Question

A ships model of scale 1: 100 had a wave resistance of 1 N at its design speed. The corresponding wave resistance (in N) in prototype will be -

• A. 1000
• B. 10000
• C. 1000000
• D. 1000

Answer 1

The correct option is C 1000000

For ship model, both Reynold's law and Froude law should be satisfied because ship is a partially submerged body. Hence, drag experienced by ship consist of-

• The wave resistance, which is resistance offered by waves on the free surface.
• Viscous resistance which is offered by water on surface of contact of ship with water.

$\text{So,}(R_e{)}_r=\frac{{\rho }_r{V}_r{L}_r}{{\mu }_r}=1$

$[F_e{]}_r=\frac{V_r}{\sqrt{L_r}}=1$

$\text{Hence,}\frac{{\rho }_r\sqrt{L_r}.L_r}{{\mu }_r}=1$

$\frac{L_r^{\frac{3}{2}}}{v_r}=1$

$\text{Wave resistance,}{F}_r={\rho }_r{L}_r^3$

$\frac{F_P}{F_m}={\left(\frac{L_P}{L_m}\right)}^3(\rho \text{is constant)}$

For a model of scale of 1:100

$L_P=100L_m$

$F_P=F_m{\left(\frac{100L_m}{L_m}\right)}^3=1\times (100{)}^{3}N=1000000N$