A flow control apparatus includes a pressure regulator fluidly coupled to an inlet region and an outlet region and configured to reduce a pressure from a first value in the inlet region to a second value in the outlet region, where the second value is lower than the first value； and a variable area orifice disposed between the outlet region and an outlet opening of the apparatus, wherein a flow rate of a gas is controlled by the variable area orifice and is discharged from the apparatus to a gas supply line. A free area of the variable area orifice that is disposed between a movable element and a surface of the variable area orifice is configured to change linearly in response to a translation of the movable element relative to the surface.
