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: Role of dimensionless numbers. 
In fluid mechanics, dimensionless numbers compare the relative importance of different forces acting within a flow. They are essential for analyzing flow regimes and for establishing similarity between model and real systems.

Step 2: Meaning of the Reynolds number.
The Reynolds number specifically compares the tendency of a fluid to keep moving due to inertia with the tendency to resist motion due to viscosity. It is expressed as:

\[ Re = \frac{\rho V L}{\mu} \]

where \(\rho\) is the fluid density, \(V\) is the characteristic velocity, \(L\) is the characteristic length, and \(\mu\) is the dynamic viscosity.

Step 3: Interpretation of Reynolds number.
- A large Reynolds number means inertial effects dominate, which often leads to turbulent flow.
- A small Reynolds number means viscous effects dominate, resulting in smooth, laminar motion.

Step 4: Checking the given choices.
(A) Reynolds number – directly represents inertial forces divided by viscous forces.
(B) Froude number – compares inertial forces with gravitational forces.
(C) Mach number – compares flow velocity with the speed of sound.
(D) Weber number – compares inertial forces with surface tension forces.

Step 5: Final conclusion.
The dimensionless number that measures the ratio of inertial forces to viscous forces is the Reynolds number.

\[ \boxed{\text{Reynolds number}} \]