This document discusses key concepts related to ship stability including: 1. Definitions and calculations for volume, mass, density, and relative density. It explains how to calculate these values using measurements of length, breadth, depth, and area. 2. Explanations of density as mass per unit volume and relative density as the ratio of a substance's density to that of fresh water. 3. Examples showing the density of fresh water is 1 t/m3 and salt water is 1.025 t/m3, so the relative density of salt water is 1.025. 4. A brief overview that density is measured using a brass hydrometer by collecting water samples and reading the instrument's

1. Ship Stability
Outcome 1 - Hydrostatics
1.1 Volume, Mass
and Density

2. Aims
To give the student an understanding of:
 Calculations involving Mass, Volume.
and Density.

3. Objectives
The Student will be able to:
 calculate Volume, Density, Relative
Density and Mass (Weight);
 define Density and Relative Density.

4. Length, Breadth, Depth
 Length (L), Breadth (B), and Depth (D) are
generally measured in Metres (m)
 However the following may also be used:
 Decimetre (dm) – 1/10 m 10dm = 1m
 1 dm = 0.1m
 Centimetre (cm) – 1/100 m 100cm = 1m
 1 cm = 0.01m
 Millimetre (mm) – 1/1000 m 1000mm = 1m
 1 mm = 0.001m

5. Area
 Area is the length and breadth of a body
multiplied together.
 L (m) x B (m) = A (m2)
Area (m2)
B(m)
L (m)

6. Volume
 Volume is the amount of space taken up by an
object.
 It is a body’s Length multiplied by it’s Breadth
multiplied by it’s Depth.
 L (m) x B (m) x D (m) = Volume (m3)
Volume (m3)
D (m)
B (m)
L (m)

7. Mass
 Mass is measured in Kilograms (kg) or
Tonnes (t).
 In stability we can treat mass and weight
as the same thing:
Mass 1t = Weight 1t
 1000kg = 1tonne

8. Density
 The mass per unit volume.
 The weight of 1m3 of material
 The symbol used is the greek letter rho (ρ)
 Density = Mass (kg or t)
Volume (m3)

9. Density
Fresh water (FW)
 Density = Mass (t) = 1(t ) = 1.000t/m3
Volume (m3) 1(m3)

10. Density
Fresh water (FW)
 Density = Mass (t) = 1(t ) = 1.000t/m3
Volume (m3) 1(m3)
Salt water (SW)
 Density = Mass (t) = 1.025 (t) = 1.025t/m3
Volume (m3) 1 (m3)

11. Relative Density (R.D.)
 The ratio of the density of a substance
compared to the density of Fresh Water.
 Since it is a ratio, it has no units
 Relative Density =Density of Substance (t/m3)
Density of Freshwater (t/m3)

12. Relative Density (R.D.)
Fresh water (FW)
 R.D. FW = Density FW = 1t/m3 = 1.000
Density FW 1t/m3

13. Relative Density (R.D.)
Fresh water (FW)
 R.D. FW = Density FW = 1t/m3 = 1.000
Density FW 1t/m3
Salt water (SW)
 R.D. SW = Density SW = 1.025t/m3 = 1.025
Density FW 1.000t/m3

14. Measurement of Density
 Density is measured using a
brass hydrometer.
 Water is collected away
from ER outlets.
 Hydrometer is spun gently
to break the surface tension.
 Instrument is read where the
water cuts the brass scale.