Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 1 / 16D (Fluid Dynamics)

For steady inviscid flow, Bernoulli's equation along a streamline isWriting steady Euler flow in divergence form and integrating over $V$ givesby incompressibility and the divergence theorem.

The speeds are $U=q/A$ upstream and $v=q/(2a)$ in either daughter vessel. Bernoulli therefore gives

Take the downstream tissue pressure as gauge zero. The two transverse momentum fluxes cancel. The force of the fluid on the junction is axial and equalswhere $U=q/A$, $v=q/(2a)$ and the pressure difference is that in part (i).