﻿778 Mr. J. H. C. Searle on the 



In the diagram o£ § 2 consider the mass of fluid bounded by 

 the contour AA'B'BA. 



Let P = resultant horizontal pressure on section AB, 

 P'= „ „ » ,. » A ' B '> 



#>= „ „ „ ., £ace o£ weir > 



M = total momentum crossing AB per second, 

 M'= „ „ „ A'B' „ 



Then, rate of change of horizontal momentum of fluid 

 within contour = rate at which horizontal momentum flows in 

 over boundary together with total surface pressure on 

 contour resolved horizontally, since the horizontal body 

 forces vanish. 

 Hence, 



= < ^ + P_P' + M-M'-7r(/i + d-/O. 

 ... ^= 7r (/ l + d-/ l ') + P , -P + M'-M, 



Jo «-■ d 



But, udz = u'dz' and u' = s/iy? + U' 2 - U 2 ) . 

 Hence, C" ^ = r^ + ^.u^ 



Jo Jd 



... ^=^+^(A'>-^+r + ^v(w'+u' j -iP)-ii}^. . (io) 



Expressing this in terms of the quantities given in (1) we 

 find 



*=^+ipa[m^-i)+J o 1 [^ 



.... (11) 



When -37 is determined from (5) ^ is found from (9). 

 It will be noticed that 



as might otherwise be expected. 



§ 5. The case of irrotational motion, although probably fa r 

 removed from Nature, has the prior claim to attention on 

 account of its simplicity and historical interest. In this 

 case we have 



m. = const. = TJ. 



Hence, by (5), <K?) = 1. 



