A rectangular pontoon has a width of 6 m, a length of 12 m, and a draught of 1.5 m in fresh water (density = 1000 kg / m³). Its draught in sea water having density of 1025 kg / m³ is

Concept:

The draught is the height of body which is submerged in water or any other fluid.

Buoyancy Force, F_B = weight of fluid displaced by body

F_B = Submerged volume  of body × unit weight of fluid in which the body is submerged

F_B = V_sub × γ_fluid

Now

By principal of Buoyancy

When rectangular pontoon submerged in fresh water, then

Weight of body = F_B = V_{sub, fresh} × f_{resh water}

When rectangular pontoon submerged in sea water, then

Weight of body = F_B = V_{sub, sea} × γ _{sea water}

From 1 and 2 it can be inferred that

V_{sub, fresh} × f_{resh water}     = V_{sub, sea} × γ _{sea water}

Calculation:

Given,

Draught in fresh water = 1.5 m

ρ_{fresh water} = 1000 kg/m³

ρ_{sea water} = 1025 kg/m³

Let h be the draught in sea water, then

1.5 × 6 × 12 × 1000 × 9.81  = h × 6 × 12 × 1025 × 9.81

∴ h = 1.463 m