A flow sensing valve includes a valve housing having an inlet port, an outlet port, and a plurality of flow sensing ports. A valve member, located within the valve housing, is configured to move between an open position and a closed position. The valve member allows fuel flow between the inlet port and outlet port in the open position, and blocks fuel flow between the inlet port and the outlet port in the closed position. A position sensor, operably coupled to the valve member, is configured to determine a valve position of the flow sensing valve. The valve position is indicative of a valve open port area. A metered flow rate of pressurized fuel through the flow sensing valve in a upstream manifold is proportional to the valve open port area because the flow sensing valve maintains a nearly constant differential pressure across the inlet and outlet ports.