BROAD-CRESTED WEIRS 



159 



the fact that Hz is in a continual state of change owing to the undulatory 

 motion of the surface, renders the submerged weir very unsatisfactory as 

 a means of measuring the flow of water. 



The above discussion of submerged weir flow is due to Dubnat, and is 

 admittedly unsatisfactory from a scientific point of view. The difficulties 

 in the way of a more rational investigation of the problem based on the 



FIG. 87. Surface Curves in Neighbourhood of Submerged Weirs. 



variations of pressure and velocity in the stream are, however, extremely 

 great, as will be realised from a study of Fig. 87. 



These curves show the profile of the stream as measured by the author 

 in the neighbourhood of such a weir, under different heads. 



Bazin gives the empirical formula 



Q = C { 



l'05 



-21 2 



where C is the coefficient in the formula 



Q = Cb *flTg - H^ c.f.s. 



for flow over a similar weir freely discharging under the head HI, and 

 where P is the depth of the approach channel below the weir crest. 



ART. 56. BROAD-CRESTED WEIRS. 



Experiments by Bazin indicate that in general the nappe will clear the 

 crest of a sharp-edged weir if this is of less width than '5 H. For widths 

 between *5 H and '66 H the condition is unstable, and any variation in 

 the flow will cause the nappe to cling or to break free, with a correspond- 

 ing variation in the discharge, while for widths greater than this the 

 nappe clings to the crest in every case. 



More recent experiments by G. S. Williams indicate that the ratio of 



