FLOW AROUND BENDS 



117 



water surface up to that line is undisturbed. The angle jSq that the line 

 makes with the tangent extended beyond point A is approximately: 

 arcsin (VgD/V). It is known as the " wave angle." 



Continuing past point .4, the side of the channel is being " pushed in " 

 against the flow at an increasingly rapid rate, so that the water surface 

 rises higher and higher around the outside wall until another effect, 

 which we shall consider next, sets in. Water-surface contours in the 

 area AMD will be a series of lines approximately parallel with the wave 

 front AM. 



Fig. 1002. Plan View of High-Velocity Flow Around a Bend in an Open Channel. 



At point B a negative wave is started which travels across the current 

 along the line BM. The water line along the inside wall drops lower, 

 and the water-surface contours in the area immediately downstream 

 tend to parallel the line BM. 



The two waves do not stop when they meet near the center of the 

 channel. It is a familiar characteristic of waves that they may cross, 

 be reflected from a wall, and recross, without much loss of form or even 

 change of velocity (in quiet water). Thus the negative wave travels 

 on across the surface of the positive wave, diminishing its height, and 

 the positive wave travels downward across the negative wave, filling in 

 the depression. If the water had the same depth and velocity that it 

 has in the area ABM the negative wave would begin to strike the out- 

 side wall at point D. The increased depth tends to make the wave front 

 curve toward the left as it approaches point D, while the changed direc- 

 tion of the velocity makes the wave front curve towards the right. The 

 net result, as observed by Ippen and Knapp in their experiments, is 

 that the wave front curves slightly to the right, first striking the outside 

 wall at point D . The central angle corresponding to the arc AD is 



