A fuel injector configured to be disposed in a combustor of a gas turbine engine, said combustor comprising: an end cover; at least one fuel nozzle extending between the end cover and a combustion liner, wherein the combustion liner extends between the at least one fuel nozzle and an aft frame and defines a combustion chamber; said fuel injector configured to be disposed downstream from the at least one fuel nozzle and in fluid communication with the combustion chamber, said fuel injector comprising a forward end wall and an aft end wall disposed opposite from the forward end wall; side walls extending between the forward end wall and the aft end wall, wherein the forward end wall, the aft end wall, and the side walls collectively define an opening for passage of air; at least one fuel injection member disposed within the opening and extending between the end walls (206, 208); and a fuel circuit defined within the fuel injector, the fuel circuit comprising: an inlet plenum defined within the forward end wall of the fuel injector; and a fuel passage extending from and in fluid communication with the inlet plenum, the fuel passage defined within the at least one fuel injection member, characterized in that the fuel passage has a cross-sectional area that varies along a length of the fuel injection member; wherein the fuel passage includes a first converging portion, a diverging portion, and a second converging portion. an end cover; at least one fuel nozzle extending between the end cover and a combustion liner, wherein the combustion liner extends between the at least one fuel nozzle and an aft frame and defines a combustion chamber; said fuel injector configured to be disposed downstream from the at least one fuel nozzle and in fluid communication with the combustion chamber, said fuel injector comprising a forward end wall and an aft end wall disposed opposite from the forward end wall; side walls extending between the forward end wall and the aft end wall, wherein the forward end wall, the aft end wall, and the side walls collectively define an opening for passage of air; at least one fuel injection member disposed within the opening and extending between the end walls (206, 208); and a fuel circuit defined within the fuel injector, the fuel circuit comprising: an inlet plenum defined within the forward end wall of the fuel injector; and a fuel passage extending from and in fluid communication with the inlet plenum, the fuel passage defined within the at least one fuel injection member, characterized in that the fuel passage has a cross-sectional area that varies along a length of the fuel injection member; wherein the fuel passage includes a first converging portion, a diverging portion, and a second converging portion. an inlet plenum defined within the forward end wall of the fuel injector; and a fuel passage extending from and in fluid communication with the inlet plenum, the fuel passage defined within the at least one fuel injection member, characterized in that the fuel passage has a cross-sectional area that varies along a length of the fuel injection member; wherein the fuel passage includes a first converging portion, a diverging portion, and a second converging portion.