= Solution
The <imaginary part> of the <complex potential of a two-dimensional potential flow> is the <stream function>. Its constant values on the wall and the free <boundary> make the potential domain the horizontal strip
$$
\boxed{0<\operatorname{Im}w<1.}
$$
The lower edge is the rigid wall, with $B$ at $w=0$. The upstream end has $\operatorname{Re}w\to-\infty$, and the downstream end has $\operatorname{Re}w\to+\infty$. The upper edge is the <free streamline>. Thus $AB$ and $BC$ are the negative and positive portions of the real $w$ axis, respectively.
Write $q=w'=u-iv$ for the <complex velocity>. Downstream $q\to1$. Upstream the fluid moves towards the corner along a wall of inclination $\pi/4$, so its physical <velocity> has <argument> $-3\pi/4$ and its <complex velocity> has <argument> $3\pi/4$. Along each straight wall the <velocity> direction is fixed. At the corner the fluid <angle> is $\pi/4$, giving local behavior $w\sim K(z-B)^4$ and hence $q\to0$: \b[$B$ is a <stagnation point>]. On the <free streamline>, the <speed> is one, so $|q|=1$.
The corresponding simple-jet <hodograph plane> is therefore the circular sector
$$
\boxed{0<\arg q<\frac{3\pi}{4},\qquad0<|q|<1.}
$$
The radius at <argument> $3\pi/4$ represents $AB$, the positive real radius represents $BC$, and the unit-circle arc represents the free <boundary>. The upstream and downstream ends are $e^{3\pi i/4}$ and one, respectively; the corner is the sector's origin.
\Image[/past-exam-of-the-applied-complex-variables-course-of-the-university-of-oxford/2011-potential-hodograph.png]
{title=The <complex potential of a two-dimensional potential flow> strip and <hodograph plane>, with an intermediate power map}
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