This sounds like an experiment of some sort. Generally the minimum distance is based on moving the fluid from Point A to Point B, not on trying to get 'hydraulically and thermally fully developed flow'. Where you get 'hydraulicaly and thermally fully developed flow' depends a lot on parameters you've not mentioned and can be highly dependent on the situation, such as the flowrate and whether different streams of fluid are joining together.
You also asked about what is the critical Reynolds number for fully turbulent flow. In general, turbulent flow is presumed if Re> 4000. However, in real life, IT DEPENDS.
My Crane Handbooks notes that laminer flow can terminate at a Reynolds number as low as 1200 and can exist at a Reynolds number as high as 40,000.
Speaking of which, you might also want to get your hands on a Crane Handbook 210 "Flow of Fluids Through Valves, Fittings and Pipes." Since your handle indicates you're an electrical, you might want to borrow it from a mechanical engineer coworker. It's also relatively inexpensive to buy and well worth having if you're going to be working with fluids.
Patricia Lougheed
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