Question

Which dimensionless number represents the ratio of inertial forces to viscous forces?

• A. Reynolds number
• B. Froude number
• C. Mach number
• D. Weber number

Hint:

Whenever inertial force vs viscous force comparison is asked, the answer is always {Reynolds number}.

Answer 1

The Correct Option is A

Step 1: Understanding dimensionless numbers in fluid mechanics.
Dimensionless numbers are ratios of different types of forces acting in a fluid flow. They help in predicting flow behavior and similarity between different flow systems.
Step 2: Definition of Reynolds number.
The Reynolds number is defined as the ratio of inertial forces to viscous forces in a fluid flow. It is given by: \[ Re = \frac{\rho V L}{\mu} \] where $\rho$ is fluid density, $V$ is flow velocity, $L$ is characteristic length, and $\mu$ is dynamic viscosity.
Step 3: Physical significance.
- High Reynolds number indicates dominance of inertial forces, leading to turbulent flow.
- Low Reynolds number indicates dominance of viscous forces, resulting in laminar flow.
Step 4: Analysis of options.
(A) Reynolds number: Correct — It directly represents the ratio of inertial to viscous forces.
(B) Froude number: Represents the ratio of inertial forces to gravitational forces.
(C) Mach number: Represents the ratio of flow velocity to speed of sound.
(D) Weber number: Represents the ratio of inertial forces to surface tension forces.
Step 5: Conclusion.
Since the question asks for the ratio of inertial forces to viscous forces, the correct dimensionless number is the Reynolds number.