A low cost valve, such as an emitter for controlling the flow from an aperture in a drip irrigation pipe, operates dynamically to maintain flow substantially constant across a wide range of pressures. A cylindrical valve seat mounted within the pipe aperture receives a valve member having a coaxial stem portion that extends through the valve seat to couple an external cap member. The interior end of the valve member comprises a diverging cone defined by integral and circumferentially separated leaf elements that engage a bearing surface of the valve seat at a root circumference when unstressed. Increasing water pressure within the pipe acts against the interior of the cone surface, distorting the leaf elements inwardly a proportional amount and shifting the valve member relative to the bearing surface through a selected limited operating range. The effective apertures between the leaf elements increase in length but decrease in width with greater pressure, providing an increasing impedance that maintains flow rate constant. The leaf elements are of selected stiffness and of relatively low friction material, and assume a stable pressure responsive position whether pressure is increasing or decreasing. The apertures between the leaf members are further shaped to provide an automatic purging flow when the pressure increases to or above a selected maximum.
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