AIIMS 2005 Physics Reynolds Number Assertion Reason Question

To analyze the assertion and reason provided in the question, we need to understand the concept of the Reynolds number and its implications on fluid flow.

Explanation of the Assertion and Reason

Assertion: For Reynolds number $R_e > 2000$, the flow of fluid is turbulent.

Reason: Inertial forces are dominant compared to the viscous forces at such high Reynolds numbers.

Reynolds Number ($R_e$) Definition: The Reynolds number is a dimensionless quantity used to predict flow patterns in different fluid flow situations. It is defined as:

$$R_e = \frac{\rho v L}{\mu}$$

where:

• $\rho$ = density of the fluid,
• $v$ = velocity of the fluid,
• $L$ = characteristic length (e.g., diameter of a pipe),
• $\mu$ = dynamic viscosity of the fluid.

Why the Correct Answer is A

1. Validity of the Assertion:

   • The assertion states that for $R_e > 2000$, the flow is turbulent. This is a widely accepted rule of thumb in fluid dynamics. It indicates that as the Reynolds number increases and surpasses 2000, the fluid flow transitions from laminar (smooth and orderly) to turbulent (chaotic and irregular).

2. Validity of the Reason:

   • The reason provided states that at high Reynolds numbers, inertial forces dominate over viscous forces. This is also true. In fluid dynamics, inertial forces are associated with the motion of the fluid, while viscous forces are related to the internal friction within the fluid. In turbulent flow, the inertial forces (which depend on fluid density and velocity) greatly outweigh the viscous forces (which depend on the fluid's viscosity). Thus, the chaotic nature of turbulent flow is a result of high inertial forces.

3. Correct Explanation:

   • The reason correctly explains why the assertion is true. Since turbulent flow occurs when inertial forces dominate, the statement logically connects the two ideas. Therefore, both the assertion and reason are true, and the reason is indeed the correct explanation of the assertion.

Why Other Options are Incorrect

• Option B: Both assertion and reason are true but reason is not the correct explanation of assertion.

  • This is incorrect because the reason does directly explain why the flow becomes turbulent at high Reynolds numbers.

• Option C: Assertion is true but reason is false.

  • This is incorrect because both the assertion and reason are true, as explained above.

• Option D: Both assertion and reason are false.

  • This is incorrect because both statements are true.

Summary

The correct answer is A: both the assertion and reason are true, and the reason is the correct explanation of the assertion. Understanding the interplay between inertial and viscous forces in the context of flow regimes is crucial for mastering fluid dynamics, especially in applications such as pipe flow, aerodynamics, and various engineering systems.