Which of the following is most likely to produce turbulent flow?

• A. 2 mm vessel with 30 cm/sec
• B. 5 mm vessel with 300 cm/sec
• C. 4 mm vessel with 30 cm/sec
• D. 1 mm vessel with 30 cm/sec

Answer: (B)

The key idea is Reynolds number, which predicts whether flow in a tube is laminar or turbulent. Reynolds number is proportional to v times D (the velocity times the vessel diameter), and increases with fluid density and decreases with viscosity. When Re gets large, flow tends to become turbulent; for pipe flow, turbulence typically occurs at higher Re values (roughly a few thousand and above).

Using typical blood properties (density around 1000 kg/m^3 and viscosity around 0.0035 Pa·s) as a reference, evaluate each scenario by the product vD:

• A vessel of 2 mm at 0.3 m/s gives a modest Reynolds number, well under the turbulence threshold—flow is laminar.

• A vessel of 5 mm at 3 m/s produces a much larger Re, well above 4000, so the flow is turbulent.

• A vessel of 4 mm at 0.3 m/s again yields a relatively small Re—laminar.

• A vessel of 1 mm at 0.3 m/s also yields a small Re—laminar.

Since turbulence arises where Reynolds number is highest, the scenario with the 5 mm vessel and 300 cm/s (3 m/s) is most likely to produce turbulent flow.