hence a plot may be prepared showing the variation of the 

 friction slope with the water-surface elevation at the section, for the 

 given discharge. Figure 903(a) shows such a plot, for the data from 

 two identical sections of the example given in Fig. 902. After the curve 

 for one value of Q has been computed, others may be obtained by 

 increasing or reducing the abscissa values in proportion to the square of 

 the discharge. A logarithmic abscissa scale is used, so that this is,easily 



Velocity Head for Q= 100,000 

 1 2 10 



770 



^760 



750 



740 



0.001 01 



Friction Slope 



(a) 



12 10 20 



Velocity Head for Q= 160,000 



(6) 



Fig. 903. Friction Slope and Velocity Curves for Stations 10 + 80 and 11+80 

 of the Example Given in Fig. 902. 



accomplished by shifting the curve horizontally without changing its 

 shape. An even simpler expedient is to shift the origin of the abscissas. 

 The different scales should be clearly labeled. 



Similar diagrams may be prepared for each section to show the vari- 

 ation of velocity head. For a given water-surface elevation, the velocity 

 head also varies with the square of the discharge, so that logarithmic 

 plotting is again convenient. Figure 903(6) illustrates the expedient 

 of shifting the origin of abscissas. 



In preparing the diagrams summarizing the hydraulic elements, the 

 range of values computed should be kept within reasonable limits. 

 Unless the curves are needlessly extended beyond the expected range, 

 the time spent in their preparation will be returned with interest during 

 the step computations. 



After the velocity head and friction slope data have been summarized 

 in the form shown in Fig. 903, the step computations can be made in 

 essentially the same way as before. Columns (3), (6), and (7) are 

 omitted from the table. 



A number of other variants of the standard step method are possible. 



