Long Waves in Canals and Standing Waves in Closed Basins 159 

 This is a standing wave with a damping coefficient 



y = (£ 2 -*? 2 )^ 



and the period 



T r 



Till 2 



£r)v 1^r\\ a 



(VI. 46) 



when T is the period according to Merian's equation. 



The value of a is determined with (VI. 42) for a given basin by its di- 

 mensions and the magnitude of the frictional constants; Table 20 gives the 

 corresponding value of 2£// which can also be taken from a graph. 



Table 20. Computation of the period of the free 



oscillation in a rectangular trough, taking 



into account the effect of friction 



Equation (VI.46) for the period of the free oscillating system has lost 

 the simple form of Merian's equation and it is only from numerical examples 

 that we can derive how much the friction increases the period. According 

 to (VI. 42) a becomes rapidly very small with increasing depth, and 2£r\ Va 

 tends to unity, so that T r will differ only little from T, i.e. the deeper the 



