Long Waves in Canals and Standing Waves in Closed Basins 181 



(4) For a basin connected with the open ocean by a narrow opening we 

 obtain, provided the dimensions of the basin are of equal magnitude in all 

 directions, 



_ igol ioc 2 



In this case, the water level in the whole basin rises and falls simultaneously 

 and higher forms of oscillation are not easily produced. The impedance is 

 composed by two parts: one given by (VI. 95), which is that of the flow-off 



igc 2 



(VI. 96) 



opening, and secondly that of the closed water volume Z 



Qa 



(VI. 97); 



which results from (VI. 93), if al/c is small, so that cot al/c can be replaced 



by c/al. 



(c) Free Oscillations of Combination of Basins 



In dealing with these oscillatory systems it is to be noticed that the impe- 

 dance of each part is added in the same manner as the resistances of electrical 

 circuits. A distinction should here be made as to whether the basins are con- 

 nected "in parallel" or in "series". The following example will illustrate 

 this. Figure 76 shows the oscillatory system of a ramified closed canal: Canal I 



I t> t , h, , (, 



Fig. 76. Closed canal which branches out. 



forks into the canals II and III. Here the canals II and III with their impedan- 

 ces Z 2 and Z 3 are placed "parallel" behind I with the impedance Z x . If P is 

 the total impedance of II and III, then we have: 



1 = 1+1 or J>=-?S_ 



(VI.97a) 



On the contrary, if I and (II and III) are connected in series, tl»e total 

 impedance of the entire system is 



Z = Z 1 ^P=^Z 1 -h 



Z2Z3 



Z0+Z3 



(VI.976) 



