98 STEP METHODS FOR BACKWATER CURVES 



If the distance between soundings is kept the same 



p = W-{- \ ^ [903] 



2w 



Wetted perimeters for stages above low water are obtained by adding 

 increments which are either scaled from the plot of the cross section or 

 computed by slide rule. The computations can be made with an ordi- 

 nary Mannheim type rule. Set the index of the B scale above the length 

 of the short side of the slope triangle on the D scale. (The short side 

 of the slope triangle will usually be the contour interval.) Set the 

 indicator to the length of the long side of the slope triangle on the D 

 scale. (The long side of the slope triangle will usually be the variable 

 horizontal distance between successive contours.) Opposite the value 

 just set, read on the B scale the ratio of the square of the long side to 

 the square of the short side. Move the indicator over to a value on the 

 B scale greater by 1.00 than the value just read. The length of the 

 hypotenuse of the slope triangle will now appear under the indicator, 

 on the D scale. This is the increment of wetted perimeter for one side 

 of the stream. The increment for the other side is determined similarly. 

 As long as the vertical interval between contours remains the same, the 

 position of the B scale with respect to the D scale does not need to be 

 changed. 



After some familiarity with the procedure of computing areas and 

 wetted perimeters has been gained, it will be found possible to dispense 

 with plotted cross sections, the needed values being computed directly 

 from the field notes. 



The determination of the hydraulic radius can often be still further 

 simplified. Wetted perimeters are first computed, by one of the 

 methods described above, for two water-surface elevations, high and low. 

 Each wetted perimeter is then divided by the corresponding surface 

 width. If the two coefficients so obtained do not differ appreciably, 

 the wetted perimeters for intermediate stages may be obtained by 

 multiplying the respective surface widths by an interpolated coefficient. 



After the areas and wetted perimeters have been computed it is a 

 simple matter to tabulate the corresponding values of water-surface 

 elevation, area, and hydraulic radius for each section. 



The roughness of an existing channel is best determined from field 

 data on its area, slope, and discharge. It is rarely possible to obtain 

 these data, and recourse must usually be had to values such as those 

 given in Table 101, and to a study of measurements on similar channels. 

 The coefficients for artificial channels are less uncertain than for natural 



