494
a
x
b
Appendix C Useful Theoretical Approaches and Formulas
z
z
f---------'\
, ,
"
,
,
,
, ,
- ,
- : P(r,f'J,z)
,
-" ,
,
"
,
O~ ____ ~ __ ~':~ __________ ~
9'
,
'
y
'~ -- - - - - - - - - - P/r, 9, 0)
y
o z =z
x
Fig. C.5: Definition of cylindrical coordinate system: a cylindrical coordinates of
point P, b radial and tangential velocities
Some applications of the velocity potential, cp, or stream function, 1/J, require a
formulation of these functions in a coordinate system other than the Cartesian
system Oxyz, namely the cylindrical coordinate system, Or(), and the spherical
coordinate system, Or()'P. Below, the basic formulas for irrotational flow in the
cylindrical coordinate system are listed without proof (see Fig. C.S for definition
of coordinates):
x = r cos () , y = r sin () , z = z,
U()
u cos () + v sin () }
:u sin () + v cos () ,
(C.7S)
(C.76)