We investigated the network topology of the wing veins of fruit flies and observed that the posterior cross vein disrupted the symmetry of the entire network. The purpose of this vein has remained unknown, notwithstanding prior study of its development and its positional variety among different species. We examined the vein's effect on hydration dynamics in the wing membrane and on the internal blood flow of the venous system, applying computational removal or repositioning of the vein rather than physical manipulation. We determined the balance of flow velocities between the water supply from the veins to the wing membrane and the evaporation from the membrane. The position of the posterior cross vein maximises the ratio of the supply flow velocity to the evaporative velocity in the adjacent membrane, with supply occurring more than seventy times faster than evaporation. We found that this vein’s position minimises the pressure loss accompanying blood flow through the vein, using iterative calculations to derive the flow distribution that satisfies pressure balances at bifurcations in the venous network. This particular vein's location exhibited the greatest reduction in pressure loss throughout the entire vein network. Our results highlight the topological adjustments in wing venation that influence circulation.