37.NA March 2019 Q.6(B)

A box shaped vessel, 50 metres long X 10 metres wide, floats in salt water on an even keel at a draft of 4 metres. A centre line longitudinal watertight bulkhead extends from end to end and for the full depth of the vessel. A compartment amidships on the starboard side is 15 metres long and contains cargo with permeability 30%. Calculate the list if this compartment is bilged. KG = 3m

UNDER PROGRESS

Given

L =  50 m
B = 10 m
d1 = 4 m
l = 15 m
b = 10/2 = 5 m (centre line bulkhead)
μ = 30 %
KG = 3 m

To find

List of compartment if bilged.

Solution

If the compartment is bilged, buoyancy is lost and must be replaced by increasing the draught. 

The volume of lost buoyancy = Volume of compartment upto water line.

The volume of compartment = l x B x d1

But permeability is given as 30 %

So Volume lost buoyancy = 0.3 x 15 x 5 x 4

                                         = 90 m3

Now we need to find area of intact water plane = Area where buoyancy is not lost

Area of intact water plane = Total area of ship - Area of compartment bilged 

                                         = (L x B) - ((l x b x μ) 

                                         = (50 x 10) - (15 x 5 x 0.3)

                                         = 477.5 m2

As we know that increase in draught = Vol of lost buoyancy / Area of intact water plane

                                                           = 90 / 477.5

                                                           = 0.19 m

New draught d2 = 4 + 0.19 = 4.19 m

As the draught changes COB also changes.

Shift in COB = (Area of compartment bilged x B/4 ) / Area of intact water plane

                     = (l x b x μ x B/4) / 477.5

                     = (15 x 5 x 0.3 x 10/4 ) / 477.5

            BB1  = 0.12 m