138 



HYDKAULICS AND ITS APPLICATIONS 



save by the resistance of the air, their velocity may be taken as sensibly 

 equal to V 2 g (a in] = V 2 g H f (Fig. 75). 



In general H r is approximately equal to *14 H, where H = height 

 of water measured to still water level, above the crest of the notch or 

 weir, so that (H H'} = depth of water at crest in feet. 



ART. 54. THEORETICAL FORMULAE FOR FLOW OVER WEIRS. 



Rectangular Weirs (Fig. 75). Let b = length of weir in feet. 



Consider the flow 

 across any element of 

 h || \ area b B x, in the plane 



^=^==J^ _|| \j r of the weir, at a depth 



x below the still water 

 surface of the supply. 



The volume passing 

 this element per second 



cub. ft. per sec. 



FlG 75 Integrating this ex- 



pression and giving x 



the upper and lower limits H and H', and assuming that C' has the same 



value for each element, we have 



Q = C' b 



- H cub. ft. per sec. 



(1) 



The value of this coefficient C' has not been experimentally determined, 

 so that the formula in its present form cannot be applied to determine 

 the discharge in any practical case. If, however, we write 



C' tf - 



=C 



the formula becomes 



Q = ? C b V% g H* cub. ft. per sec. 



o 



(2) 



and the value of this coefficient is known with fair accuracy for different 

 values of H. 



Formula (2) may be deduced with less reason by assuming the depth 

 of water in the plane of the notch to be H, i.e., neglecting the fall from 

 still water level, and assuming that the velocity of the surface filaments 

 is zero, and therefore by integrating the expression SQ = CbS 



