Page 139 - Aerodynamics for Engineering Students

122 Aerodynamics for Engineering Students

giving

and from v = -&)/ax

v=- m
27rx2 + y2
from which the local velocity can be obtained from q = d m and the direction
given by tan-' (vlu) in any particular case.

3.3.6 Source-sink pair
This is a combination of a source and sink of equal (but opposite) strengths situated
a distance 2c apart. Let fm be the strengths of a source and sink situated at points
A (cy 0) and B (-c, 0), that is at a distance of c m on either side of the origin (Fig. 3.15).
The stream function at a point P(x, y), (r, e) due to the combination is
me1 me2 m
$=---=-((e 1 - 02)
27r 27r 27r
m
i=z;;P (3.26)

Transposing the equation to Cartesian coordinates:
Y Y
tanel =- , tan 62 = -
x-c x+c

Therefore
2CY
p = el - e2 = tan-' (3.27)
x2 + y - c2
and substituting in Eqn (3.26):

(3.28)

Fig. 3.15