354 HYDRAULICS 



must be set carefully at right angles to the top. Means for 

 admitting air under the falling sheet of water must be made; 

 otherwise, there will be formed a partial vacuum that tends to 

 increase the discharge. The sides of a weir without end con- 

 tractions should be smooth and straight and should project 

 a slight distance beyond the crest. 



Standard Dimensions for Weirs. The distance from the 

 crest of the weir to the bottom of the feeding canal or reser- 

 voir should be at least three times the head H, Fig. 1 (c) 

 -and (d) ; and, with a weir having end contractions, the distance 

 from the vertical edges to the sides of the canal should also 

 be at least three times the head. The water must approach 

 the weir quietly and with little velocity; theoretically, it should 

 have no velocity. It is often necessary to place one or more 

 sets of baffle boards or planks across the stream at right angles 

 to the flow, and at varying depths from the surface, to reduce 

 the velocity of the water as it approaches the weir. 



Theoretical and Actual Discharge of Weirs. The theoretical 

 discharge of a weir is 



Q = 5.347 bH$ 



in which b is the length of the crest and H is the effective depth 

 producing the discharge. When the velocity of approach is 

 inappreciable, the effective depth is the distance from the crest 

 of the weir to the surface of the water at a point up-stream 

 beyond the curve assumed by the flowing water as it approaches 

 the weir; but, when the velocity of approach v is considerable, 



v z Q = 5.347 & (H+ A)i 



in which h = . 



The actual discharge of weirs is, when the velocity of approach 

 is not considered, 



and when the velocity of approach is considered 

 = 3.33 U>- H) (# + /Ot-Ai 



In these formulas n denotes the number of end contractions; 

 hence, for a weir with two end contractions, n = 2; for a weir 



