Doublet

A Doublet is formed when the source and sink approach each other,i.e., $a\rightarrow 0$ and at the same time $m \rightarrow \infty$ such that $ma /\pi$ is constant, we see that

$${r \over {r^2 - a^2}}\rightarrow {1 \over r}$$ (4.86)

As a consequence the stream function becomes

$$\psi = -{{K \sin \theta} \over r}$$ (4.87)

The velocity potential is

$$\phi = {{K \cos \theta} \over r}$$ (4.88)

Figure 4.23: Doublet Flow

The streamlines and the equipotential lines for a doublet are sketched in Fig.4.23. It is seen that the streamlines are circles which are tangential to the x-axis while the equipotential lines are also circles but tangential to y-axis.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney