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 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:
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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.
Updated On: Jun 3, 2026
- 20
- 40
- 100
- 200
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The Correct Option is B
Solution and Explanation
Concept:
The Reynolds number ($Re$) is a dimensionless quantity used in fluid mechanics to help predict flow patterns. It represents the ratio of inertial forces to viscous forces within a fluid.
Step 1: Identify the given values
• Velocity ($v$) = $2$ m/s
• Diameter ($D$) = $0.01$ m
• Density ($\rho$) = $1000$ kg/m$^3$
• Viscosity ($\mu$) = $0.5$ kg/m$\cdot$s
Step 2: Apply the Reynolds number formula.
The formula for flow through a pipe is: \[ Re = \frac{\rho v D}{\mu} \] Substituting the values: \[ Re = \frac{1000 \times 2 \times 0.01}{0.5} \]
Step 3: Perform the calculation.
\[ Re = \frac{20}{0.5} \] \[ Re = 40 \]
Step 1: Identify the given values
• Velocity ($v$) = $2$ m/s
• Diameter ($D$) = $0.01$ m
• Density ($\rho$) = $1000$ kg/m$^3$
• Viscosity ($\mu$) = $0.5$ kg/m$\cdot$s
Step 2: Apply the Reynolds number formula.
The formula for flow through a pipe is: \[ Re = \frac{\rho v D}{\mu} \] Substituting the values: \[ Re = \frac{1000 \times 2 \times 0.01}{0.5} \]
Step 3: Perform the calculation.
\[ Re = \frac{20}{0.5} \] \[ Re = 40 \]
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