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The Reynolds Number Calculator (Biological) computes the Reynolds number for fluid flow in biological systems. The Reynolds number is a dimensionless quantity that predicts whether fluid flow will be laminar (smooth) or turbulent (chaotic). In biology, this applies to blood flow in vessels, swimming of microorganisms, air flow in respiratory passages, and fluid dynamics in bioreactors.
Microorganisms live in a world of very low Reynolds numbers where viscous forces dominate and inertia is negligible, fundamentally different from the high-Reynolds-number world of large animals.
The Reynolds number is calculated as:
Re = (ρ × v × L) / µ
Flow classification: Re less than 2000 is laminar (0), 2000-4000 is transitional (1), above 4000 is turbulent (2). Most biological micro-flows are highly laminar.
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Bacteria swim at Reynolds numbers far below 1, in a regime where viscous drag dominates and coasting is impossible.
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Aortic blood flow is in the transitional range. During peak systole, it can become briefly turbulent, which is detectable as heart murmurs.
Reynolds number determines the physics of fluid flow at different scales. Microorganisms at Re much less than 1 experience a viscosity-dominated world where swimming mechanisms differ fundamentally from large organisms. Blood flow turbulence affects vascular health, and airflow patterns in the lungs determine gas mixing efficiency.
Laminar flow moves in smooth parallel layers with no mixing between them. Turbulent flow is chaotic with eddies and mixing. In blood vessels, laminar flow is normal and efficient, while turbulence increases shear stress on vessel walls and can promote atherosclerosis. The transition occurs around Re = 2000.
At very low Re, reciprocal motions (like a scallop opening and closing) produce no net movement. Bacteria use rotating flagella, and sperm use asymmetric wave propagation. These non-reciprocal strategies overcome the time-reversibility of low-Reynolds-number flow, a principle known as the Scallop Theorem.
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