Question

Explain the concept of types of similarities between model and prototype. What do you mean by distorted model? What are its advantages?

      It is proposed to design a ship. The proposed hip (prototype) is having a length of 150 m and a wetted surface area of 2000 m² with a speed of 40 km/h. A model of 1 : 20 is to be tested in the laboratory at a velocity corresponding to the wave resistance.

      The total drag of the model is 50 N. Determine the following:                                     15+25

1. Wave resistance drag of the model
2. Wave resistance drag of the prototype
3. Friction drag of the prototype

Give,

Friction drag, $R_f=\frac{1}{2}C_D \rho A V^2$

Where

A = Wetted surface area

C_D = Average friction drag coefficient

= $\frac{0.074}{(Re)^{1/4}}$ for Re =2 x 10⁷

= $\frac{0.01}{(Re)^{1/5}}$ for Re > 2 x 10⁷

_{$\rho_{model}$}= 100 kg/m³

_{$\nu_{model}$}=1.110 ´ 10^–6 m²/s

_{$\rho_{prototype}$}= 1020 kg/m³

_{$\nu_{prototype}$}= 1.125 ´ 10^–6 m²/s