100 STEP METHODS FOR BACKWATER CURVES 



(6) Hydraulic radius corresponding to the elevation listed in 

 column (2). 



(7) Four- thirds power of the hydraulic radius. This is most con- 

 veniently obtained on the ordinary Mannheim type of slide rule. 

 Set R on the CI scale opposite R on the K scale. Read R*''^ on the D 

 scale opfKDsite the index of the C scale. 



(8) Friction slope corresponding to the area, hydraulic radius, and 

 roughness. By the Manning formula this is 



/ nVV 1 

 \1.4867 R^' 



For the assumed condition of constant n, 



^ 2g 2.21 *■ ■■ 



Thus the friction slope is obtained by multiplying the value of the 

 velocity head in column (4) by a constant, and dividing by the value of 

 R^l^ from column (7). 



(9) Average friction slope through the reach. This is approximated 

 by taking the arithmetic mean of the value of the friction slope just 

 computed in column (8), and that for the previous step. 



(10) Length of the reach. This is the distance between the successive 

 sections, measured along the center line of the stream. 



(11) Friction loss in the reach. This is the product of the values in 

 columns (9) and (10). 



(12) Eddy loss. No rational method of evaluating the eddy loss is 

 known. It is zero when the velocity head increases through the reach, 

 and some proportion of the difference of velocity heads at the end 

 sections when the velocity head decreases through the reach. Since the 

 amount of the eddy loss is a matter of individual judgment and is 

 roughly approximate at best, the part of the decrease of velocity head 

 to be used can be selected mentally. It should be relatively small where 

 conditions favor a smooth, gradual reduction of velocity. 



(13) Elevation of the total head line (a check value). This is com- 

 puted by adding^ the values of friction and eddy loss in columns (11) 

 and (12) to the elevation at the lower end of the reach, which will be 

 found in column (13) of the previous step. If the value so obtained 

 does not agree closely with that entered in column (5), the entire line 

 just computed should be neatly crossed out and a new line started with 



^ If the step computations are proceeding in the downstream direction, these losses 

 must be subtracted. 



