A sprinkler apparatus, a flow rate control valve assembly, and a sprinkler irrigation system for providing an even distribution of water across an asymmetrically shaped water receiving area. The sprinkler apparatus comprises a pop-up sprinkler head with a base housing for confiningly receiving a pressurized water flow that actuates a nozzle housing slidingly and rotationally cooperating with the base housing to pop-up into an operating position for discharge of water through at least one pair of nozzle assemblies. The pair of nozzle assemblies comprise an upper nozzle assembly and a lower nozzle assembly near the top end of the nozzle housing. The upper nozzle assembly controllably projects the pressurized water flow for a precisely set distance, while the lower nozzle assembly comprises a vertical slit-shaped aperture through which water is discharged in a curtain effect. Together, the pair of nozzle assemblies achieve a substantially uniform elliptical linear spray pattern with a bias to outermost end. A flow rate control valve assembly is further described and comprises a flow control valve assembly that can be fluidly coupled to a pop-up sprinkler head to controllably supply the pressurized water flow, the flow control valve assembly comprising a water inlet fluidly coupled to a water supply and a water outlet fluidly coupled to the pop-up sprinkler head, the water outlet cooperatively engaging with a rotary disc valve having a tapered passage wherein sliding rotation of the rotary disc valve incrementally adjusts the valve between an opened position and a closed position to control the pressurized water flow through the water outlet.