96 STEP METHODS FOR BACKWATER CURVES 



methods, however, having significant differences. The choice between 

 them depends upon the type of problem to be solved and the kind of 

 data available. (1) If the data include measurements of the channel 

 shape, a method may be used that has been developed by many authors. 

 It is applicable to the most complicated examples, and always involves 

 trial-and-error computations. This method will be hereinafter referred 

 to as the standard step method. (2) If profiles of the stream at a num- 

 ber of different discharges are available, a convenient method is that of 

 C. I. Grimm, which may be used where velocity head changes are 

 relatively unimportant. Ordinarily trial-and-error computations are 

 used, but they may be eliminated if desired. (3) If the channel is uni- 

 form, a direct step method may be used, in which friction and velocity 

 head changes are taken into account. Trial-and-error computations 

 are not necessary. 



Any one of the step methods may be used to obtain the basic data for 

 a diagram devised by H. R. Leach which greatly facilitates the compu- 

 tations when a large number of curves for the same discharge, but 

 starting at different elevations, must be obtained. A detailed descrip- 

 tion of the different methods follows. 



Standard step method. The data necessary for the use of the stand- 

 ard step method for computing backwater curves are : 



(1 ) The discharge for which the curve is desired, or data from which 



the discharge may be determined. 



(2) A water-surface elevation at the downstream end of the desired 



profile, if the depth of flow is greater than the critical; or at the 

 upstream end, if the depth of flow is less than critical. 



(3) The cross-sectional area and hydraulic radius at various points 



along the channel, for all depths of flow within the range 

 expected. 



(4) The hydraulic roughness of the various sections of the channel. 



If the discharge is not given, it may have to be determined from the 

 head on a spillway, the flow through an obstruction, or other means. 



It is not absolutely necessary to have a water-surface elevation at one 

 end of the profile. If none is given, the computations may be started 

 from an assumed elevation above or below the section through which 

 the profile is desired, and the correct elevation found as explained on 

 page 95. 



The cross-sectional area and the hydraulic radius at points along the 

 stream may be determined from maps which show contours in the bot- 

 tom of the channel, from soundings giving the depth of the water, or 



