A valve assembly for a fluid dispenser includes a housing having at least a first opening and a second opening, and a valve member fitted in the housing, the valve member being rotatable about an axis and comprising a first channel, extending along said axis and communicating with the first opening in the housing, and at least two outlet channels radially extending from the first channel to the circumference of the valve member, wherein each of the radially extending outlet channels can be brought in register with the second opening by rotating the valve member.