Q & A – Fluid Mechanics – Buoyancy – Q.5

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Q & A – Fluid Mechanics – Buoyancy – Q.5

Q & A – Fluid Mechanics – Buoyancy – Q.5

Question No.5

Check the stability of the given floating unit.

Given :

  • W=64  ton
  • Floating in water
  • G lies at 3 meters from the free surface

Solution :

First, we should calculate the height of the immersed part of the unit h :

W=FB

64ton=γwAh

64=1(224)h

h=m

Second , check the stability of the floating body :

MG=IminVimmersedGB

Vimmersed=Ah

Vimmersed=2244=64  m3

GB=h2+3

GB=42+3=m

Imin=minimum(Ix,Iy)

Ix=2(4)3122=21.33  m4

Iy=24(2)312+2443=261.33  m4

Imin=Ix=21.33  m4

MG=21.33645=4.67  m

Since MG is negative, therefore the unit is unstable !

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