[farmer] determination OF COEFFICIENT OF DISCHARGE 



5S 



The balance is provided with long screws, on which large cast ii'on 

 weights can be screwed, \x]) or down, in order to raise or lower its centre 

 of gravity, thus making it more or less sensitive. The centre of gravity 

 of the balance is considerably altered, as the attachments holding the 

 vane are raised or lowered to suit the requirements of an experiment. 



It is necessar}^ to consider how the force of impact is balanced by a 

 dead weight in one of the pans. 



A D â 



W 





Diagram of Impact Balance. 



Supi^ose the water issues from the orifice of area S with theoretical 

 velocity f, and coefficients of velocity and contraction (?„, c^. When it 

 reaches the centre of the bucket C it will be inclined at an angle a, 

 and will be moving with velocity V say, whose horizontal component 

 F cos a — f.c,.. 



The theoretical force of imjjact will be 



MV 



—-(1 _(.us qj) 



where qj is the angle through which the water is turned by the shajje of 

 the vane. 



The mass of water per unit time is 



pc,*S'c,i7, 

 .'. the force of impact is 



pCcSc,vc,v 



— TTTiT (1 — cos œ). 



(/ cos a' ^ ^^ 



The actual force will probably be some fraction t\ of this. 



c,.c,'-'pSf'- , 



.. 1 = C; (1 — cos qj). . 



<j cos a ^ ^^ 



The moment of this force about the knife-edge at D will be — 

 I . CD = I . CI) . cos (X 



c c c '^pSv' 



