Question

A 1/10 scale of a blimp is tested in a wind tunnel under dynamically similar conditions. If the drag force on the model blimp is measured to be 1530 N, what corresponding force could be expected on the prototype? The air pressure and temperature are the same for both model and prototype.

Answer 1

To determine the expected drag force on a full-size blimp using a 1/10 scale model tested under dynamically similar conditions, square the scale factor and multiply by the model's drag force, resulting in an expected drag force of 153,000 N on the prototype.

Step-by-step explanation:

The question concerns the concept of dynamic similarity and the use of wind tunnel testing to predict the drag forces on full-scale prototypes based on scale model testing under similar conditions. Using a 1/10 scale model, if the drag force on the model blimp is 1530 N, the corresponding drag force on the actual blimp can be found using the square of the scale factor.

To calculate the force on the prototype, one must square the scale factor (because drag force is proportional to the square of linear dimensions for dynamically similar conditions) and then multiply by the force on the model:

• Scale factor: 1/10
• Scale factor squared: (1/10)^2 = 1/100
• Corresponding force on prototype: 1530 N × 100 = 153,000 N

Therefore, the expected drag force on the actual blimp would be 153,000 N, assuming that the air pressure and temperature remain consistent and that the drag coefficient is constant.