Abstract: In accordance with the present invention, a constant flow rate control valve is provided including a cup member disposed in the flow passage through the valve. The cup member has a port located in an end wall of the cup member and a plurality of ports in the sidewall of the cup member. The cup member is movable axially within the valve, with such movement being opposed by a resilient spring member downstream of the cup member. A fixed shear ring in the valve body surrounding the sidewall of the cup member blocks or exposes areas of the sidewall ports in response to movement of the cup member. Fluid pressure acting on the end wall of the cup member urges the cup member against the spring, so that the shear member exposes only that sidewall port area appropriate to the pressure being exerted. The sidewall ports have non-identical shapes and areas, with one or more longer sidewall ports extending further toward the end wall of the cup member than the other, shorter sidewall ports.