Past exam of the mathematics course of the University of Cambridge / 2025 / ib / Paper 1 / 16D / ii

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- Solution ii

Solution

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 equals

F = [A (p_{up} - p_{down}) + ρq (U - v cos α)] e_{x},

where

U = q / A

,

v = q / (2 a)

and the pressure difference is that in part (i).

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