Stability -I : Chapter 1

  1. A rectangular tank measures 16mx15mx6m. How many tonnes of oil of RD 0.78 can it hold?
SOLUTION:

Given : L =16m , B = 15m, H = 6m, RD=0.78qes 1

Volume of rectangle =(LxBxH)
=16x15x6
=1440m3

We know that :
Density = Mass /Volume
0.78 =Mass/1440m3

Hence, Mass =1123.2 tonnes

 

  1. A cylindrical tank of diameter 8m is 10m high.400t of oil of RD 0.9 is poured in to it. Find the ullage, assuming π to be 3.1416.
SOLUTION:

Given: Diameter = 8m,

Radius = (d/2)m
=(8/2)m
=4m
Height =10m
Mass = 400t
RD =0.9qes 2

We know that:
Volume of the cylindrical tank = π2h
= 3.1416 x 4 x 4 x 10
=502.656m3

We know that:
Density = (Mass/Volume)
0.9 = 400/ (Volume of the oil)

Hence, Volume of the oil = 400/0.9
=444.44m3

Depth of oil = volume/area
Area of cylinder   =( π2r)
 =(3.1416 x 4 x 4)
 =502656m3

We can calculate Depth of oil = (volume of oil)/ ( area of cylinder)
 = (444. 44)/(50.2656 )
=8.8418 m

Hence, ullage  = (10 – 8.8418)  =1.1582m
  1. A tank of 2400m3 volume and 12 depth, has vertical side and horizontal bottom. Find how many tonnes of oil of RD 0.7 it can hold, allowing 2% of the tank for the expansion .state the ullage of loading.

Solution :-

Given :
Volume of the tank = 2400m3
Depth of tank =12m
RD =0.7qes 3

According to question 2% of the volume is allowed for expansion.
As we know that

Density = Mass/ Volume
Since volume =(L x B x H)
= 2400m3( given )

So, Area = (volume / depth)
= (2400/12)
=200m2

Mass  =  ( volume x density)
Mass  =  (2400×0.7)
 =1680 t

Since 2% of the volume of the tank allowed for expansion
 = (2/100) x 2400
 = 48m3

Volume of the oil = (volume of the tank – free space )
= ( 2400 -48)
= 2352 m3

Mass of the oil = (volume x density)
 =2352 x 0.7

Depth of oil = (volume of oil /area)
= 2352/(L x B)
= (2352/ 200)
=11.76 m

About the author

Amit Sharma

Graduated from M.E.R.I. Mumbai (Mumbai University), After a brief sailing founded this website with the idea to bring the maritime education online which must be free and available for all at all times and to find basic solutions that are of extreme importance to a seafarer by our innovative ideas.

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