Question

A 1/4th scale model of a new automobile design is tested in a wind tunnel. The Reynolds number of the model is the same as that of the full-scale prototype. Assuming the model and prototype are exposed to the same air conditions, the velocity in the wind tunnel is then:

A. One-fourth of the velocity of the full-scale prototype.
B. Half of the velocity of the full-scale prototype.
C. The same as the velocity of the full-scale prototype.
D. Four times the velocity of the full-scale prototype.

Answer 1

To maintain the same Reynolds number, the velocity in the wind tunnel for the 1/4th scale model would need to be four times that of the full-scale prototype.

Step-by-step explanation:

The question of what velocity a 1/4th scale model of an automobile in a wind tunnel would need to achieve the same Reynolds number as the full-scale prototype assumes that the model and prototype are exposed to the same air conditions.

The Reynolds number is a dimensionless number used in fluid mechanics to predict flow patterns in different fluid flow situations and is directly related to fluid velocity, characteristic length (such as diameter or length), fluid density, and viscosity.

Since the scale of the model is 1/4th that of the prototype, maintaining the same Reynolds number would require the velocity of the wind tunnel to be adjusted. Specifically, the velocity must be four times that of the prototype (Option D) because the characteristic length in the Reynolds number equation is one-fourth for the model, so the velocity must be inversely scaled.