The geometrical similarity between model and prototype is achieved by using the same model scale throughout.

Achieving geometrical similarity between a model and a prototype is essential in many engineering and scientific applications. Geometrical similarity refers to the similarity in shape and proportions between the model and the prototype. This similarity allows for accurate testing and analysis of the prototype's behavior based on the behavior observed in the model.

There are several ways to achieve geometrical similarity, but the correct answer in this case is option 'B', using the same model scale throughout. Let's understand why this is the correct answer:

1. Understanding model scale:
- Model scale refers to the ratio between the dimensions of the model and the corresponding dimensions of the prototype.
- For example, if the model is 1/10th the size of the prototype, the scale would be 1:10.
- The model scale determines how much smaller or larger the model is compared to the prototype.

2. Importance of using the same model scale:
- To achieve geometrical similarity, it is crucial to use the same model scale throughout the model.
- Using different scales for horizontal and vertical dimensions, as mentioned in option 'A', would result in a distorted representation of the prototype.
- If the model scale is not consistent, the proportions and shapes of the prototype would not be accurately represented in the model, leading to inaccurate testing and analysis.

3. Consistency in model scale:
- By using the same model scale throughout, the model accurately represents the dimensions, proportions, and shapes of the prototype.
- This consistency ensures that the behavior observed in the model is a reliable representation of the behavior that would occur in the prototype.

4. Advantages of using the same model scale:
- Using the same model scale throughout simplifies the testing and analysis process.
- It allows for direct comparisons between the model and the prototype, making it easier to interpret the results.
- It also facilitates the extrapolation of the model's findings to the prototype, allowing engineers and scientists to make accurate predictions about the prototype's behavior.

In conclusion, achieving geometrical similarity between a model and a prototype is crucial for accurate testing and analysis. Using the same model scale throughout ensures that the dimensions, proportions, and shapes of the prototype are accurately represented in the model, enabling reliable predictions about the prototype's behavior.