A metering valve or an injector includes: a valve-seat member which closes a valve chamber and has a central valve opening, and a spray orifice disk downstream from the valve-seat member in the flow direction of the fluid, which has at least one spray orifice. The spray orifice disk has a swirl chamber concentric with the spray orifice and at least one swirl duct leading from the swirl chamber to beneath the valve opening, and the swirl chamber and swirl duct are integrally formed as recesses into the disk surface of the spray orifice disk facing the valve body. The swirl duct has a duct cross section and the spray orifice has an orifice cross section such that the ratio of the duct cross section to the orifice cross section is equal to or greater than 1.5.