288 Fluid Discharges as affected by Resistance to Flow. 

 can be shown that curves such as those shown in fio\ 1 are 



o 



an immediate consequence of equation (3). 



By including the resistance head R in equation (1) we get 



v 2 

 h=^(jn 2 -l) + av + bv 2 (4) 



The discharge coefficient C is given by 



G =-rw (5) 



Solving (I) for v, the equation for C then becomes 



where M and N are constants. 



Assuming N = '98 and — =-'02 when A = 256 feet of 



water, the higher graph of fig. 1 is the curve obtained. 



M 

 Assuming, however, . = + '02, the lower curve is 



obtained. ' l 



Resistance to fluid motion, therefore, of the kind denoted 

 generally by equation (3), may give discharges greater than 

 would be obtained in non-viscous flow. Apart from any 

 practical value, this fact is interesting enough in itself. It 

 implies, of course, that in cases where ll a" is negative, 

 regeneration of energy must be taking place. It does not 

 appear that such energy regeneration (or rather recupera- 

 tion) is impossible. The conditions necessary may be 

 present in certain cases, which in the present state of 

 knowledge are not well defined. 



The coincidence in the form of the curves of fig. 1 with 

 those experimentally obtained is considered too close to be 

 accidental, and it is for this reason that the writer has 

 ventured to submit the results (paradoxical though they 

 appear) of the foregoing analysis. The assumption of a 

 resistance function of the form Ra v n does not give similar 

 results. 



