A variable area restrictor is disclosed that is preferably used in a turbine engine to provide improved matching between the pressure required for aerofoil cooling and the somewhat lower pressure requirement for supplying air to the interstage seals and disc cavities. In a preferred embodiment, the valve of the present invention comprises a spring loaded valve assembly with a fixed minimum flow area controlled by pre-setting a minimum dimension for the opening between an inlet and the housing or body of the valve. A pre-loaded spring maintains the lift at this minimum dimension until the pressure drop across the flow area exceeds a certain value. Above this critical pressure drop, the valve lifts, causing the flow area to increase, and thereby reducing the supply pressure that would be otherwise necessary to achieve a disc cavity flow adequate to maintain the temperatures within specifications.