Effect of change of density when the displacement is constant

When a ship moves from water of one density to water of another density, without there being a change in her mass, the draft will change.

Mass = Volume x Density

The effect on box-shaped vessels 

New Volume  =  Old  density         or     New draft   =   Old density
Old Volume        New density                 Old draft         New density

sample 1:
A box-shaped vessel floats at mean draft of 2.1 metres, in dock water of density 1020 kg/m3. Find the mean draft for tha same mass displacement in salt water of density 1025 kg/m3.

answer: New draft = 2.09 metres (you can try the above formula)

sample 2:
A box-shaped vessel float upright on an even keel as shown in fresh water of density 1000 kg/m3 and the CoB is 0.50 m above the keel. Find the height of the CoB above the keel when the vessel is floating in salt water of density 1025 kg/m3.

CoB of Box shaped vessel :  KB = 0.5 draft

Answer:
In fresh water:   KB=0.5m and since KB = 0.5draft, then draft = 1 m

In salt water :  New draft     =   Old draft x (Old density / New density)
                                              =   1 x 1000/1025
                                              =    0.976 m
                        New KB        =   0.5 new draft
                                              =   0.488 ~0.49 m

 The effect on box-shaped vessels 

 New displacement  =  Old Displacement

New volume x New density  =   Old volume x Old density

New volume  =  Old density

   Old volume       New density

FWA (Fresh Water Allowance) = number of millimeters by which the mean draft changes when a ship passes from salt water to fresh water or vice versa, whilst floating at the loaded draft.

FWA (in mm) = Displacement (W in tonnes) / (4 x TPC)

Dock Water Allowance = FWA (1025 - density of Dock Water) /25

sample 3:A ship is loading in dock water of density 1010 kg/m3 FWA=150 mm. Find the change in draft on entering salt water.

answer:

Let x = the change in draft in mm, then:

x / FWA = (1025 - 1010) / 25

           x  = 150 x (15/25)

           x  =  90 mm

Draft will decrease by 90 mm, i.e. 9 cm