SUDDEN CHANGE OF SECTION 88 



The assumption is commonly made that the pressure p' over the face 

 EE is uniform, and is sensibly equal to p. Although the actual dis- 

 tribution and magnitude of this pressure probably vary with the ratio of 

 the areas and relative position of the two branches, and with the velocity, 

 we have not sufficient experimental data to frame any definite law con- 

 necting the two. The above assumption, however, appears to be fairly 

 well justified by the results of such experiments as are to hand, and 

 making use of this we have, on combining equations (1) and (2) 



IV 



( P -P)A = {AV-av*} (3) 



Also for continuity of flow A V = a v .'. v = 



V. (4) 



If now H' = loss of head due to shock at the enlargement, we 

 have 



V V* P V* 



F + 2-, = F + 2^ + H ' < 5 > 



p _ p V 2 A* F 2 



^ _ p 



Substituting for * from (4) we get 



(*) 



Writing m for , relations (7) and (8) become : 



H' = (- I? (10) 



1,V- m j (11) 



Recent experiments by the author 1 indicate that the percentage loss 

 increases slightly with the ratio of enlargement, and in pipes with the 

 same ratio of enlargement is greater the smaller the pipe. 



Denoting the ratio of enlargement by m, and the smaller diameter by 

 rf, the loss at a sudden enlargement for values of m between 2 and 12, 



"Trans. Roy. Soc. Edinburgh," vol. 48, 1911, p. 97. 



Q 2 



