Ideal (inviscid, incompressible) fluid behavior: Which fundamental relationship does an ideal flow strictly obey in continuum mechanics?

Introduction / Context:

An ideal fluid is inviscid (μ = 0) and incompressible. Recognizing which governing equations remain applicable helps in simplifying many hydraulics and aerodynamics problems, particularly when using Bernoulli’s theorem and potential flow theory.

Given Data / Assumptions:

• μ = 0 (no viscous stresses), ρ = constant (incompressible).
• Continuum hypothesis holds; body forces and pressure act normally.

Concept / Approach:

All real flows respect conservation laws. For an ideal fluid, the viscous constitutive relation (Newton’s law of viscosity) is irrelevant. However, mass conservation — the continuity equation — must be satisfied in any flow. Momentum conservation (Euler’s equations) also apply, but the question asks what an ideal flow “obeys” distinctively compared with real-fluid constitutive behavior.

Step-by-Step Solution:

Verification / Alternative check:

In potential flow (ideal), velocity field derives from a scalar potential satisfying Laplace’s equation with ∇·V = 0 — a direct expression of continuity.

Why Other Options Are Wrong:

• Newton’s law of viscosity characterizes viscous fluids, not ideal ones.
• F = m a is true but not a constitutive relation specific to ideal flow; it governs dynamics in general.
• “Dynamic viscosity law” reiterates viscous behavior.
• Bernoulli without continuity is incomplete; continuity is essential.

Common Pitfalls:

• Assuming Bernoulli alone characterizes ideal flow; mass conservation still constrains velocity fields and discharge.

Final Answer:

Continuity equation (mass conservation)