Question

A ship is 100m long and designed to cruise at 10m/s. The ship is to be tested in a tow tank with a model 2 m long. What should be the appropriate tow velocity?

Answer 1

Answer: the appropriate tow velocity for the 2-meter long model ship is approximately 1.416 m/s

Step-by-step explanation:

To determine the appropriate tow velocity for the model ship, we can use the concept of dynamic similarity, which involves maintaining a constant Froude number for both the actual ship and the model ship. The Froude number (Fr) is a dimensionless number used in fluid mechanics to compare the influence of gravity and inertia forces in fluid flow. It is defined as:

Fr = V / √(gL)

Where:
Fr = Froude number
V = velocity of the ship or model
g = acceleration due to gravity (approximately 9.81 m/s²)
L = length of the ship or model

Since we want the Froude numbers to be the same for both the actual ship and the model ship, we can set up the following equation:

Fr_ship = Fr_model

For the actual ship:
Length (L_ship) = 100 m
Velocity (V_ship) = 10 m/s

For the model ship:
Length (L_model) = 2 m
Velocity (V_model) = unknown

Now, we can set up the equation:

(V_ship / √(g * L_ship)) = (V_model / √(g * L_model))

Plug in the given values:

(10 / √(9.81 * 100)) = (V_model / √(9.81 * 2))

Now, we can solve for V_model:

(10 / √981) = (V_model / √19.62)

(10 / 31.30495) = (V_model / 4.43041)

0.31961 = V_model / 4.43041

V_model ≈ 1.416 m/s

So, the appropriate tow velocity for the 2-meter long model ship is approximately 1.416 m/s to maintain dynamic similarity with the actual ship.