Flow from a Disturbed Area, 445 



Hence each stream-line -*^<0 for which | ^r | is small will 

 behave as in fig. 2. 



Fig. 2 has been plotted for the values -v/r — -1, 6 = 1'2, 

 c-l/30,d='5. l<0<l-7. 



It shows that the disturbed area may be expected to 

 embrace part of CD' and to come close up to the plate.. 



The dotted lines show on which side of ty— —'la stream- 

 line -\\r< —'1 will lie. 



Hence equation (1) will represent the motion of a fluid 

 past a plate except inside the area B corresponding to B . 



In this area a very disturbed motion is to be expected. 



There may, however, be other places at which a slight 

 amount of viscosity will cause vortices to form which in 

 appearance may be regular in contrast with the motion 

 inside the area corresponding to B . 



This will be seen in the next paragraph. 



(d) Choice of the constants b, c } and d. 



The ratio CB : C'B (fig. 1) gives one relation between them. 



In order to give results which may be expected to have 



some resemblance to actual conditions, the velocity at the 



1 cd 



corner B, viz. qo = j e b " must not be allowed to become small 



compared with q m =e~ c . 



Along tJt = and <f><0, j3= V^0 ? 



n L £ . 2c(3b($ 2 + d) . , 



d_6__ b 2cb(3/3 2 + d) 8cb{3 2 (/3 2 + d) 



d/3~ 6 2 + # 2 + (6 2 + /3 2 ) 2 (b' z + J3 2 ) 3 " 



For a turning value 



(3\l-2c) + 2/3 2 (b 2 + 2cb 2 -3cd) + b i + 2cdP = 0. {\2) 



Now since b > 1 and < d < 1 the coefficient of ft' 2 is > 0. 



Hence if 2c < 1 there will be no positive root for j3 2 , and so 

 no turning value for 6. 



If 2c>l 6 will have one maximum value somewhere 

 between A and B, 



This single maximum corresponds to the right-ano*led 

 bend in the electrical solution, and the above equations may 

 be looked upon as giving a motion intermediate between 

 the electrical case and the discontinuous stream-line. The 

 dotted curve in fig. 1 illustrates this point of view. 



