Question

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 ?​

Answer 1

Answer:

The model ship should be towed at an velocity of 2m/s

Explanation:

Given data.

Prototype

Length of the ship=100m

Velocity with which it travels=10m/s

Model

To find length of the model ship,we use scale ratio.

Scale ratio is given as 1:25

Therefore

$\frac{L_{m}}{L_{p}} = \frac{1}{25}$

Substituting given data,we get

$L_{m} = \frac{1}{25} \times 100 = 4m$

Similarly to find velocity we use a non dimensional number called froude number

$Fr = \frac{v {}^{2} }{gL}$

Considering dynamic similarity,we get

$(\frac{v {}^{2} }{gL} ) _{m} = (\frac{v {}^{2} }{gL} ) _{p}$

Substituting given values,we get

$v _{m} {}^{2} = 4 \times \frac{10 {}^{2} }{100} = > v _{m} = 2ms {}^{ - 1}$

Therefore,The model ship should be towed at an velocity of 2m/s

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