Stability Chapter 1 – Density and relative density Solutions.

Exact ullage where pump should be shut = (2.898 + 0.5)m
                                                                             = 3.398m.

7. A tank with a horizontal base and vertical sides is 10m deep and has rectangular trunkway 1m high. The volume of the tank alone is 8000m3 and that of the trunkway 500m³ . Find the ullage when 5320t of vegetable oil of RD 0.7 is loaded.

Given :

The depth of tank = 10m
Height of the trunkway = 1m
Volume of the tank alone =8000m³
Volume of the trunkway = 500m³
The mass of the oil =5320 t
RD =0.7

We know that,

Density = (mass /volume)
Volume   = mass /density
 = (5320 /0.7)
 = 7600m³

Depth of oil = (volume /area)
= (7600/800)
=9.5m

Ullage insides the tank = (10 – 9.5)
=0.5m

Total ullage = (1 +0 .5)
                          = 1.5m.

8. A rectangular tank has a total depth of 21m and volume of 20600 m³, which includes of trunkway of depth 1m and volume 600m³. find the ullage when 16320 t of oil of RD 0.8 is loaded.

Given :

The total depth of tank =21m
Volume of the tank = 20600m³
The height of the trunkway = 1m
Volume of the trunkway =  600m³
Oil loaded = 16320t
RD= 0.8

The height of the tank = (21-1)
= 20m

Volume of the tank= (20600 – 600)
 =20000m³

Area of tank = (20000 /20)
=10000m²

Volume of the oil = (mass /density)
=(1620 /0.8)
= 20400 m³

Hence, Volume of the oil inside the trunkway = (Total volume of the oil – volume of the tank)
= (20400 – 20000)
 =400m³

Depth of the oil = (volume /area)
= (400/600)
 = 0.66m

Hence, Ullage = (1 -0.66)
                             = 0.33m

9. A rectangular tank has a total depth of 10.5m and volume 8200m3, which include a trunkway of depth 0.5 m and volume 200m³ . find the mass of oil of oil of RD 0.8 loaded and the ullage, if 2% of the volume of the tank is left for expansion.

Given :

Depth of the tank is = 10.5m
Volume of the tank = 8200m³
Depth of the trunkway = 0.5m
Volume of the trunkway = 200m³
RD of the oil = 0.8

According to question, 2% of the tank volume left for expansion .
Volume of the tank alone = (8200-200)
= 8000m³

Height of the tank alone = (10.5 -0.5)
= 10 m

2% of the volume of the tank left for expansion .
= (2/100 x 8200)
=164m³

Volume of the oil to be load = (8200 -164)
=8036 m³

Mass of oil to be load = ( volume x density)
= (8036 x 0.8)
= 6428.8t

Volume of the trunkway = (L x B x 0.5)
= 200m³ ( given)

We can calculate Area as = (200 /0.5)
=400m²

Volume of the free space = ullage= (volume of the free space)/(area)
                                                                   = (164/ 400)m
                                                                   =0.41m.