114 BENDS, TRANSITIONS, AND OBSTRUCTIONS 



evident that the entire energy of the spiral flow will be dissipated, so 

 that a greater friction loss would be expected than in an equal length 

 of straight channel without a bend. Another reason for increased 

 energy loss in bends is that the high velocity part of the stream comes 

 closer to the banks than in normal straight channel flow. The actual 

 dissipation of energy due to both of these effects takes place largely in 

 the straight reach below the bend, where the helicoidal motion and 

 turbulence die out. If the bend is followed by another bend of equcJ 

 radius and length, but in the opposite direction, and the spiral set up by 

 the first bend is neutralized in the second, the energy loss might be less 

 than for two equal bends in the same direction. However, tests of pipe 

 bends flowing full, in which two spirals form, show exactly the opposite 

 effect, with greater loss for two adjacent bends in the opposite direction 

 than for two equal adjacent bends in the same direction. Whatever 

 the result is in any given case, it is evident that in determining the 

 energy loss due to curvature, the spacing and sequence of the bends 

 must be considered, as well as their radius and central angle. On the 

 basis of his tests of the Tiger Creek Flume, which has considerable 

 curvature alternating in direction, Scobey^ suggests that the value of 

 Kutter's n be increased 0.001 for each 20 degrees of curvature in 100 feet 

 of flume. Until more data are available, the effect of spacing and 

 sequence of bends, and of their radii, cannot be evaluated, and Scobey's 

 suggestion can only be safely followed with flumes similar to the Tiger 

 Creek Flume. 



The next point for consideration is the condition at the junction 

 points of straight channels and bends. In actual rivers there is always 

 some sort of a gradual transition curve at both the beginning and ending 

 of a curve, but it will be simpler to discuss a theoretical channel in which 

 two tangents are connected by a circular curve of constant radius. 

 Since the transverse profile is level on the approaching tangent but must 

 be inclined around the bend, the question arises as to how the change 

 takes place from one state to the other. Perhaps, theoretically, the 

 level cross section could be transformed to the slanting shape most 

 simply by raising the water surface at the outer bank and lowering it 

 at the inner bank by equal amounts. Blue, Herbert, and Lancefield 

 found an eddy at the outside of the sharp Iowa River bend, indicating 

 a rise in the water surface at the beginning of the curve. This is rarely 

 found except in the sharpest bends. Usually the longitudinal slope at 

 the outer bank flattens or becomes practically level for a short distance. 

 The remainder of the required transverse slope results from a rather 

 sudden depression in the water surface at the inner bank at the begin- 

 ning of the curve. 



^ Loc. cit. 



