Desai and Lieber 



basis of the criteria of (a) mathematical simplification and (b) experimental jus- 

 tification on the final results of the analysis. 



I 

 The no-slip condition in the case of the flow under consideration is ex- 

 pressed as a kinematic condition 



v(a,^,t) = (1.10b) 



for all fluid elements on the boundary of the cylinder. 



The two conditions of Eqs. (1.10a) and (1,10b) together represent the con- 

 tinuity of the velocity vector at the interface of the two media, viz., the fluid and 

 the solid cylinder. It should be noted that the conditions on u and are ob- 

 tained through the ideas of impermeability and no- slip and that the idea of ri- 

 gidity is involved only as the particular form these conditions have taken here. 

 The continuity of the velocity vector at a boundary separating the two media 

 does not require the boundary to be rigid. 



Condition at Infinity and the Idea of Physically Infinite Distance 



Generally, this condition for the motion of a fluid around an obstacle is ex- 

 pressed by the statement that the velocity at infinity is uniform in direction and 

 has a magnitude which is either constant or a function of time alone. Such a 

 statement, in particular for a sudden relative motion which brings about a con- 

 stant relative velocity from rest between a circular cylinder and an infinite 

 mass of fluid, is expressed mathematically in either of the following two ways: 



(i) At ? = CO, 



u (co,0, t) = t = 



= -u^ cos e t > 



V(00,§, t) = t :: 



= +u^ sin 5 t > 



p(oo,0,t) = P(j, , a constant. 

 (ii) As r — ► CO , 



u 0,e,t) = t = 



— -G^ COS 5 t > 



v(r,§, t) = t = 



t > 



p(r,i9,t) — > Poo , a constant, 

 508 



