326 



HYDRAULICS AND ITS APPLICATIONS 



so that if by any means such as drawing off a considerable amount of 

 water suddenly by opening a lock gate, the velocity can be made equal 

 to V g h, a wave with vertical crest will be produced. 



ART. 91. CHANGE OF LEVEL IN A STREAM PRODUCED BY BRIDGE, 



PIERS, ETC. 



Where a series of piers are placed across the bed of a stream, the effect 



is to raise the up-stream level 

 exactly as if a dam were placed 

 in the stream, and the form of 

 the surface curve will depend on 

 whether the stream satisfies the 

 conditions of Case 1 (c) or 2 (c) 

 (pp. 316 and 317). 



The height will be a maximum 

 at the up-stream end of the pier. 

 On arriving at the contracted 

 section of the stream, the velocity 

 will be increased, the increase in 

 kinetic energy necessitating a 

 corresponding loss of potential 

 energy, and the depth is dimin- 



FIG. 143. 



ished. On again arriving at the 

 open channel the velocity di- 

 minishes and the depth increases 

 (Fig. 143). 

 Neglecting losses by friction between the sections (1) and (2), if bi and 



/> 2 are the effective breadths and hi, // 2 the depths at these points, we 



have 



and 



assuming the kinetic energy to be that given by ~ and J^- where 



t? 2 are the mean velocities at the two sections, an assumption which 

 within narrow limits is j ustified by experiment. 



.-. i? 2 * = vi z -+ 2 g x, where x = h l h 2 . 



If the discharge through the contracted area at (2) is given by c b% h% v%, 

 we have 



v = Q 



C 6 a fca 



