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

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  1. 1.04 m
  2. 1.24 m
  3. 1.46 m
  4. 1.50 m

Answer (Detailed Solution Below)

Option 3 : 1.46 m
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Detailed Solution

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Concept:

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

Buoyancy Force, FB = weight of fluid displaced by body

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

FB = Vsub × γfluid

Now

By principal of Buoyancy

When rectangular pontoon submerged in fresh water, then

Weight of body = FB = Vsub, fresh × fresh water

When rectangular pontoon submerged in sea water, then

Weight of body = FB = Vsub, sea × γ sea water

From 1 and 2 it can be inferred that

Vsub, fresh × fresh water     = Vsub, sea × γ sea water

Calculation:

Given,

Draught in fresh water = 1.5 m

ρfresh water = 1000 kg/m3

ρsea 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

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