Topic: Fluid Mechanics
The model of a propeller 3m diameter, cruising at 10 m/sec in air, is tested in a wind tunnel on a 1:10 scale model. If thrust of 50N is measured on the model at 5 m/sec wind speed, then thrust on prototype will be
- A. 20000 N
- B. 2000 N
- C. 5000 N
- D. 500 N
Answer: A. 20000 N
Explanation: Using aerodynamic scaling laws, the ratio of forces between the model and the prototype depends on velocity and diameter squared: $\frac{F_M}{F_P} = (\frac{v_M}{v_P})^2 (\frac{d_M}{d_P})^2$. Substituting $v_M = 5$, $v_P = 10$, and the scale ratio $\frac{d_M}{d_P} = \frac{1}{10}$, we get $\frac{F_M}{F_P} = (\frac{5}{10})^2 \times (\frac{1}{10})^2 = \frac{1}{4} \times \frac{1}{100} = \frac{1}{400}$. With $F_M = 50$ N, $F_P = 400 \times 50 = 20000$ N.