Topic: Fluid Mechanics
An oil of kinematic viscosity of 0.5 stokes flow though a pipe of 20cm diameter. What is the velocity if the flow is critical?
- A. 0.5 m/s
- B. 0.9 m/s
- C. 1.5 m/s
- D. 2 m/s
Answer: A. 0.5 m/s
Explanation: For pipe flow, the critical Reynolds number ($Re_{critical}$) is 2000. The kinematic viscosity $\nu = 0.5$ stokes = $0.5 \times 10^{-4}$ m²/s. The pipe diameter $D = 20$ cm = $0.2$ m. Using the formula $Re = \frac{VD}{\nu}$, we substitute the values: $2000 = \frac{V \times 0.2}{0.5 \times 10^{-4}}$. Solving for $V$ yields $V = \frac{2000 \times 0.5 \times 10^{-4}}{0.2} = \frac{0.1}{0.2} = 0.5$ m/s.