Q & A – Fluid Mechanics – Buoyancy – Q.7

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Q & A – Fluid Mechanics – Buoyancy – Q.7

Q & A – Fluid Mechanics – Buoyancy – Q.7

Question No.7

A barge is deployed in sea water (S.G = 1.03). The dimensions of the barge are as shown in the figure. The total weight of the barge is 32 tons. Check if the barge will float or sink and check its stability in both directions.

Given :

  • γseawater=1.03tonm3
  • W=32  tons

Solution :

To check if the barge will float or sink :

γbarge=wV

γbarge=32383=0.444tonm3

Since γbarge<γseawater

Therefore , the barge will float !

To check the stability :

First, we should get the height of the immersed part of the barge h :

W=FB

32ton=γseawaterAh

32=1.03(83)h

h=1.29  m

Second , check the stability of the floating body :

MG=IminVimmersedGB

Vimmersed=Ah

Vimmersed=831.29=30.96  m3

Since the body is uniform → GB=H2h2

GB=321.292=0.855  m

Imin=lb312 l>b

Imin=83312=18  m4

MG=1830.960.855=0.274  m

Since MG is negative, therefore the barge is unstable in the critical condition !

For the other direction :

I=bl312 l>b Imin=38312=128  m4

MG=12830.960.855=3.28  m

Since MG is positive, therefore the barge is stable in the other direction !

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