When the ratios of all corresponding forces acting at corresponding points in a model and its prototype are equal, what type of similarity exists between them? Choose the most appropriate classification.

Introduction:
Engineering similarity is categorized into geometric (shape), kinematic (motion), and dynamic (forces). For accurate force and performance prediction, matching the force ratios or, equivalently, the relevant dimensionless numbers is essential.

Given Data / Assumptions:

• Model and prototype are compared under conditions where multiple forces act (inertia, pressure, viscous, gravity, surface tension).
• Ratios of corresponding forces are stated equal.

Concept / Approach:
Equal ratios of corresponding forces define dynamic similarity. This implies the equality of the relevant dimensionless parameters (Reynolds, Froude, Euler, Weber, Mach as applicable). Geometric or kinematic similarity alone cannot guarantee correct scaling of loads or performance.

Step-by-Step Solution:
1) Identify that the condition given is “equal force ratios”.2) Map this to dynamic similarity by definition.3) Note that geometric similarity concerns shapes; kinematic similarity concerns velocity and acceleration fields.4) Therefore, the correct classification is dynamic similarity.

Verification / Alternative check:
In turbine model testing, matching Re and specific speed ensures force fields scale correctly; this is a dynamic similarity requirement.

Why Other Options Are Wrong:
Geometric: needs similar shapes but says nothing about forces.

Kinematic: matches motion patterns but not force magnitudes.

None/geometric+kinematic only: incomplete without force equivalence.

Common Pitfalls:
Equating geometric similarity with complete similarity; overlooking dominant force regimes (e.g., Froude vs Reynolds) for the application.

Final Answer:
dynamic similarity