The permeating solvent flux across a lipid bilayer membrane depends on both mechanical and osmotic stresses. In the absence of osmolarity, we use numerical simulations to show that the mechanically induced semipermeability (albeit small) can alter the equilibrium shape of a relaxing vesicle over long timescales, or the hydrodynamics of a vesicle going through the strong confinement of a narrow channel. We further quantify the role of membrane tension and bending on the permeating solvent flux.