In a wet press for dewatering a web of material, for instance a paper web, a contact pressure device is provided which presses against a rotating roll and exerts an incrementally increasing pressure in the direction of travel of the paper web. The contact pressure device comprises only a single pressure element arranged in the direction of travel of the paper web. The pressure element has two or more pressure pockets arranged sequentially in the direction of web travel and which are connected with a common pressure chamber by conduits. The increasing contact pressure is attained by arranging the pressure element unsymmetrically in relation to the pressure chamber. The effective pressure cross-sectional areas of pressure pockets arranged sequentially in the direction of web travel can additionally be reduced in the direction of web travel or the cross-sections of the associated bores can be increased.
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