Long Waves in Canals and Standing Waves in Closed Basins 193 



Possibly an error was made in applying the energy principle, inasmuch as 

 the energy equation used is not satisfied at all times. We can distinguish three 

 parts in a Haff as shown in Fig. 82: sections 1 and 2, situated on either side 



Zq, b, h, ( 



L_"-l__ 



u 



Fig. 82. Computation of the free period of a sea partially closed. 



of the opening are considered as separate areas of oscillation with the impe- 

 dances Z x and Z 2 , the outlet opening has the impedance Z q . During the oscilla- 

 tions, water from 1 will flow both into 2 and through the lateral outlet. 2 and 3, 

 therefore, must be regarded as connected "in parallel" to each other and 

 these two connected "in series" to 1. Consequently, the condition of the 

 natural frequency is 



^-"X ^2 



= 



With the corresponding expressions for Z, we obtain, assuming Z x and Z 2 

 are basins closed on one side: 



•Si 4. a k , $2 * <*h a 



— tan — - + — tan — - = - , 



C\ C]_ C-± C% & 



if a = bh/l (dimensions of the outlet). In case the outlet opening is moved 

 towards the far end of the lake, we get / 2 = and the equation for the period 



a 



a ' 



S x al x 

 — tan— - 

 c x c x 



This relations shows that the period is shortened compared to the period 

 of the fully closed basin. 



In applying this to the Frisches Haff, the section 1 is the narrow south- 

 western part from the mouth of the Nogat to the deep of Pillau, section 2 the 

 remaining part of the Haff to the mouth of the Pregel including the Fisch- 

 hauser Wiek, and section 3 the Pillauer Seetief. The application of Defant's 

 method gave for 1 and 2 the partial periods 6-63 and 3 11 h and with the 

 numerical values: 



Length 

 Sect. 3: 204km 



The above-mentioned equation gives as the period of the free oscillation 

 of the entire Haff basin 8 05 h, which is in agremeent with the observed 



13 



