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Chapter 7: Problem 51

The fluid dynamic characteristics of an airplane flying \(240 \mathrm{mph}\) at \(10,000 \mathrm{ft}\) are to be investigated with the aid of a 1: 20 scale model. If the model tests are to be performed in a wind tunnel using standard air, what is the required air velocity in the wind tunnel? Is this a realistic velocity?

Short Answer

Expert verified
The required air velocity in the wind tunnel should be 4800 mph according to dynamic similitude between the model and the airplane. But in reality, this is not a feasible speed.

Step by step solution

01

Understand the given information

A 1:20 scale model of an airplane is to be tested in a wind tunnel. This implies that the model is 20 times smaller than the actual plane. The real plane is said to travel at a speed of 240 mph at an altitude of 10,000 ft.
02

Understand scaling

When using models, the conditions of the model should match with that of the actual object under similar conditions. This is referred to as dynamic similitude. Here, as the model is 1/20th the size of the actual plane, the speed of the wind in the tunnel should be 20 times faster as per dynamic similitude.
03

Calculate the wind tunnel velocity

Given that the speed of the real plane is 240 mph, multiply this speed by the scaling factor to get the velocity of the wind in the tunnel. So, the required wind tunnel velocity \(V = 20 * 240 \mathrm{mph} = 4800 \mathrm{mph}\).
04

Evaluate the feasibility of the obtained velocity

4800 mph is a very high speed for a wind tunnel. So, in practicality, reaching this speed can be challenging and hence, this is not a realistic velocity for the wind tunnel.

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