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So I have a crude understanding of some fluid dynamics already, but here is my dilemma and I would like any answers or clues to help me fully understand these principles.

According to Poiseuille's Law, the volumetric flow rate is a function of differential pressure, pipe radius, and fluid viscosity. However this is only applicable to laminar flow situations. So with this calculable flow rate, it is possible to evaluate/design large piping systems as long as the flow stays laminar.

What precisely makes Poiseuille's Law ineffective at calculating flow rates in turbulent flow even though the fluid is still incompressible? I understand that there are eddies and unpredictable flow patterns associated with turbulent flow. But the way I am thinking about it is that since the fluid is still incompressible, the differential pressure would still drive the same flow rate of the fluid. Basically saying that the flow rate should be independent of the flow pattern. Why is this wrong?