Stability Chapter 1 – Density and relative density Solutions.

10. A rectangular tank has a total depth of 21m and volume 10250m³ which include a trunkway of trunkway of depth 1m and volume 250m3. Oil of RD 0.9 is to be loaded for expansion. find the mass of oil to be loaded and the final ullage.

Given :

Total depth of the tank =21m

Total volume of the tank =10250m³
RD =0.9

According to question , Space left for expansion is
=(3% of the volume of the oil)

Let ‘v’ be the volume of the oil
3 /100 x v = volume of free space
(Volume of free space) + (volume of oil) = (volume of tank)
( 3/100 x v + v ) = 10250m³
(3v /100 + v) = 10250m³
(103v /100)  = 10250m³
V = (10250×100 /103)
 = 9951.456m³

Volume of the free space = (10000 -9951.456) m³
= 48.544m³

Depth of the free space = (volume / area )

= (48.544 /500)
= 0.0970m
Hence ,  final  Ullage  =( 1.0 + 0.0970)
                   = 1.097m .