Continuity equation in fluid mechanics: foundational conservation principle The continuity equation for a control volume or along a streamline is fundamentally based on the conservation of which quantity?

Introduction / Context:
The continuity equation is one of the three cornerstone equations in fluid mechanics (with momentum and energy). It enforces that matter is neither created nor destroyed within a system.

Given Data / Assumptions:

• Continuum hypothesis holds (density is well-defined locally).
• Single-phase flow without phase change (for simple forms).

Concept / Approach:
The general, integral continuity equation states: rate of increase of mass within a control volume + net mass outflow across its control surface = 0. For steady, incompressible flow, it reduces to A1 V1 = A2 V2 in a single streamtube.

Step-by-Step Solution:

Verification / Alternative check:
Differential form for compressible flows: ∂ρ/∂t + ∇·(ρ V) = 0; still a statement of mass conservation.

Why Other Options Are Wrong:
Momentum and force relate to Newton’s second law and lead to the Navier–Stokes equations, not continuity. “None” is incorrect because mass conservation is explicit.

Common Pitfalls:
Using A V = constant where density varies significantly; in compressible flows, ρ A V = constant is the correct form.

Final Answer:
mass