You generally size pipes for the maximum or design flowrate. When you say "minimum flow", I don't know if you mean the minimum stable flowrate that your centrifugal pump can deliver or if you mean something else.
Closed or open system is not particularly relevant. Pipes are generally sized based on velocity and/or pressure drop. Many E&C company guidelines have (maximum) recommendations for both. Sometimes, you have "pressure to burn", and you might not be worried about pressure drop. Other times, you might have a hydraulically tight system, and pressure drop considerations would dominate. If you have a slurry, you might be hemmed in. Too low a velocity and the solids would drop out; too high a velocity and you'd experience excessive erosion. HTH.