Question

A liquid flows with velocity $2$ m/s through a pipe of diameter $0.01$ m. Density = $1000$ kg/m$^3$, viscosity = $0.5$ kg/m$\cdot$s. Reynolds number is:

• A. 20
• B. 40
• C. 100
• D. 200

Hint:

For flow in a pipe, $Re < 2000$ generally indicates laminar flow, while $Re > 4000$ indicates turbulent flow. In this specific problem, a Reynolds number of 40 confirms that the flow is highly laminar.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The Reynolds number (\(Re\)) is a dimensionless parameter used to predict the transition from laminar to turbulent flow.
It represents the ratio of inertial forces (due to mass and velocity) to viscous forces (due to internal friction).
Step 2: Key Formula or Approach:
For a pipe: \[ Re = \frac{\rho v D}{\mu} \]
where \(\rho\) is density, \(v\) is velocity, \(D\) is diameter, and \(\mu\) is dynamic viscosity.
Step 3: Detailed Explanation:
Given:
Velocity (\(v\)) = 2 m/s
Diameter (\(D\)) = 0.01 m
Density (\(\rho\)) = 1000 kg/m$^{3}$
Viscosity (\(\mu\)) = 0.5 kg/m$\cdot$s
Substitute values into the formula:
\[ Re = \frac{1000 \times 2 \times 0.01}{0.5} \]
\[ Re = \frac{20}{0.5} = 40 \]
Step 4: Final Answer:
The Reynolds number is 40.