An arrangement for supplying ink to a print bar with small pressure fluctuations may include an ink reservoir and a damping vessel. The print bar may include at least two print heads and is connected with the ink reservoir via a supply line. Each of the print heads is connected with the damping vessel via at least one damping line. The damping vessel is connected with a discharge line. The end of the damping line ends at a first height in the damping vessel. The end of the discharge line ends at a second height above the first height in the damping vessel. The arrangement may supply ink to the print bar with small gas fraction in the ink.