Fluid mechanics – force on immersed body and momentum change The force exerted by a moving fluid on an immersed body is directly proportional to the rate of change of momentum caused by the body's presence. This statement is called:

Introduction:
The question tests your understanding of how fluid forces on bodies are interpreted using momentum principles. In many hydrodynamics applications (impact of jets on plates, drag on bluff bodies, and flow deflection), the fluid's change in momentum due to a body gives the resisting force experienced by that body. This concept is often summarized in practice as Newton's law of resistance.

Given Data / Assumptions:

• Uniform stream of fluid interacts with a solid body.
• Measured force is the net effect required to change the fluid's momentum.
• Density and velocity may be considered steady for the interval of interest.

Concept / Approach:
Apply the momentum equation: the resultant force on a control volume equals the rate of change of linear momentum of the fluid across it. When a body is inserted, the fluid accelerates/decelerates and/or turns, creating momentum change. The equal and opposite reaction is the hydrodynamic force (resistance) on the body.

Step-by-Step Solution:
1) Choose a control volume enclosing the body.2) Evaluate inflow and outflow momentum flux: m_dot * V for each face.3) Compute net change of momentum vector between outlets and inlets.4) The required external force on the control volume equals this momentum change.5) The reaction on the body is equal and opposite, i.e., the resistance/drag.

Verification / Alternative check:
Classic jet-impact problems show force F proportional to m_dot * (V_out - V_in). If a jet of density rho and area A strikes and is brought to rest, F = rho * A * V * (V - 0) = rho * A * V^2 which is exactly the momentum change.

Why Other Options Are Wrong:

• Newton's law of motion: General mechanics statement, not the specific resistance formulation.
• Newton's law of cooling: Concerns heat transfer, not momentum/force.
• Newton's law of viscosity: Relates shear stress to velocity gradient in a viscous fluid, not overall momentum change on a body.

Common Pitfalls:
Confusing drag proportionality (sometimes ~ V^2 at high Reynolds number) with the broader momentum principle; mixing up viscosity law (shear in laminar layers) with overall resistance on a body.

Final Answer:
Newton's law of resistance