Question

Problem 1: Laminar and Turbulent Flow When fluids flow, the motion of the flow can either be steady and smooth (called laminar flow) or unsteady and chaotic (called turbulent flow). Streamlines for illustrative flows are shown to the right. A long time ago we discussed the Reynolds number Re for an object of “size” ?? moving at speed ?? through a fluid of density ?? and viscosity ??. Re = ?????? ?? Recall that for large Re, the relevant drag force was viscous, while for small Re the relevant drag was inertial. Reynolds number also tells us about how a fluid flows through a pipe, tube, or artery. To use Reynolds number in such a case, ?? now refers to the “size” (diameter) of the pipe (not its length!), and ?? is now the speed of the flowing fluid. For a flowing fluid, the cutoffs for determining whether flow is laminar or turbulent are: Re < 1000 gives laminar flow, while Re > 4000 gives turbulent flow. These cutoffs are not hard – they can vary depending on the exact geometry of the tube or pipe (kinks or sharp turns tend to make turbulent flow arise at lower Reynolds numbers), but for this course we will treat these cutoffs as exact to make things simple.

A. Consider a narrowing in a coronary artery where the diameter is 2 mm, and the blood flow is 5 mL/s. The viscosity of blood is 10 mPa ⋅ s, and the density of blood is about 1000 kg/m3. Compute the Reynolds number for this flow.

B. Is this blood flow turbulent, laminar, or is it hard to say?

Answer 1