108 



STEP METHODS FOR BACKWATER CURVES 



reading elevations first from one axis, and then from the other, as 

 shown by the dotted line. 



Step method for uniform chamiels. If the channel is uniform, a 

 simplified step method may be used. It is more convenient than the 

 trial-and-error standard step method, but not so convenient as the 



Elevation at Section 1 

 (a) 



Elevation at Sections 1,3.- 

 (b) 



Fig. 905. Leach's Diagram for Different Backwater Curves at the Same Discharge, 

 (a) For a single reach. (&) For several reaches. 



methods described in Chapters VI and VII. It is easily remembered, 

 however, and can be used when tables are not available. For a step of 

 length Ax, Bernoulli's equation may be written 



SoAx + Pi + -^ = SfAx + ^2 + ^ 

 2g 2g 



Solving for Ax, 



Ax = 



V2^ V^ 



5o- 5 



[908] 



To use this equation, assume a value of D^ slightly greater than the 

 known value of D\. The difference should be small to keep systematic 

 errors to a minimum. The velocity head at each end of the step will 

 be known, as will the bottom slope Sq- The value of 5/ may be approxi- 

 mated by the mean of its values at each end of the step. The right- 

 hand member of equation (908) can then be computed, giving the length 

 of the step. Before the computations are started, curves similar to 

 those of Fig. 903 should be prepared. Only one set of curves will be 

 needed for a uniform channel. 



Care is needed in the application of equation (908), to insure that 

 positive and negative quantities are correctly interpreted. The com- 

 putations progress upstream, if the depth of flow is greater than the 

 critical; or downstream, if it is less than the critical. The friction slope 

 Sf may be evaluated by either the Manning or Kutter formulas. 



