Question

An oil of kinematic viscosity \(0.4\) stokes flows through a pipe of diameter \(10\) cm. The flow may not be essentially laminar at a velocity of ____

• A. \(0.8\,\mathrm{m/s}\)
• B. \(8.0\,\mathrm{m/s}\)
• C. \(800\,\mathrm{m/s}\)
• D. \(8000\,\mathrm{m/s}\)

Hint:

For pipe flow, \[ \boxed{ Re=\frac{VD}{\nu} } \] Laminar flow: \[ \boxed{Re\lt 2000.} \]

Answer 1

The Correct Option is A

Step 1: Convert the given data to consistent SI units. \[ \nu = 0.4\ \text{stokes} = 0.4\times10^{-4} = 4\times10^{-5}\,\mathrm{m^2/s}, \qquad D = 10\,\text{cm} = 0.1\,\text{m} \]
Step 2: Work backward from the critical Reynolds number.
Laminar flow in a pipe holds only up to $Re = 2000$, so find the velocity that puts the flow exactly at this boundary, \[ V_{critical} = \frac{Re \cdot \nu}{D} = \frac{2000\times 4\times10^{-5}}{0.1} = \frac{0.08}{0.1} = 0.8\,\mathrm{m/s} \]
Step 3: Interpret this critical velocity.
At $V = 0.8\,\mathrm{m/s}$ the flow sits right at the laminar to turbulent transition, so this is the velocity beyond which the flow may not stay essentially laminar.
\[ \boxed{0.8\,\mathrm{m/s}} \]