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Speeds of vertical flows in quiescent solar filaments are typically much less than the local Alfvén speed. This is why the flows in filament barbs can be modeled by perturbing a magnetostatic solution describing a balance between the Lorentz force, gravity, and gas pressure in a barb. This approach explains why some of the flows are neither aligned with the magnetic field nor controlled by gravity. Both the observed upflows and the magnetic field dips in barbs are likely to be caused by photospheric magnetic reconnection.