The continuous <transonic branch> passes from $dj/du>0$ to $dj/du<0$, so $j(u)$ has a maximum where its derivative vanishes. At this <critical speed of a polytropic flow>,
$$
\boxed{u=c_s=c_{\rm cr}}.
$$
The maximum mass flux is therefore attained at the <sonic point>.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 314 / 2 / b / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-314/2/b/solution