Topic: Fluid Mechanics
Water having kinematic viscosity of 0.01 stoke flows at a velocity of 2m/sec in a pipe of 15 cm diameter. For dynamic similarity, the velocity of oil of kinematic viscosity of 0.03 stoke in a pipe of same diameter will be
- A. 0.33 m/sec
- B. 0.66 m/sec
- C. 2 m/sec
- D. 6 m/sec
Answer: D. 6 m/sec
Explanation: For dynamic similarity in pipe flow, the Reynolds numbers must be equal: $\left(\frac{VD}{\upsilon}\right)_{1} = \left(\frac{VD}{\upsilon}\right)_{2}$. Since the pipe diameter is the same ($D_1 = D_2 = 15$ cm), the equation simplifies to $\frac{V_1}{\upsilon_1} = \frac{V_2}{\upsilon_2}$. Solving for $V_2$ gives $V_2 = V_1 \times \frac{\upsilon_2}{\upsilon_1} = 2 \times \frac{0.03}{0.01} = 6$ m/s.