LARGE ORIFICES 135 



the top of the orifice, with free discharge over a depth di, and 

 fcubmerged over the remainder d% of its depth we have 



2 - ( - ) 



Discharge over depth di = Qi = Cib V 2 g \ (H + di) 2 H 2 ! 



i 



Total discharge Q = Q 1 -\-Q z = bV%g 



If Ci = C 2 = C we get 



If h = the head equivalent to the velocity of approach, the formula 

 becomes 



(H + d, + h)* (H +d, + h) + ck 



The difficulty in exactly estimating di and d^ and the undulatory 

 motion of the surface which is usually found in a partially submerged 

 orifice, renders this a most unsatisfactory method of estimating the flow 

 of a stream. 



The coefficients so far given only apply where the jet is wholly sub- 

 merged or where discharge takes place freely into the air. If the issuing 

 stream, instead of springing clear of the orifice adheres to its face, the 

 formation of a true vena contracta is prevented and we have an abnormal 

 increase in C. Thus if the jet is discharging freely into air, and if the 

 level on the discharge side is allowed .to rise, at some point before the 

 level reaches that of the notch sill the discharge ceases to be free and a 

 sudden increase in the value, of C results. As d% increases, C resumes 

 its normal value. 



From a scientific point of view the above treatment, due to Dubuat, is 

 not satisfactory. A rational treatment would require to take into 

 account the distribution of pressures and velocities in the issuing stream, 

 and from the nature of the case would lead to results too cumbersome for 

 practical application. 



ART. 52. LAW OF COMPARISON FOR ORIFICES. 



Similar orifices are such as may be represented by the same drawing 

 to different scales. If similarly situated, the free water surface will be 

 represented by the same line, whatever the scale of the drawing. 



