Question

Water with kinematic viscosity $\nu = 1\times10^{-6}\ \text{m}^2/\text{s}$ flows through a circular pipe of diameter 8 mm. If flow is laminar and fully developed with maximum velocity 0.5 m/s, the Reynolds number is \(\underline{\hspace{2cm}}\) (round off to nearest integer).

Hint:

For laminar pipe flow, the maximum velocity is always twice the average velocity—use this relation for correct Reynolds number estimation.

Answer 1

Correct Answer: 1995 - 2005

For fully developed laminar pipe flow: \[ U_{\max} = 2 U_{\text{avg}} \] Thus: \[ U_{\text{avg}} = \frac{0.5}{2} = 0.25\ \text{m/s} \] Reynolds number: \[ Re = \frac{U_{\text{avg}}\, D}{\nu} = \frac{0.25 \times 0.008}{1\times10^{-6}} = 2000 \] Rounded to nearest integer: \[ 2000 \]