﻿954 Mr. F. M. Lidstone on the Full Effect of the 



the coefficient of the K.E. term being taken as unity. This 

 equation is true provided the head h is constant ; but unless 

 some compensating mechanical contrivance is used, such as 

 that adopted by Hyde (Proc. Roy. Soc. A, xcvii. 1920), this 

 condition is never absolutely realized in practice, since no 

 matter how the pressure is applied or maintained, as soon as 

 flow starts, there is a change in the hydrostatic head and the 

 total head becomes at once a variable. 



"We have then, by making dt depend upon dh, first to 

 integrate the whole expression with respect to h over the 

 interval H — F. 



we nave ?? = 



iri A qp . , Vp 



WT :=A and ^l 



Ah(R-F)dt Bdh 



Putting 4^ = A and ^ = B, 



dh (R-F)dt 



dt 



-.2 



■ rfWAB v /A+ i Jg 



2AA(H-Fj"- A(H-F)/i 



The plus sign being obviously the only one permissible, we 



v 2 

 get, writing C for j^-g, 



J^-2A(H-F)J P x + VA(H-F)J F ~" * **' 

 which, after a little manipulation, gives finally 



V = 



TrrVp^(H-F) 



8T^lo g ^ C tH-VCXVC + y+ VC-) + ^ 1+ H_^ i+ ^ 



.... (1) 

 Now, since C contains rj, to evaluate r\ from this expression 

 would lead to a number of very un wieldly power series. 

 However, it will be seen that must be large in comparison 

 with H or F ; hence a small change in C will not greatly 

 affect the result. As a first approximation, then, we can take 

 C as equal to 



7rVy 2 (H-F) 2 

 4V»(log.H/F)*" 



Calling this Ci, we get a value for tj which we will call rji* 

 We can now get a closer value for C, namely ~~ — ^ or C 2 . 



or 



