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We simultaneously measure the flow rate and the normal force on the base, near the outlet, during the discharge through an orifice of a dense packing of monosized disks driven by a conveyor belt. We find that the normal force on the base decreases even when a constant flow rate is measured. In addition, we show, by changing the mass of the disks, that pressure can be changed while the flow rate remains constant. Conversely, we are able, by changing the belt velocity, to set different flow rates for the same pressure. The experiment confirms that, contrary to what has been implicitly assumed in numerous works, the flow rate through an aperture is not controlled by the pressure in the outlet region.