Page 141 - Aerodynamics for Engineering Students

124 Aerodynamics for Engineering Students

Therefore
m x2+y2+c2-2xc
+=-ln
47r x2 + y2 + c2 + 2xc
Rearranging

Then
(x2 +yz + 2 +2xc)X = 2 +yz + c2 - 2xc
(x2+y2+c2)[X-l]+2xc(X+1) =o

X+1
x2 + y2 + 2xc (-) A-1 + = 0 (3.30)

which is the equation of a circle of centre
x = -c (S)
,
0
y
=
i.e.

and radius

= 2c cosech- 274
m
Therefore, the equipotentials due to a source and sink combination are sets of
eccentric non-intersecting circles with their centres on the Ox axis (Fig. 3.17). This
pattern is exactly the same as the streamline pattern due to point vortices of opposite
sign separated by a distance 2c.

Fig. 3.17 Equipotential lines due to a source and sink pair