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 kinematic viscosity. \[ 1\ \text{stoke}=10^{-4}\ \mathrm{m^2/s} \] \[ \nu=0.4\times10^{-4}=4\times10^{-5}\ \mathrm{m^2/s} \] Diameter, \[ D=10\ \text{cm}=0.1\ \text{m} \]

Step 2: Use Reynolds number. \[ Re=\frac{VD}{\nu} \] For \(V=0.8\ \mathrm{m/s}\), \[ Re=\frac{0.8\times0.1}{4\times10^{-5}} =2000 \] Since laminar flow exists only for \[ Re\lt 2000, \] the flow may not remain essentially laminar at this velocity. Hence, \[ \boxed{0.8\ \mathrm{m/s}} \] Therefore, \[ \boxed{(A)} \] is the correct answer.