Flow from a Disturbed Area. 

 If <p is large arid negative, 



7} — > e 2 siiH , 



151 



> — e 



cos -5- , 



write |0| = ; 



= esin f/3e 2 cos-^ ) cosh | /3^ 2 sin-^-). 



(19) 



Hence there is a tendency to steadiness when -^r— >0 or 7r, 

 i. «?. near the centre of: the jet and near its bounding surface. 



Equation (19) shows, however, that the stream-lines begin 

 to curl back on themselves, and to develop double points, as 

 soon as <f> assumes even moderately large values. 



The domain B will be close to the mouth of the pipe, and 

 vortices will be formed there or else the motion become 

 sinuous (Rayleigh, ' Sound,' vol. ii. pp. 106-108) as in the 

 case of a sensitive jet. 



When \cf)\ is large, and passes through values for which 

 sin/3f=0, the angle changes rapidly for small changes 

 in |0|. 



The velocity q = . e -ccoBp£smhpii w j]} remain practically 

 -constant so that in this neighbourhood the stream-line is 

 circular. 



Hence there will be a tendency for circular eddies to 

 form 



The steadying effect of the boundary is very noticeable, 



Fig. 5 shows the shape of the bounding stream-line near 

 the mouth of the pipe. 



Kar. 5. 



As one of the constants c, j3 is at our disposal if may 

 taken a function of the time. 



2 12 



be 



