A fuel supply system for a turbomachine. The supply system includes a starter circuit, at least one first hydraulic resistance and a purge circuit. The purge circuit includes a duct including an opening at the exterior of the supply system. The purge circuit is configured to make purge air flow between a starter injector and the opening through the first hydraulic resistance. The supply system includes a device for measuring a value representative of pressure, which devices are configured to measure a value representative of pressure between the starter injector and the first hydraulic resistance when purge air flows between the starter injector and the first hydraulic resistance.