Page 125 - Aerodynamics for Engineering Students

108 Aerodynamics for Engineering Students
++w
A
Y 4
( Q(x +8x,y+8yI

0

Fig. 3.4

Thus, equating terms

and

(b) In polar coordinates Let a point P(r, 0) be on an equipotential q5 and a neigh-
bouring point Q(r + Sr, 0 + SO) be on an equipotential q5 + Sq5 (Fig. 3.5). By definition
the increase Sq5 is the line integral of the tangential component of velocity along any
path. For convenience choose PRQ where point R is (I + Sr, 0). Then integrating
along PR and RQ where the velocities are qn and qt respectively, and are both in the
direction of integration:
Sq5 = qnSr + qt(r + Sr)SO
= qnSr + qtrSO to the first order of small quantities.

Fig. 3.5