104 STE'f METHODS FOR BACKWATER CURVES 



ditions without the backwater effect, we may write 



n 

 according to Manning's formula. For flow with backwater 



n 



in which Sw represents the water-surface slope corresponding to the 

 given discharge Q, if velocity head changes due to the backwater are 

 neglected. 



From the discharge-elevation curves, determine the value of Qn 

 corresponding to the known elevation of the backwater curve at the 

 first section. The value of Q for the backwater curve is less, and since 

 the values oi A, R, and n are the same, the slope of the backwater curve 

 must be 



S^ = Sn (^^^ [906] 



The slope at the first section having thus been determined, the elevation 

 of the backwater curve at the second section may be estimated. This 

 elevation is likely to be in error, for the average slope across the reach is 

 poorly approximated by the slope at one end. The elevation may be 

 used, however, to determine a value of Qn at the second section, and 

 thus a slope at the second section, after which the elevation may be 

 recomputed, using for the average slope across the reach the better 

 approximation of the mean of the slopes at the first and second sections. 

 Further corrections are seldom necessary. After a little experience, it 

 is found to be possible to avoid revisions by arbitrarily altering the first 

 estimated elevation in the right direction. When the elevation at the 

 second section has been checked, the process is repeated on through the 

 length of the backwater curve. 



In making the computations it is more convenient to work with the 

 fall in a given reach than with the slope. 



F^F.(£f [907] 



The value of the normal fall Fn is read directly from the profiles. 



Illustrative Example 



Grimm's method should only be applied to natural watercourses, but to save 

 reproducing numerous curves, and to afford a comparison, the problem of the 



