The helix exerts on the fluid the torque
$$
N=BU+D(\Omega+\omega).
$$
Overall torque balance also gives $N=-D_0\Omega$. Hence
$$
\boxed{N=\frac{D_0[(A+A_0)D-B^2]}{(A+A_0)(D+D_0)-B^2}\omega.}
$$
For the usual choice $\omega>0$, this is positive when the resistance matrix is positive definite.


Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 355 / 2 / d / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-355/2/d/solution