Discussion
In two-dimensional fluid flow consider a source of strength \(m\) at \(z = f\), where \(f\) is real, outside the circular cylinder of radius \(a\) whose centre is at the origin. The image of the source in a cylinder is :
Answer: B
The image is a source of strength \(m\) at \(z = a^{2}/f\) and a sink of strength \(m\) at the origin.
By the circle theorem, a source at \(z = f\) outside the cylinder \(|z| = a\) has complex potential \(-m\log(z - f)\). Its image is obtained from \(-m\log(a^{2}/z - f)\), which equals \(-m\log(z - a^{2}/f) + m\log z\) plus a constant. That is a source of strength \(m\) at the inverse point \(a^{2}/f\) and a sink of strength \(m\) at the centre.
The sink at the origin keeps the net flux out of the cylinder zero, so no fluid is created inside it. The other options get the signs of the two image singularities wrong.
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