Question

The ratio of inertia force to viscous force, is known as

• A. Euler number
• B. Froude number
• C. Reynolds number
• D. Rayleigh number

Hint:

The Reynolds number ($Re$) is the most fundamental dimensionless group in fluid dynamics, measuring the balance between inertial forces (which promote turbulence) and viscous forces (which suppress it).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Dimensionless numbers are used in fluid mechanics and heat transfer to describe flow behavior and scale up engineering systems.
These numbers represent ratios of different physical forces acting on the fluid.
The ratio of inertial forces to viscous forces determines whether the flow in a pipe or around an object is laminar or turbulent.

Step 2: Detailed Explanation:
The Reynolds number ($Re$) is a dimensionless group defined as:
\[ Re = \frac{\text{Inertial Forces}}{\text{Viscous Forces}} \]
Mathematically, it is expressed as:
\[ Re = \frac{\rho \cdot v \cdot L}{\mu} \]
Where:
$\rho$ is the fluid density.
$v$ is the flow velocity.
$L$ is a characteristic length (such as pipe diameter).
$\mu$ is the dynamic viscosity.
If the Reynolds number is low, viscous forces dominate, and the flow is smooth and laminar.
If the Reynolds number is high, inertial forces dominate, and the flow is turbulent.
For comparison:
- The Euler number (A) represents the ratio of pressure forces to inertial forces.
- The Froude number (B) represents the ratio of inertial forces to gravitational forces.
- The Rayleigh number (D) represents the ratio of buoyancy-driven forces to thermal diffusivity forces.
Therefore, the Reynolds number is the correct dimensionless group.

Step 3: Final Answer
The ratio of the inertia force to the viscous force is known as the Reynolds number.