Lieber and Yajnik 



1 , 1 



(27) 



J'i} , C u! = i^V^u! , ;,... (26) 



and ■i.'f-' '■ ^^' ."^n ■.-.:■■. ^j.*,, ..i^vi -nV?- .:J,--:i'^ ?in:' 



w'(0 „„+u' ) - (<P +u' ) w' = . (30) 



CONCLUSIONS ' J ■ " ' 



1. When a flow is symmetrical about a plane, the pressure is also 

 symmetrical. 



2. When a flow is antisymmetrical about a plane, the antisymmetrical 

 part of the pressure is harmonic. Also, such a flow of homogeneous incom- 

 pressible Newtonian fluid can be written as 



U; = . + U- 



where 



and 





3. Antisymmetrical solutions are available and are of physical interest. 

 More than ten such solutions have been noted. There are steady and nonsteady, 

 two-dimensional as well as three-dimensional flows in this category. Bound 

 vortices behind a cylinder come close to enjoying this property. 



REFERENCES 



1. Lieber, P., and Wan, K.S., "A Principle of Minimum Dissipation for Real 

 Fluids," Office of Scientific Research, USAFOSR, report TN57-477, p. 43 (1957) 



2. Lieber, P., and Wan, K.S., "A Minimum Dissipation Principle for Real 

 Fluids," Int. Cong. Mech., Proc. DC, 1957 (amplified in Rensselaer Poly- 

 technic Institute and USAF Office of Scientific Research Report TN 

 57-477, AD 136 469, Aug. 1957) (See Ref. 1) 



690 



