Dimensionless groups – force ratios in fluid flow The ratio of inertia force to viscous force in a flow is known as:

Introduction:
Dimensionless numbers help predict similarity and regimes in fluid mechanics. This question asks you to identify which group compares inertia effects with viscous effects.

Given Data / Assumptions:

• Characteristic velocity V, length L (or diameter D), density rho, viscosity mu.
• Internal or external flows where both inertia and viscosity matter.
• Steady characteristic scaling.

Concept / Approach:
Reynolds number Re is defined as Re = (rho * V * L) / mu. It compares inertia force scale (rho * V^2 * L^2 over area) to viscous force scale (mu * V * L over area), leading to the ratio Re. Other numbers compare different effects (gravity, surface tension, pressure).

Step-by-Step Solution:
1) Identify target ratio: inertia / viscous.2) Recall Re = rho * V * L / mu.3) Conclude that Reynolds number is the required dimensionless group.

Verification / Alternative check:
Laminar–turbulent transition and drag correlations widely use Re, confirming its role as inertia–viscous comparator.

Why Other Options Are Wrong:

• Froude number: inertia / gravity (V / sqrt(gL)).
• Weber number: inertia / surface tension (rho * V^2 * L / sigma).
• Euler number: pressure / inertia (Δp / (0.5 * rho * V^2)).

Common Pitfalls:
Mixing up which physical effect is in the denominator; memorize each group’s comparison for clarity.

Final Answer:
Reynolds number