Flow from a Disturbed Area. 



443 



Therefore no stream-line outside the plate can cut itself 

 and the domain B does not extend into the upper half 

 2£>-plane. 



At infinity the fluid is flowing at right angles to the plate 

 with velocity e~ c . 



(c) How behind the plate, i.e. \jr<0. 



If (f> negative and , -, small, 



j3 a= v| <*> I? V — ^ 1— </> approximately, 







I 2 //32_l_ /^2 approximately if </> be large. 



(/3 2 + 6 2 ) 2 



The angular change over this part of a stream-line is 

 <7r/2 and there will be no tendency for double points 

 to appear. 



As (/> decreases the term 







(V-d 



*»•♦&) 



may become large. 



This can be the case when both ft and b-{- ~~ are small, 



i. e. when | s]r small and <f> = b 2 approximately. 



The difference between the tan -1 terms is always <^ir 

 except along i/r = where it is equal to it. 



Hence, if c be small, the domain corresponding to B 

 lies close to CD'. 



Again, the term e {bW '^ 



r ^-^){(6 + «) 2 -/3 2 } +2/3(6 + ^^ 1 



" p L W+") 2 +£ 2 } 2 -I 



+ exp.zc^ {(ft + ^ + W J 



= exp. (A + iJB). 



When yjr<0, a<0 and j3>0. 



When <p>d and (7> + a) 2 >/S 2 , B is <0, and if ^ be small 

 enough, A is >0. 



As <f> increases b + a — >0, and B — ->0, rises to a maximum 

 and then finallv tends to zero. 



