Which scenario is most likely to produce turbulent flow?

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

Answer: (B)

Turbulent flow arises when inertial forces far exceed viscous forces, which is captured by Reynolds number. In pipe-like flow, Reynolds number grows with the product of velocity and diameter (v times D). So higher velocity and a larger diameter push the flow toward turbulence.

Among the scenarios, the combination of the highest velocity (3 m/s) with the largest diameter (5 mm) gives the biggest vD value, and thus the highest Reynolds number. That makes turbulence most likely in this case.

The other options have smaller vD values because either the velocity is much lower or the diameter is smaller, which keeps the flow more laminar.