r-1 



where A 



Equation 9 is satisfied when 



,12b ^zm 



h '=S C0S T^ (10 > 



and 



where 



h z -Hcosf*?p-+e) (11) 



A V41T 2 C 2 



I4ir z C 



and 



tanc= |2L (13) 



These expressions given by equations 10 and 11 show that the fluctuations of 

 the water surfaces in the two reservoirs are sinusoidal with a phase differ- 

 ence £. 



Substituting the value of h]_ s from equation 10 in equation 7 it is 

 seen that 



?Tft 



q=Q m sin£p- (u) 



which was the first assumption„ 



Since the results of the test cases show that the values computed on the 

 first assumption deviated slightly from the actual gaged data, it is reason- 

 able to assume as a second assumption that the introduction of a third harmonic 

 into the basic equation would produce more accurate results „ 



FIRST HARMONIC 



K 2 



THIRD HARMONIC 



FIGURE 3 



Hence 



q=Kl sin^l + K 2 sin^- (15) 



T 



Since r% 



V 4 <"» (16) 



Substituting the value of q from equation 15 and integrating 



*{"♦«* 



(17) 



19 



