Question

What is the Reynolds number for the flow with velocity 2 m/s, flowing through a 10 cm diameter pipe carrying water with viscosity 1 centipoise?

• A. \( 2.00 \times 10^3 \)
• B. \( 2.00 \times 10^4 \)
• C. \( 2.00 \times 10^5 \)
• D. \( 2.00 \times 10^6 \)

Hint:

Reynolds number determines flow type: - \( Re<2000 \) (Laminar), - \( 2000<Re<4000 \) (Transition), - \( Re>4000 \) (Turbulent).

Answer 1

The Correct Option is B

Step 1: Reynolds Number Formula
Reynolds number (\(Re\)) is given by: \[ Re = \frac{\rho V D}{\mu} \] where: - \( \rho \) = Density of water (\( 1000 \) kg/m³) - \( V \) = Velocity of flow (\( 2 \) m/s) - \( D \) = Diameter of pipe (\( 0.1 \) m) - \( \mu \) = Dynamic viscosity (\( 1 \) centipoise = \( 0.001 \) Pa.s)
Step 2: Substituting Values
\[ Re = \frac{1000 \times 2 \times 0.1}{0.001} \] \[ Re = 2.00 \times 10^4 \]
Step 3: Conclusion
The calculated Reynolds number matches option (B).