Fuel supply system of a turbomachine, with regulation of the fuel flow

A fuel supply system of a turbomachine, comprising a fuel circuit comprising pressurizing means at the outlet of said circuit, a pump arranged to send a flow of fuel into said circuit which is an increasing function of the speed of rotation of a shaft of the pump, the circuit comprising a flow sensor placed in a fuel supply duct between an outlet of the pump and the pressurizing means, the flow sensor comprising a sliding drawer, a return means and a sensor for the position of said drawer, the position of said drawer being controlled by a pressure difference across the terminals of the flow sensor shaped to compensate for the force applied by the return means on said drawer, the circuit being arranged so that the position of said drawer indicates an injected fuel flow passing through the flow sensor, wherein the fuel circuit comprises a device for regulating a passage cross section between the pump and the flow sensor, and activated by control means, the shaft of the pump being associated with detection means recording a speed of rotation of the shaft and, if these detection means record a speed of rotation above a variable predetermined threshold, the regulating device is configured to be activated to reduce and meter the injected fuel flow sent to the flow sensor.