Forehearth tank assembly for a glass distribution channel. The assembly includes a single liner, two plungers and more and a single flow washer that has first and second orifices. The plungers are arranged, at least in part, in the liner. More than three grooves are created on the inner surface of the liner. Each has, in an inner part of the liner that is intended to be in contact with molten glass, a lower portion extending over more than 10% of the length of the lower part and having a length, measured following the groove, of greater than 0.1 times the length of the lower part. The length of the lower part is measured along the axis of the liner.