NOTCHES AND WEIRS 



137 



EXAMPLE. 

 In two triangular notches having the same value of 6, we have two 



similar and similarly situated orifices, so that l = ( - - ) 2 . 



(^2 \ -fia / 



ART. 53. FLOW OVER NOTCHES AND WEIRS. 



Where the free surface on the supply side is below the level of the 

 upper edge of an orifice, this is termed a notch, and, if of large dimen- 

 sions, a weir. 



The theoretical treatment for flow over such notches follows exactly 

 similar lines to that for flow 

 through large orifices, and is 

 subject to the same erroneous 

 assumptions. The errors in- 

 volved in assuming that the 

 velocity of efflux perpendicular 

 to the plane of the notch, at the 

 notch, at any depth h, is propor- 

 tional to V 2 g h, is indicated in 

 Fig. 74, where the horizontal 

 ordinates of the parabola m n q 

 show the theoretical velocity at 

 any depth below the free surface 

 of the still water at S, while the 

 ordinates of the curve a n c b 

 denote the actual velocities in 



this direction in the plane of the notch. The coefficient of discharge will 

 then be equal to the ratio of the volumes represented in elevation by the 

 shaded area a n c b and the area m n q b. 



The fact that owing to the curvature of the stream lines the pressure 

 over a cross section is nowhere uniform, renders a rigorous treatment 

 impossible, and the next best method is to consider the state of affairs in 

 the plane of the notch. 



An examination of the contour of the escaping stream shows that in 

 the plane of the notch its upper surface is lower than the free surface 

 at a point a short distance up-stream where the motion is steady. 



This fall from s to a (Fig. 74) is essential if the surface filaments are to 

 have the required velocity of efflux at the notch, and since their motion 

 is approximately perpendicular to the plane of the orifice and is unaffected 



FIG. 74. 



