Discussion
In a uniform stream with complex potential \(Uz\), a two-dimensional source of strength \(m\) is situated at the point \((a, 0)\). The stagnation point is at :
Answer: D
The keyed stagnation point is \(z = a + m/U\).
The key follows the convention common in Indian textbooks, where the complex potential is \(w = \phi + i\psi\) with velocity \(\mathbf{q} = -\nabla\phi\), so \(dw/dz = -u + iv\). Then \(w = Uz\) is a uniform stream in the negative \(x\)-direction, and a source of strength \(m\) at \(a\) is \(-m\log(z - a)\). The total potential and its derivative are
\[ \begin{aligned} w &= Uz - m\log(z - a) \\ \frac{dw}{dz} &= U - \frac{m}{z - a} = 0 \\ z &= a + \frac{m}{U} \end{aligned} \]
Physically, the stagnation point lies upstream of the source, here on the side of larger \(x\), at distance \(m/U\). (Under the opposite convention, with the stream along the positive \(x\)-axis, it is at \(a - m/U\), which is not offered.) The other options have the ratio inverted or no dependence on \(a\).
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