LARGE ORIFICES 129 



while experimental evidence as to the precise nature 01 the variation is 

 wanting. The best way out of the difficulty appears to be to write 



// j (H' + d'ft - 



Os^ I 



= C v - 



b 



where H = depth of top of orifice below the free surface. This then 

 gives us 



Q = | C b V~27 | (H + d)* - fltj. (2) 



The reason for this substitution is that the value of C in this formula 

 has been determined with some accuracy for various types of orifice and 

 for different heads. 



Formula (2) is that obtained by the inaccurate process of reasoning 

 outlined at the beginning of this article, for, assuming that the flow 

 through any element b B y of the orifice is the same as that through the 



corresponding element of the vena contracta of area b f -j . S y, and that 



this flow is "therefore given layCbSyVZgy, where C has the same 

 value for each element, and therefore for the whole area, we have 



Q = Cb 



Comparing this with the simple formula 



lined by considering the head over the section as sensibly equal to 

 it at its centroid, we see that the two values of Q are in the ratio 



3 ? 



_ (H + d) 2 - H^ For yalues of H greater than d the difference 



a 



amounts to less than 1*0 per cent., so that for all larger values of H, the 

 simpler formula is to be preferred. 



The velocity of approach may be taken into account by increasing the 

 head by an amount h as explained on p. 120, thus making the effective 

 head = H + h. 



Then Q-jCbV^g['(H + h + d$-(H+ fc)*] (2) 



H.A, K 



