Question

You want to test the aerodynamics of a new arquitectural design by building a model and putting it inside a wind tunnel. The actual building will be 37.0 m tall and subjected to wind speeds of 11 m/s. If the model is 2.1 m tall, what should be the speed in the wind tunnel to accurately model the winds around the building?

Answer 1

To simulate the wind around a full-sized building at 11 m/s wind speed with a model that is 2.1 m tall, the wind tunnel speed should be approximately 194 m/s, based on geometric similarity and dynamic scaling.

Step-by-step explanation:

To determine the appropriate wind tunnel speed for the model to accurately simulate the wind conditions of the actual building, we can use the concept of geometric similarity in combination with Reynolds number, assuming the flow is similar in both cases and the model is a good representation of the building. Since we want the aerodynamic forces to scale correctly, we can compare the two scenarios using the formula for dynamic similarity which states that the wind speeds should be in the same ratio as the linear dimensions of the model and the actual building:

V_model / V_building = L_building / L_model

Given:

L_building = 37.0 m (height of the actual building)

L_model = 2.1 m (height of the model)

V_building = 11 m/s (wind speed for the actual building)

We need to find V_model, the wind speed for the model. Substituting the known values into the formula, we obtain:

V_model = (L_building / L_model) * V_building
V_model = (37.0 m / 2.1 m) * 11 m/s
V_model = 17.619 * 11 m/s
V_model ≈ 194 m/s

Therefore, to accurately model the wind speeds around the building, the wind tunnel speed for the model should be approximately 194 m/s.