Appendix C Useful Theoretical Approaches and Formulas
495
u
Fig. C.6: Flow around horizontal circular cylinder
and
(C.77)
apw 1 a
1 a
a
- + -- (p ru ) + -- (p un) + -(p U ) = 0
at r ar w r r ao W U a z W z ,
(C.7S)
(C.79)
where U r , Ufl and U z are the components of velocity along r, 0 and z cylindrical coordinates. Equations (C.7S) and (C.79) are the mass conservation and
Laplace equations, respectively, for the cylindrical coordinate system.
Let us now demonstrate an application of cylindrical coordinates to a flow
of perfect fluid around a horizontal, infinitely long, solid cylinder, as shown in
Fig. C.6. The stream function, 'lj;, and velocity potential function, ¢, for flow
around a cylinder are (Lamb, 1932):
'lj;(r, 0) = U (r _ :2) sin 0,
(C.SO)
and
¢(r,O) = U (r + :2) cosO.
(C.S1)