Question

In $\frac{1}{{100}^{th}}$ model of a harbour, what length of the time should correspond to prototype tidal time period of 12.4 hrs?

• A. 1.24 min
• B. 40 min
• C. 75 min
• D. 12.4 min

Answer 1

The correct option is C 75 min

Tide is a gravitational phenomenon. Hence, Froude number must be same between model and prototype for their dynamical similarity

i.e
${\left(\frac{V}{\sqrt{gL}}\right)}_m={\left(\frac{V}{\sqrt{gL}}\right)}_p$

i.e
$\frac{V_m}{V_P}=\sqrt{\frac{L_m}{L_p}}$

$V_r=\sqrt{L_r}$

$T_r=\frac{L_r}{V_r}=\frac{L_r}{\sqrt{L_r}}=\sqrt{L_r}$

$\therefore \frac{T_m}{T_p}=\sqrt{\frac{1}{100}}$
i.e

$T_m=\frac{12.4}{10}=1.24hrs=75min$