BRIDGE PIERS AS CHANNEL OBSTRUCTIONS 129 



creased K only 5 per cent (net width of pier, not including its pro- 

 jection, subtracted in computing W2)- All these values are from 

 Yarnell's tests, and though they lack verification in the field, they are 

 believed to be the best available. 



For Class 3 flow, the D'Aubuisson formula fits Yarnell's experimental 

 data better than the Nagler formula. D'Aubuisson assumed that the 

 water-surface drop at the contracted section is merely the difference in 

 the velocity heads, and he did not distinguish between the depths D2 

 and 7)3. In practical cases there will be little difference. Using the 

 notation of Fig. 1005, the formula may be written 



Q = KW2D3V2gHs + Vi" [1012] 



Yarnell gives the following values of K in D'Aubuisson's bridge pier 

 formula, for Class 3 flow between standard bridge piers. 



Square noses and tails 0.95 

 Semicircular noses and tails 



Parallel with current 1.03 



10-degree angle . 93 



20-degree angle 0.88 



90-degree triangular noses and tails 0.98 



Twin-cylinder piers, with or without diaphragms 0.99 



Lens-shaped noses and tails 0.95 



The value of K decreased from 3 to 5 per cent for longer piers, with 

 lengths up to thirteen times the width. The addition of batter to the 

 ends of the piers slightly increased their hydraulic efficiency, that is, 

 raised the value of K. 



The following coefficients, based on Yarnell's tests, are recommended 

 for use in computing the backwater due to pile trestles : 



The amount of channel contraction is to be taken as the average 

 diameter of the piles plus the thickness of the sway bracing. When the 

 bents are at an angle with the current, the channel contraction is to be 

 taken as the same as for the same bent placed parallel with the current. 

 The effect of the angle is included in the coefficient. 



