The correct answer is option ‘B’ which is the Reynolds number. The Reynolds number is a dimensionless number used in fluid mechanics to characterize the flow of a fluid. It is defined as the ratio of inertia force to viscous force and is named after Osborne Reynolds, a British engineer who first introduced the concept.

In order to understand why the Reynolds number represents the ratio of inertia force to viscous force, let's break down these terms and their significance.

Inertia Force:
- Inertia force is the force exerted on a fluid due to its mass and acceleration.
- It is a measure of the fluid's resistance to changes in motion.
- Inertia force is directly proportional to the density of the fluid, the velocity of the fluid, and the cross-sectional area of the flow.
- It represents the tendency of a fluid to keep moving in the absence of any external forces.

Viscous Force:
- Viscous force is the force exerted on a fluid due to the internal friction between fluid layers.
- It is a result of the fluid's viscosity, which is a measure of its resistance to flow.
- Viscous force is directly proportional to the viscosity of the fluid, the velocity gradient across the flow, and the cross-sectional area of the flow.
- It represents the resistance of a fluid to flow and the dissipation of mechanical energy into heat.

Reynolds Number:
- The Reynolds number (Re) is defined as the ratio of inertia force to viscous force.
- Mathematically, it is given by the formula Re = (ρ * V * L) / μ, where ρ is the density of the fluid, V is the velocity of the fluid, L is a characteristic length scale, and μ is the dynamic viscosity of the fluid.
- The Reynolds number represents the relative importance of inertial forces to viscous forces in a fluid flow.
- A low Reynolds number indicates that viscous forces dominate, resulting in laminar flow (smooth and ordered flow).
- A high Reynolds number indicates that inertial forces dominate, resulting in turbulent flow (chaotic and irregular flow).

In summary, the Reynolds number is a dimensionless quantity that provides insight into the flow characteristics of a fluid. It represents the ratio of inertia force to viscous force and helps determine whether a fluid flow is laminar or turbulent.