18
a
x
b
z
o
r-------2 Water at Rest and in Motion
, W - - - - - - - - - - - - - - - - - ~ ' "
,
,
V'
,
, ,
_________________ _ ' .:.V '"
U
y
N (0°)
p
W (270°) -E------~----~ E (90°)
S (180°)
Fig. 2.1: Coordinates systems: a Cartesian, b geographic
The vector of velocity of fluid particles, U, in Fig. 2.1 is inclined at an angle
'P from the vertical axis and its projection on a plane 0, x, y forms angle () with
the x axis. By the convention, positive angle () increases in a counterclockwise
direction, relative to the x axis, the reverse of the geographic convention. The
components of vector U along x, y and z axes are u, v and w, respectively.
Thus, U = i1 = (u, v, w). A full definition of vector notations used in this book
is given in Appendix C.l.
In instances where the Cartesian system is inappropriate, the conventional
geographic system is used (Fig. 2.1b). Also for the specific applications it
is useful to use the polar and spherical coordinate systems rather than the
Cartesian one. An example of such application is given in Appendix C.