# 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
• Cylindrical boiler of weight 70 tons
• Floats in sea water ( 1.03 )

### Solution :

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

$W=FB$

$W1+W2=γwAh$

$1410=1∗9810∗(1.20∗0.66)h$

Second , check the stability of the floating body :

$MG=IminVimmersed−GB$

$Vimmersed=Ah$

$Imin=bh312$

For the horizontal case : $74∗2.42+70∗(2.4+5.52)=(74+70)∗OG$

$GB=3.12−h2$

For the vertical case : $74∗2.42+70∗(2.4+10.32)=(74+70)∗OG$

$GB=4.29−h2$

a) Horizontal :

$Since MG is positive, therefore the system is stable !$

b) Vertical :

$Since MG is negative, therefore the system is unstable !$