15.2.4. Concept of Similarity or Similitude

In fluid dynamics, when you conduct the experiments, we should have a relationship between full scale or the prototype and the flow with smaller ones which is the model. We need to have a relationship between that. If that is the conditions either you conduct the experiment with the full scale as we saw lot of experiment facilities for automobile industry they do, to tell full scale models okay, but many of the cases we cannot go for the full scale models like a dam which is in generally of having dimensions for 30 meters high, it is width of 40 meters, more than that, we cannot conduct these type of big experiment scale experiment in any big set up.

This chunk introduces the concept of similarity in fluid dynamics. It emphasizes the importance of having a relationship between full-scale prototypes and their smaller model counterparts when conducting experiments. For instance, full-scale experiments may be feasible and common in the automobile industry, but for large structures like dams with dimensions that are impractically large for physical testing, scaled-down models become necessary.

Think of a chef trying out a new recipe. Instead of making a huge cake immediately, the chef may opt to bake a smaller version first. This smaller version allows the chef to test the flavors and textures without the risk of wasting ingredients or time. Similarly, engineers use smaller models to evaluate designs before committing to full-scale constructions.

This 4 type of the similarities happens geometric similarity, kinematic similarity, dynamic similarity and the thermal similarity. So as we are not talking about energy, conservations much more in these lectures, we focus on these 3 similarity, geometry, kinematics and the dynamic similarity.

The chunk lists the four types of similarity that are important in fluid dynamics: geometric similarity, kinematic similarity, dynamic similarity, and thermal similarity. In this context, the lecture will primarily focus on geometric, kinematic, and dynamic similarities. Geometric similarity refers to the proportionality in shape between the model and the prototype, kinematic similarity refers to the relationship in motions (like velocity patterns), and dynamic similarity deals with the forces and pressures acting on the model and prototype.

Consider a scale model of a famous building, like the Eiffel Tower. The model maintains the same proportions and shapes (geometric similarity). If wind is blown over both the model and the actual tower and they experience similar flow patterns (kinematic similarity), the results of how each structure responds to the wind can be anticipated. If their structural responses—such as stresses and strains—also match effectively, we achieve dynamic similarity.

If you look it, this is what the prototypes, pole scale okay, that is what is the Boeing X48B but we cannot conduct this big scale experiments, what we do it we scale down it. We make it exactly the same in terms of a scale down models so that we keep all the angle, the flow direction are preserved.

This chunk discusses geometric similarity, which is the process of scaling down models to maintain the same proportions and angles as the prototypes. This preservation is critical in ensuring that the model accurately reflects the behavior of the full-scale version under similar conditions.

Imagine using a map to navigate. If the map is drawn to scale, a smaller representation will maintain the true distances and angles between roads. This allows us to use the map as a reliable guide, just like a scaled model serves to predict the behavior of a full-scale structure in tests.

When you talk about the kinematics what it says that we have the model, we have the prototypes, that this is the prototypes, this is the models, that means in the model and prototypes would have the same velocity factor, the stream lines patterns that means the velocity factors what we have the velocity direction that stream line and the models would have a scale factors.

Kinematic similarity refers to the relationship between the velocity patterns of the model and the prototype. This means the flow behavior in the model must match the flow behavior in the prototype in terms of speed and direction, ensuring that the same streamlines are represented in both cases.

Think about a race track and a tiny car racing game. Even though the toy cars are much smaller than actual race cars, they must be driven at speeds that reflect the same proportionality. If the toy car travels at a certain speed, it needs to correspond with the full-size car's speed to provide an accurate racing experience, paralleling kinematic similarity.

These similarity adjust when you have the 3 scale ratios, like the length, time and the force. So are the same or model and the prototypes. So the dynamic similarity happens not only this length and the time scale but also the force scale similar ratios will be there, what do you mean by that if you have a let you have a problems like this, you have a prototype, you have a gate.

Dynamic similarity encompasses the relationship between length, time, and force parameters between the model and the prototype. For dynamic similarity to hold true, all force vectors acting on both the model and prototype must be crisscrossed in a manner that accurately represents the real-world behavior of fluids around the structures. This allows predictions about how these structures will behave under operational conditions.

Imagine testing the strength of a bridge using a small model made from the same materials. If the forces acting on the small model (like weight, wind pressure, and vibrations) are accurately scaled down, engineers can extrapolate how the larger, full-size bridge will react under similar forces, ensuring safety and stability before actual construction.

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