528 



XL HYDRODYNAMICS. 



flowing as in a) Fig. 166, the water flows as in b), the flow being 

 discontinuous at the dotted line. In actual fluids such surfaces of 

 discontinuity give rise to vortex motion, so that we see eddies formed 

 at projecting corners. 



a) 



The function 



Fig. 166. 



with 



= logr 4- 



gives us radial stream lines forming a uniplanar squirt, while 



y> = co, ijf = log r 



Fig. 167. 



and for a free surface, p = 0, 

 133) C - 



gives us flow 

 in circles with 

 a velocity 



dcp 



The velocity at the center is 

 infinite. This flow is exactly 

 what we found in 195 to be 

 produced by a vortex filament 

 at the center. 



If the fluid is under the 

 influence of gravity, we have 



42) p = const. gqz 



