Model–Prototype Similarity — When All Linear Dimension Ratios Match If the ratios of all corresponding linear dimensions between a model and its prototype are equal (constant scale factor) and shapes are identical, what type of similarity is satisfied?

Introduction:
Engineering models are built to predict prototype behavior. The first level of similarity required is geometric similarity, which ensures that the model is a scaled replica of the prototype so that corresponding points and angles are well-defined.

Given Data / Assumptions:

• All linear dimensions in the model maintain a constant ratio to the prototype (same scale factor in x, y, z).
• Angles and shape proportions are preserved.

Concept / Approach:
Similarity is categorized as geometric, kinematic, and dynamic. Geometric similarity concerns only size and shape. Kinematic adds equality of non-dimensional velocities/accelerations; dynamic requires equality of non-dimensional forces (e.g., Reynolds, Froude, Euler numbers) in addition to the first two.

Step-by-Step Solution:
Check dimension ratios: all constant ⇒ shapes are identical up to scale.No statement about velocity/acceleration fields ⇒ kinematics not guaranteed.No statement about force ratios or dimensionless numbers ⇒ dynamics not guaranteed.Therefore, only geometric similarity is assured.

Verification / Alternative check:
Wind-tunnel and hydraulic-lab practices explicitly distinguish geometric similarity before targeting kinematic/dynamic similarity via matched dimensionless groups.

Why Other Options Are Wrong:

• Kinematic similarity needs velocity/acceleration ratios equal.
• Dynamic similarity needs force ratios (dimensionless groups) equal.
• None of these: incorrect because geometric similarity is indeed satisfied.

Common Pitfalls:
Assuming geometric similarity automatically implies correct forces or flows; it does not.

Final Answer:
geometric similarity