Dynamics to statics transformation – name the principle A moving fluid mass can be analyzed at a notional static equilibrium by applying an imaginary inertia force equal in magnitude and opposite in direction to the real accelerating force. This statement is called:

Introduction:
Converting a dynamics problem into an equivalent statics problem by introducing inertia forces is a classic technique in mechanics and fluid dynamics. The question asks for the name of the principle embodying this equivalence for accelerating systems.

Given Data / Assumptions:

• Finite mass of fluid undergoes acceleration.
• We conceptually add an inertia force equal and opposite to m * a.
• Analysis is then performed as if forces sum to zero (static equilibrium).

Concept / Approach:

D’Alembert’s principle reformulates Newton’s second law as an equilibrium condition by adding the fictitious inertia force F_inertia = − m * a to the system’s external forces. In fluid mechanics, this is used in accelerating containers (e.g., tilting free surfaces), rotating systems, and unsteady Bernoulli derivations, enabling static-like pressure field computations in non-inertial frames.

Step-by-Step Solution:

Verification / Alternative check:

Applications include deriving pressure fields in linearly accelerated tanks (free surface tilts with tan(theta) = a/g) and rotating fluids (parabolic free surface), both obtained via D’Alembert’s construct.

Why Other Options Are Wrong:

Pascal / Archimedes / Bernoulli: Respectively deal with pressure transmission, buoyancy, and mechanical energy conservation, not the statics–dynamics transformation.None of these: Incorrect because the statement exactly matches D’Alembert’s principle.

Common Pitfalls:

Calling the method “fictitious forces” and assuming they are arbitrary. They are systematic constructs that allow equilibrium methods in accelerating frames.

Final Answer:

D'Alembert's principle