A 1/150 scale model is to be usedin a towing tank to study the water motion near the bottom of a shallow channel as a large barge passes over. (See Video V7.16.) Assume that the model is operated in accordance with the Froude number criteria for dynamic similitude. The prototype barge moves at a typical speed of 15 knots. (a) At what speed (in ft/s) should the model be towed

Respuesta :

Answer:

The speed will be "3.58 ft/s". The further explanation is given below.

Explanation:

Number of knots

= 15

For the similarity of Froude number:

⇒  [tex]\frac{V_{m}}{\sqrt{g_{m}l_{m}} }=\frac{V}{\sqrt{gl} }[/tex]

Here,

[tex]l = length[/tex]

[tex]g_{m}=g[/tex]

⇒  [tex]\frac{V_{m}}{V}=\sqrt{\frac{l_{m}}{l} }[/tex]

    [tex]V_{m}=\sqrt{\frac{1}{50} }\times number \ of \ knots[/tex]

         [tex]=\sqrt{\frac{1}{50}}\times 15[/tex]

         [tex]=2.12 \ knots[/tex]

Now,

⇒  [tex]1 \ knots=0.514\times 3.281[/tex]

                 [tex]=1.69 \ ft/s[/tex]

So that,

⇒  [tex]V_{m}=2.12\times 1.69[/tex]

          [tex]=3.58 \ ft/s[/tex]