BRIDGE PIERS AS CHANNEL OBSTRUCTIONS 



127 



fication may be easily derived on the basis of the definition of the classes. 



Both are plotted in Fig. 1004. Values on the boundary between the 



Yarnell classifications may be checked by reference to Fig. 1003. 



Yarnell's tests, however, indicate (as he himself points out) that the 



Rehbock classification is more useful than his classification, though 



there is no conclusive evidence 

 that a single formula might 

 not be developed which would 

 have satisfactory accuracy 

 over the entire range of tran- 

 quil normal flow in the unob- 

 structed section. 



Vi 



P^ 



T 



H, ^t 



'^A'^wAWWWA^^<'A^w^^WJ^WAI^yA^^w.'^^W 

 Longitudinal Profile 



1 lii«i t 



Fig. 1004. Classifications of Flow 

 Channels Obstructed by Bridge Piers. 



(After U.S.D.A. Tech. Bull. 442.) 



Plan 



Fig. 1005. Diagram 

 Bridge Pier. 



of 



Yarnell tested the types of piers most commonly used in American 

 practice with contractions of 11.7, 23.3, 35, and 50 per cent, and pile 

 trestles with contractions of 12.3 to 16.2 per cent. 



His tests showed that for flow in Class 1 and Class 2, the Nagler 

 formula showed the least variation with the amount of contraction, 

 over the range tested.^ ^ Figure 1005 shows the notation used in the 

 Nagler formula, which is 



Q = KW'^ 



'^[^^"^W 



^3 + 



2g 



[1011] 



The coefficient ^ is a correction coefficient, the factor dVs^/lg being 

 intended to correct D3 to give a smaller depth of flow similar to that at 



^^ " Obstruction of Bridge Piers to the Flow of Water," F. A. Nagler, Trans. Am. 

 Soc. Civil Engr., v. 82 (1918), p. 334. See also " Experiments on the Flow of Water 

 through Contractions in an Open Channel," E. W. Lane, Trans. Am. Soc. Civil Engr., 

 V. 83 (1919), p. 1149. 



