What is the ratio condition for geometric similarity between a prototype and a model?

Conditions

• The compared objects must have corresponding linear dimensions.
• Each ratio pairs a prototype length with the matching model length.
• Applies to corresponding linear dimensions of two objects or domains.

Reasoning, step by step

1. Introduce a prototype-like larger box and identify its linear dimensions.
2. Introduce a smaller model box with corresponding dimensions.
3. State the geometric-similarity condition as equality of corresponding length ratios.

Example

The board shows the geometric-similarity relation $\frac{B}{b}=\frac{H}{h}=\frac{W}{w}$. A large rectangular prism is labeled with uppercase dimensions and a smaller prism is labeled with corresponding lowercase dimensions.

Common misconceptions

• Scaling one dimension independently: thinking a model can shrink only one dimension while leaving the others on a different scale.
• Assuming that geometric similarity alone is sufficient for a valid fluid-mechanics model.

Watch the explanation

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