Ascertaining fuel cell inlet humidity by means of pressure sensors, and a mass flow rate-dependent control of the humidifier bypass

A fuel cell arrangement (1) comprising at least one fuel cell (2) with a cathode (3) and an anode, wherein the cathode (3) and the anode each have a reactant feed (4) and a reactant discharge (5), a humidifying device (10) and sensors (12, 13, 14) being provided at least at one of the reactant feeds (4), characterized in that the sensors (12, 13, 14) are at least one fluid mass sensor (12) and two pressure sensors (13, 14), the fluid mass sensor (12) and one of the pressure sensors (13) being arranged upstream of the humidifying device (10) and one of the pressure sensors (14) being arranged downstream of the humidifying device (10), and in that the humidifying device (10) is configured to be operated in a controlled manner on the basis of the measurements of the sensors (12, 13, 14), and wherein a bypass line (16) is provided in the at least one reactant feed (4), which bypass line is configured to be controlled by means of a valve (15) and by means of which bypass line the humidifying device (10) is configured to be at least partially bypassed, and further wherein the bypass line is connected to the reactant feed at a point downstream of the humidifying device and upstream of the one of the pressure sensors being arranged downstream of the humidifying device, wherein a control circuit programmed to calculate humidity as linearly dependent on a measured fluid mass flow rate and linearly dependent on a difference between measured pressures is configured to determine the humidity of the reactant in the at least one of the reactant feeds on the basis of measurement values from no sensors other than the fluid mass sensor and the two pressure sensors.