Question

the drag characteristics of a prototype blimp 5 m in diameter and 60 m long are to be studied in a wind tunnel. if the speed of the prototype blimp through still air is 15 m/s, and if a 1/15 scale model is to be tested, what airspeed in the wind tunnel is needed for dynamically similar conditions? assume the same air pressure and temperature for both model and prototype.

Answer 1

To achieve dynamically similar conditions between the prototype blimp and the 1/15 scale model in the wind tunnel, an airspeed of 0.2 m/s is needed. This ensures that the ratio of airspeed to blimp size remains the same for both the prototype and the scale model.

To achieve dynamically similar conditions between the prototype blimp and the 1/15 scale model in the wind tunnel, we need to ensure that the ratio of airspeed to the size of the blimp remains the same for both.

1. Determine the ratio of airspeed to blimp size for the prototype:

The airspeed of the prototype blimp through still air is given as 15 m/s. The diameter of the prototype blimp is 5 m. So, the ratio of airspeed to blimp size for the prototype is 15 m/s / 5 m = 3 m/s per meter.

2. Determine the required airspeed for the scale model:

Since the scale model is 1/15 the size of the prototype, we need to maintain the same ratio of airspeed to blimp size. Therefore, we can set up the equation: required airspeed for the scale model / (1/15) = 3 m/s per meter.

3. Solve for the required airspeed for the scale model:

Simplifying the equation, we find that the required airspeed for the scale model is 3 m/s per meter * (1/15) = 0.2 m/s.