FLOW AROUND BENDS 113 



inside of a bend cannot be taken advantage of in laying out the walls 

 of flumes, for the water surface there is more wavy than at the outside 

 of the bend, and more freeboard is needed. 



Another detail regarding the curved motion around a bend should be 

 noted at this place. Referring again to Fig. 1001, the excess of pressure 

 required at D over that at C varies as the square of the velocity of the 

 moving water, other things being equal . But the layer near the bottom 

 has a much slower velocity than a layer near the top like CD. It 

 follows then that the same superelevation at B cannot furnish precisely 

 the required excess pressure for both layers CD and EF. What really 

 happens is that the two layers do not bend around the same center of 

 curvature and do not have the same radius of curvature. The super- 

 elevation at B takes an intermediate value, and the motion of each 

 layer adjusts itself to the corresponding pressure difference. The 

 layer EF has a shorter and the layer CD a greater radius of curvature 

 than the average. As a result the fastest moving water gradually shifts 

 toward the outer bank as it moves around the bend, and there is a 

 compensating creep of the slower moving water near the bed of the 

 channel towards the inner bank. This effect cumulates with the length 

 of the bend, so that in a long bend, such as a semicircular curve, finally 

 all the water with highest velocity is near the outer bank while in the 

 inner half of the cross section the velocity of the water is much slower. 

 This phenomenon was observed and studied in a small experimental 

 channel by Professor James Thomson about 1870, and has become 

 known as the " spiral flow " in bends. 



The spiral or helicoidal flow set up in the bend is clockwise if the 

 stream curves to the left, looking downstream, or counterclockwise, if 

 the stream curves to the right. Helicoidal flow was observed and 

 studied by Blue, Herbert, and Lancefield^ in a sharp bend in the Iowa 

 River. The spiral-forming tendency of the sharp bend or turn was 

 found to be so pronounced that it reversed the direction of helicoidal 

 flow due to a milder bend in the opposite direction which was imme- 

 diately upstream. The cross section of the Iowa River at these bends 

 is comparatively deep and narrow. Where the cross section is wide 

 and shallow the spiral is much attenuated, and may be so weak as to be 

 difficult, if not impossible, to observe. 



Consideration of the helicoidal flow throws interesting light upon the 

 question of the energy loss due to bends. If the bend is followed by a 

 long tangent, the helicoidal flow will persist for some distance down- 

 stream, until it finally dies out because of the eff'ect of friction. It is 



^ " Flow Around a River Bend Investigated," by Blue, Herbert, and Lancefield, 

 Civil Engineering, v. 4, p. 258, May, 1934. 



