Question

Water having a kinematic viscosity of 0.01 stoke flows at a velocity of 2 m/s in a pipe of 15 cm diameter. For dynamic similarity, the velocity of oil of kinematic viscosity 0.03 stoke in a pipe of the same diameter will be

• A. 0.33 m/s
• B. 0.66 m/s
• C. 2 m/s
• D. 6 m/s

Hint:

- Reynolds number similarity ensures that two flows exhibit similar flow characteristics. - Higher kinematic viscosity results in lower velocity for maintaining dynamic similarity.

Answer 1

The Correct Option is B

Step 1: Concept of Dynamic Similarity Dynamic similarity between two fluid flows requires that the Reynolds number (\(Re\)) remains the same for both cases. Reynolds number is given by: \[ Re = \frac{V D}{\nu} \] where, \( V \) = Velocity of the fluid (m/s) \( D \) = Diameter of the pipe (m) \( \nu \) = Kinematic viscosity (stoke or m\(^2\)/s) Step 2: Equating Reynolds Number For dynamic similarity: \[ \frac{V_1 D}{\nu_1} = \frac{V_2 D}{\nu_2} \] Since the diameter \( D \) is the same in both cases, we simplify to: \[ \frac{V_1}{\nu_1} = \frac{V_2}{\nu_2} \] Substituting given values: \[ \frac{2}{0.01} = \frac{V_2}{0.03} \] Step 3: Solving for \( V_2 \) \[ V_2 = \frac{2 \times 0.03}{0.01} = 0.66 { m/s} \] Conclusion: The correct answer is (B) 0.66 m/s.