Question

The Reynolds number is a ratio of:

• A. Inertial forces to viscous forces
• B. Gravitational forces to inertial forces
• C. Viscous forces to pressure forces
• D. Surface tension forces to inertial forces

Hint:

Every dimensionless number in fluid mechanics is a ratio of physical forces.
For example:
- Reynolds ($Re$) $\to$ Inertial Viscous
- Froude ($Fr$) $\to$ Inertial Gravitational
- Weber ($We$) $\to$ Inertial Surface Tension

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This fluid mechanics question asks for the physical definition and significance of the Reynolds number ($Re$).

Step 2: Key Formula or Approach:
The Reynolds number is a dimensionless parameter defined as:
\[ Re = \frac{\rho \cdot v \cdot L}{\mu} \]
where:
$\rho$ is the fluid density,
$v$ is the flow velocity,
$L$ is the characteristic linear dimension, and
$\mu$ is the dynamic viscosity of the fluid.

Step 3: Detailed Explanation:

• The Reynolds number represents the ratio of dynamic forces inside a moving fluid.

• The numerator ($\rho \cdot v^2$) is proportional to the inertial forces, which represent the momentum of the fluid trying to keep it in motion.

• The denominator ($\mu \cdot v / L$) is proportional to the viscous shear forces, which act as internal friction resisting fluid movement.

• Therefore, we can write:
\[ Re = \frac{\text{Inertial Forces}}{\text{Viscous Forces}} \]

• If the Reynolds number is low ($Re < 2300$ for pipe flow), viscous forces dominate, and the flow is smooth and orderly (laminar).

• If the Reynolds number is high, inertial forces dominate, leading to instabilities, eddies, and rapid mixing (turbulent flow).

Step 4: Final Answer:
The Reynolds number is the ratio of inertial forces to viscous forces.