Q & A – Fluid Mechanics – Buoyancy – Q.6

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Q & A – Fluid Mechanics – Buoyancy – Q.6

Q & A – Fluid Mechanics – Buoyancy – Q.6

Question No.6

A rectangular pontoon 10.3 m long , 7.3 m wide and 2.4 m deep has a displacement weight of 74 tons. If an empty cylindrical boiler of 5.5 m diameter and 10.3 m long is mounted on its deck , check the stability of the system while floating in sea water ( 1.03 ) , when the boiler's axis is :

  1. horizontal ( parallel to pontoon axis )
  2. vertical

The boiler weighs 70 tons.

Given :

  • Rectangular pontoon of dimensions 10.3 * 7.3 * 2.4 m
  • W=74  tons
  • Cylindrical boiler of weight 70 tons
  • Floats in sea water ( 1.03 )

Solution :

First, we should get the height of the immersed part of the pontoon h ( same in both cases ) :

W=FB

W1+W2=γwAh

1410=19810(1.200.66)h

h=1.86  m<2.4  m (O.K)

Second , check the stability of the floating body :

MG=IminVimmersedGB

Vimmersed=Ah

Vimmersed=10.37.31.86=139.85  m3

Imin=bh312

Imin=10.37.3312=333.9  m4

For the horizontal case :

742.42+70(2.4+5.52)=(74+70)OG

OG=3.12  m

GB=3.12h2

GB=3.121.862=2.19  m

For the vertical case :

 

742.42+70(2.4+10.32)=(74+70)OG

OG=4.29  m

GB=4.29h2

GB=4.291.862=3.36  m

a) Horizontal :

MG=333.9139.852.19=0.198  m

Since MG is positive, therefore the system is stable !

b) Vertical :

MG=333.9139.853.36=0.972  m

Since MG is negative, therefore the system is unstable !

 

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