A ship of 5000 tonne displacement has a rectangular double bottom tank 9 m wide and 12 m long, half full of sea water. Calculate the virtual reduction in metacentric height due to free surface.

A ship of 5000 tonne displacement has a rectangular double bottom tank 9 m wide and 12 m long, half full of sea water. Calculate the virtual reduction in metacentric height due to free surface.

Reference: REED'S NAVAL ARCHITECTURE FOR MARINE ENGINEERS (4^th edition), Exercise – 5.9

 

Solution:

I = 1/12 * LB³

  = 1/12 * 12* 9³

  = 729

Here, ρ_f = ρ_w

∇ = 5000/1.025

Free surface effect = ρ_f * I/ ρ_w * ∇

                                     = 729 * 1.025/5000

                                     = 0.149 m