126 BENDS, TRANSITIONS, AND OBSTRUCTIONS 



tance, the piers " split " the high-velocity flow, throwing water and 

 spray into the air. Though the flow is much disturbed downstream, 

 there is no upstream efl^ect, and in the center of the spans the flow con- 

 tinues under the bridge at normal depth until it encounters the waves 

 started by the piers. Except when the bridge and its piers so constrict 

 the flow that the water immediately upstream from the bridge is dammed 

 up to greater than critical depth, it is impossible for the bridge piers to 

 affect the upstream water surface.^ If the flow is constricted to this 

 extent, the water surface upstream from the bridge will follow an SI 

 curve for a short distance, starting at a hydraulic jump with its down- 

 stream end where the depth of the SI curve becomes sequent to the 

 normal depth of the stream. 



The more common condition of low- velocity flow obstructed by bridge 

 piers or pile trestles has been the subject of several experimental investi- 

 gations. For an extensive bibliography, as well as the description of a 

 large number of tests of different kinds of piers and trestles, see " Bridge 

 Piers as Channel Obstructions,"^ and " Pile Trestles as Channel Ob- 

 structions, "^° both by D. L. Yarnell. The experiments seem to show 

 the need of further subdivision of low-velocity flow. The most logical 

 basis is that proposed by Yarnell : 



Class A — Flow in contracted section is at greater than critical depth 



(tranquil flow). 

 Class B — Flow in contracted section is at less than critical depth 



(shooting flow). 



The Rehbock classification, proposed by T. Rehbock when he found 

 that the results of some 2,000 small-scale tests could not be formulated 

 in a single category, is as follows: 



Class 1 — Ordinary or " steady " flow, in which the water passes the 

 obstruction with very slight turbulence or no turbulence. 



Class 2 — Intermediate flow, in which the water passing the obstruc- 

 tion displays a moderate degree of turbulence. 



Class 3 — " Changed " flow, in which the water passing the obstruc- 

 tion becomes " completely " turbulent. 



The boundaries of the Rehbock classification are defined by empirical 

 equations, while the equation of the boundary of the Yarnell classi- 



* " Backwater Wave in the Spillway Channel, Gatun, Panama Canal," Edward 

 C. Sherman, Engineering News, v. 67, p. 813, April 25, 1912. 

 ^ Technical Bulletin 442, U. S. Department of Agriculture. 

 '" Technical Bulletin 429, U. S. Department of Agriculture. 



