Economy, for one. For a variety of reasons, valves might not need to be the full port size of the pipeline. For pipeline pigging, and other reasons, they sometimes do need to be full port size. It all depends on the specific situation.
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A full port or more commonly known full bore ball valve has an over-sized ball so that the hole in the ball is the same size as the pipeline resulting in lower friction loss. Flow is unrestricted but the valve is larger and more expensive so this is only used where free flow is required, for example in pipelines which require pigging.
In reduced port or more commonly known reduced bore ball valves, flow through the valve is one pipe size smaller than the valve's pipe size resulting in flow area being smaller than pipe. As the flow discharge remains constant and is equal to area of flow (A) times velocity (V), A1V1 = A2V2 the velocity increases with reduced area of flow.
Hope that helps with your homework.
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"Do not worry about your difficulties in Mathematics. I can assure you mine are still greater". - Albert Einstein