Question

In a 1:100 scale model of a harbour, the time which will correspond to the prototype tidal period of 12 hours will be ............

• A. 0.12 hour
• B. 1.2 hours
• C. 12 hours
• D. 120 hours

Hint:

In Froude similarity, time in the model is proportional to the square root of the length scale ratio: \[ \frac{T_m}{T_p} = \sqrt{\frac{L_m}{L_p}} \] Always apply this when dealing with free-surface flows like tides or waves.

Answer 1

The Correct Option is B

In hydraulic models, for Froude model law, time scale ratio is given by: \[ \frac{T_m}{T_p} = \sqrt{\frac{L_m}{L_p}} = \sqrt{\frac{1}{100}} = \frac{1}{10} \] Hence, the model time \( T_m \) corresponding to prototype time \( T_p = 12 \) hours is: \[ T_m = \frac{1}{10} \times 12 = 1.2 \text{ hours} \] \[ \boxed{1.2 \text{ hours}} \]