Question

A 1:20 scaled model of a surface ship is tested in a towing tank. The model is towed at 3 m/s and drag force measured is 10 N. The velocity of the prototype and the drag force acting on the prototype, respectively, are ________________ m/s and ________________ kN.

• A. 60.4 and 80
• B. 13.4 and 80
• C. 13.4 and 4
• D. 60.4 and 4

Hint:

In ship model testing, velocity scales with \( \sqrt{\lambda} \) and force scales with \( \lambda^3 \) under Froude similarity.

Answer 1

The Correct Option is B

This is a case of hydrodynamic similarity using Froude scaling. The length scale ratio is \( \lambda = 20 \).
Step 1: Velocity scaling.
Velocity in Froude similarity scales as: \[ V_p = V_m \sqrt{\lambda} \] Substituting, \[ V_p = 3 \times \sqrt{20} = 3 \times 4.472 = 13.4\ \text{m/s} \]
Step 2: Drag force scaling.
Drag force scales as: \[ F_p = F_m \lambda^3 \] \[ F_p = 10 \times 20^3 = 10 \times 8000 = 80,000\ \text{N} = 80\ \text{kN} \]
Step 3: Conclusion.
Prototype velocity = 13.4 m/s, Prototype drag force = 80 kN.