A cooling section for flat rolling stock has a working region, through which the flat rolling stock is guided. The working region can be supplied with a liquid coolant by means of a number of spray beams. The liquid coolant is fed from a reservoir for the liquid coolant to the spray beams by means of a pump and a supply system. Valves are arranged upstream of the spray beams in the supply system. Opening positions of the valves are set by a control unit of the cooling section according to a respective sub-flow that is to be applied to the flat rolling stock by means of each spray beam. Also, the delivery rate of the pump and/or a line pressure generated by the pump in the supply system are set by the control unit according to the total flow that is to be applied to the flat rolling stock by means of all the spray beams.