Question

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

Answer 1

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

Step-by-step explanation:

Number of knots

= 15

For the similarity of Froude number:

⇒
`\frac{V_(m)}{\sqrt{g_(m)l_(m)} }=(V)/(√(gl) )`

Here,

`l = length`

`g_(m)=g`

⇒
`(V_(m))/(V)=\sqrt{(l_(m))/(l) }`

`V_(m)=\sqrt{(1)/(50) }* number \ of \ knots`

`=\sqrt{(1)/(50)}* 15`

`=2.12 \ knots`

Now,

⇒
`1 \ knots=0.514* 3.281`

`=1.69 \ ft/s`

So that,

⇒
`V_(m)=2.12* 1.69`

`=3.58 \ ft/s`