TRIANGULAR NOTCHES 



151 



Except with a freely discharging nappe the state of aftairs is very 

 unstable. Any pulsation in the stream flow, any floating body piercing 

 the nappe and allowing admission of air, or even a sudden gust of wind, 

 blowing the nappe into contact with the weir face may totally alter 

 the conditions of flow, and no attempt should be made to use a weir, 

 except when discharging freely, as a measuring device. 



For steep down-stream slopes where the nappe tends to break free from 

 the apron, the discharge is increased by the partial vacuum formed beneath 

 the nappe. As this slope becomes flatter the conditions approach those 

 for a horizontal crest, while for slopes of 3 to 1 the discharge is approxi- 

 mately the same as for a thin-crested, freely discharging weir. 



ART. 54fc. TRIANGULAR NOTCH. 



Let H be the head of water above the vertex P of the notch (Fig. 81), 

 H being measured to the 

 level of the still water sur- 

 face behind the notch. Let 

 B = breadth of notch at 

 height H. 



Then assuming the velocity 

 of efflux at any depth x to 

 be given by V 2 g x, a for- 

 mula for the discharge can 

 be deduced as for the rect- FIG. 81. 



angular notch. 



Thus the area of an element of the area at a depth x and of width 8 x 



x. 



Flow over this element 



(1) 



= 



(2) 



