1. Chapter 4
LAWS OF FLOATATION

2. Laws of floatation Archimedes’ Principle
When a body is wholly or partially immersed in a fluid it appears to suffer a loss in mass equal to the mass of fluid it displaces.

3. Laws of floatation

4. Example: When a box measuring 1 cu
Example: When a box measuring 1 cu. m and of 4000 kg mass is immersed in fresh water it will appear to suffer a loss in mass of 1000 kg. If suspended from a spring balance the balance would indicate a mass of 3000 kg.
1 cubic
meter
4000 k.g
In Air
In Fresh water
3000 k.g
1 cubic
meter
4000 k.g
4000 k.g

5. Laws of floatation

6. Laws of floatation

7. Laws of floatation

8. Laws of floatation

9. Laws of floatation
10 m 3
5 tons
5 m 3
5 tons
4 m 3
5 tons

10. Laws of floatation
10 m 3
5 m 3
0 ton
0 ton
4 m 3
1 ton

11. 5 tons
Resultant force = zero G B
5 tons

12. the box shown in Figure (a) has a mass of 4000 kg, but has a volume of 8 cu. m. If totally immersed in fresh water it will displace 8 cu. m of water, and since 8 cu. m of fresh water has a mass of 8000 kg, there will be an up thrust or force of buoyancy causing an apparent loss of mass of 8000 kg. The resultant apparent loss of mass is 4000 kg. When released, the box will rise until a state of equilibrium is reached, i.e. when the buoyancy is equal to the mass of the box. To make the buoyancy produce a loss of mass of 4000 kg the box must be displacing 4 cu. m of water. This will occur when the box is floating with half its volume immersed, and the resultant force then acting on the box will be zero.

13. The box to be floating in fresh water with half its volume immersed
The box to be floating in fresh water with half its volume immersed. If a mass of 1000 kg be loaded on deck the new mass of the body will be 5000 kg, and since this exceeds the buoyancy by 1000 kg, it will move downwards. The downwards motion will continue until buoyancy is equal to the mass of the body. This will occur when the box is displacing 5 cu. m of water and the buoyancy is 5000 kg,

14. Laws of floatation

15. Laws of floatation

16. Laws of floatation

17. Laws of floatation

18. Laws of floatation

19. Laws of floatation

20. Tons Per Centimeter (TPC)
The TPC is the mass which must be loaded or discharged to change a ship’s mean draft by one centimeter in salt water

21. Tons Per Centimeter (TPC)L1 W1 L W
One cm
W = ? ?
one centimeter

22. Tons Per Centimeter (TPC)
TPC = WPA X DENISTY
100
WPA is the water plan area in meters
DENISTY of sea water is in ton/m3
DENISTY of sea water is ton/m3
TPC = WPA X 1.025
100

23. TPC in dock water
When a ship is floating in dock water of a relative density other than the weight to be loaded or discharged to change the mean draft by
1 centimetre (TPC dw) may be found from the TPC in salt water (TPC sw) by simple proportion as follows: =
RELATIVE DENSITY sw
TPC sw
RELATIVE DENSITY dw
TPC dw

24. TPC curves
When constructing a TPC curve the TPCs are plotted against the corresponding drafts. It is usually more convenient to plot the drafts on the vertical axis and the TPCs on the horizontal axis.

25. is provided by the volume of the enclosed spaces under the water line
The force of buoyancy
is provided by the volume of the enclosed spaces under the water line
Reserve buoyancy
is the volume of the enclosed spaces
above the water line

26. Reserve Buoyancy

27. Reserve buoyancy It may be expressed as: Volume or,
The volume of the enclosed spaces above the waterline are not providing buoyancy but are being held in reserve.
If extra weights are loaded to increase the displacement, these spaces above the waterline are there to provide the extra buoyancy required
It may be expressed as:
Volume or,
Percentage Of The Total Volume

28. Reserve Buoyancy

29. Reserve Buoyancy