A ship whose hull length is 100 m is to travel at 10 m/sec. For dynamic similarity, at what velocity should a 1:25 model be towed through water ? A. 10 m/sec B. 25 m/sec C. 2 m/sec D. 50 m/sec

10 m/sec
25 m/sec
2 m/sec
50 m/sec

The correct answer is C. 2 m/sec.

The Froude number is a dimensionless number that is used to compare the flow of fluids around two objects of different sizes. It is defined as:

$Fr = \frac{v}{\sqrt{gL}}$

where $v$ is the velocity of the object, $g$ is the acceleration due to gravity, and $L$ is a characteristic length of the object.

For dynamic similarity, the Froude numbers of the ship and the model must be equal. Therefore, the velocity of the model must be:

$v_m = \sqrt{\frac{g_m L_m}{g_L L_L}} v_L$

where $g_m$ and $g_L$ are the accelerations due to gravity at the model and ship locations, respectively, and $L_m$ and $L_L$ are the characteristic lengths of the model and ship, respectively.

In this case, $g_m = g_L$ and $L_m = \frac{1}{25} L_L$. Therefore, the velocity of the model is:

$v_m = \sqrt{\frac{g_L L_L}{25 g_L L_L}} v_L = \frac{1}{5} v_L = 2 \text{ m/sec}$

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