BRIDGE PIERS AS CHANNEL OBSTRUCTIONS 125 



less than the critical, the transition must have a " throat," that is, it 

 must narrow down to the value of W^IWx corresponding to the critical 



depth at an intermediate value of ^r — vertically above the value of 



on Fie:. 1003. The transition then becomes similar to that 



shown in Fig. 203, with flow from right to left. 



Cases SDn and w seldom occur, though they are theoretically possible. 

 Figure 203, with flow from left to right, could illustrate either case, 

 depending upon where the transition ended at the right. Hinds illus- 

 trates a similar transition in which the bottom is humped.® It is not 

 known whether a successful transition of this type has ever been built. 

 What usually happens is that a hydraulic jump forms upstream from 

 the transition, and flow through the transition becomes DDn or w. 



In general, the transition profiles for which the water surface is level 

 or falling, going downstream, are stable and dependable. Those 

 leading to a rising or uphill water surface are likely to be undependable. 

 The flow conforms to the theoretical best when the water-surface profile 

 through the transition, computed by applying Bernoulli's equation to 

 a succession of short reaches, is a smooth curve tangent to the normal 

 flow at each end, and when the maximum angle of divergence or con- 

 vergence of the walls is less than the wave angle.^ 



Bridge piers and pile trestles as channel obstructions. Bridges and 

 pile trestles, even when built without approach embankments, obstruct 

 part of the area of flow of the stream. If the normal depth of flow of 

 the stream is deeper than the critical, the water upstream from the 

 bridge is deeper than the normal, while the depth a short distance down- 

 stream differs but little from the normal. The resulting drop in the 

 water surface is known as the " backwater " caused by the bridge. It 

 causes a backwater curve which extends on upstream, and which may, 

 if it is high enough and deep enough, result in flood damage in excess of 

 that which would be caused by normal flow in the stream. 



If the normal depth of flow of the stream is less than the critical, 

 a condition which does not often occur where backwater is of impor- 



^ " Hydraulic Jump and Critical Depth in the Design of Hydraulic Structures," 

 Julian Hinds, Engineeting News-Record, Nov. 25, 1920, p. 1034. 



^ " The Hydraulic Design of Flume and Siphon Transitions," Julian Hinds, 

 Trans. Am. Soc. Civil Engr., v. 92 (1928), p. 1423. Many practical suggestions for 

 the design of transitions are given in this paper. According to Hinds, friction losses 

 in well-designed transitions where the flow is accelerated may be taken as 5 per cent 

 of the difference of the velocity heads, and where it is decelerated, as 10 per cent of 

 the difference of the velocity heads. 



