116 BENDS, TRANSITIONS, AND OBSTRUCTIONS 



sary, it is most needed on the outer bank in the lower part of the curve, 

 and to a less degree on the inner bank at the beginning of the curve. 



It frequently happens that navigation improvements such as training 

 walls or dams partially obstruct the main stream in such a way that the 

 current is deflected away from a re-entrant angle or pocket. The water 

 surface in the re-entrant corner will have a higher elevation than that 

 of the main stream. The pocket will contain a large eddy. If the 

 stream lines for a given condition of flow are known or can be approxi- 

 mately located, integration based on equation (1001) can be applied to 

 compute roughly the amount of superelevation needed to deflect the 

 main stream as it curves out to miss the re-entrant angle. 



Flow around bends : velocity greater than the critical. Flow around 

 curves in alignment, when the velocity is greater than the critical, is 

 entirely unlike that which occurs when the velocity is less than the 

 critical. The water surface, instead of being smooth and showing only 

 a slight superelevation, is likely to have a broken and varying transverse 

 profile, with greater difference in elevation at the inner and outer banks 

 than would be indicated by any of the formulas used to estimate the 

 superelevation in low-velocity flow. High-velocity flow around bends 

 is uncommon, and is, therefore, likely to be unfamiliar even to those 

 who have had much experience with bends having low-velocity flow. 

 For this reason many of the flume bends for high-velocity flow that 

 have been constructed in the past do not operate satisfactorily. Study 

 of the problem during the last ten years, however, has shown the reason 

 for the difficulties which have been encountered.'* Methods are being 

 developed for the design of bends having greatly improved flow con- 

 ditions, and also for the correction of bad flow conditions in existing 

 bends. 



Consider first a circular curve of constant radius between two long 

 tangents in a rectangular channel having a bottom which is level trans- 

 versely. The high-velocity flow approaching the curve is level trans- 

 versely. If the side of the channel were suddenly moved inward a 

 small distance, a wave would start which in quiet water of the same 

 depth would travel across the channel, with a velocity equal to the 

 critical, and be reflected back and forth until it finally died out. With 

 respect to the moving water, the side of the channel is being continuously 

 " pushed in " starting at a point A, Fig. 1002. This causes a wave to 

 travel across the channel, which at the same time is swept downstream 

 by the swift current. The wave begins along the line AM, £ind the 



■* " Curvilinear Flow of Liquids with Free Surface at Velocities above that of Wave 

 Propagation," R. T. Knapp and A. T. Ippen, Proceedings of the Fifth International 

 Congress for Applied Mechanics, p. 531. John Wiley and Sons, 1938. 



