An apparatus for use in a wellbore is disclosed that in one non-limiting embodiment includes a flow restriction device that that contains a channeling element having a fluid flow passage, a restriction element spaced from the channeling element defining a gap between the restriction element and the channeling element, wherein relative movement between the restriction element and the channeling element obstructs flow of a fluid flowing through the flow passage to increase pressure in the fluid across the device. In one embodiment an activation device displaces one of the channeling element and the restriction element to adjusts or alter gap in response to certain changes in the pressure across the restriction device.