Drag Reduction by Suction 



At y = 0. U = Uj. 4^= C-^-H 



From the above it can be found that: 



12 + A 



6 + /3 



6/i - 3 A 



6 + /3 



■12- 8/3' + 3 A 6+ 3/3 - A 



d = 



6 + /3 



6 + /3 



(6) 



where 



A= i^i^ 

 J^ dx 



The displacement thickness s* can be expressed as: 



1 _ a_ _b c _ d 

 2 ~ 3 ' 4 5 



v/hile the momentum thickness is given by: 



(7) 



a^ ab (2 ac+b^) ( ad + be ) (2bd+c^) , cd df 

 32 5 3 7 +49 



(8) 



The shape parameter K can be calculated from 



K = - ^ 2b. 



s2 



(9) 



For an axi- symmetric body with suction, the Karman momentum integral 

 equation is written as 



de 



du, 



dr 



U, -r- + (29 + S ) U, — ;— + U/ :r + VU, = 



1 dx ^ ^ 1 dx 1 r dx ° pu ^ 



(10) 



r ^ is the body radius at any x . 



In the above all velocities are dimensionless with respect to the free- stream 

 velocity U^ and all distances with respect to a reference distance. The dimen- 

 sionless shearing stress r /pU ^ can be determined from 



pu. 



(11) 



1011 



