# Chapter 1- Density & Relative Density Exercise-1(Stability Calculation)

Updated: Jun 2, 2020

**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=0.78

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

** Density=Mass /Volume**

0.78=Mass/1440m3

Hence, Mass =1123.2 tonnes

**2. A cylindrical tank of diameter 8m is 10m high.400t of oil of RD 0.9 is poured into 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 =0.9

**Volume of the cylindrical tank** **= π2h**

= 3.1416 x 4 x 4 x 10=502.656m3

**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

**3.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 =0.7

According to the question, 2% of the volume is allowed for expansion.

**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