1. Archimedes Principle

2. Learning Objectives Describe Archimedes’ Principle.
Define density, buoyancy, and specific gravity.
Correctly calculate the buoyancy of an object in either fresh or salt water.
Correctly solve lifting problems.
Correctly calculate surface air volume equivalents.

3. Main Points Density Buoyancy Specific gravity Archimedes’ Principle
Surface Equivalent air volume
Lifting problems

4. Density Definition Density of air at sea level Hydrostatic Density
Mass per Unit Volume
Density of air at sea level
.08 lbs. per cu. ft.
Hydrostatic Density
Salt Water
64 lbs. per cu. ft.
Fresh Water
62.4 lbs. per cu. ft.

5. Buoyancy
Force that allows an object to float.

6. Specific Gravity
Density of a substance vs. density of pure
water.

7. Archimedes’ Principle
An object partially or wholly immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object.
Buoyancy of an object =
Weight of the water displaced by the object - Weight of the object

8. When placed in seawater, what is the state of buoyancy for each of these objects? Where will they end up?
Positive
_______________________________________________
Neutral
________________________________________________Negative_
32 lbs
1 cu ft
64 lbs
1 cu. Ft.
96 lbs
1 cu. ft
Consider: The weight of the object. The volume of water displaced when the object is completely submerged. The density of seawater and the weight of the water displaced.

9. States of Buoyancy Positive buoyancy Neutral Negative
Specific Gravity of the object is less than that of the fluid
Neutral
Specific gravity of the object is equal to the specific gravity of the fluid
Negative
Specific gravity of the object is greater than that of the fluid

10. Example 1
What is the buoyancy of an anchor with a dry weight of 100 lbs., and a volume of .22 cu. ft., when it is dropped in the ocean?

11. Answer to Example 1 Displaced wt.=
.22 cu. ft. x 64 lbs. per cu. ft lbs.
-Dry wt.
lbs.
Buoyancy
lbs

12. Example 2 How many 50 lb. lift bags will it take to lift
an object with a volume of 3.1 cu. ft. and a
dry weight of 289 lbs.?
Each lift bag weighs 2 lbs. and the object is
in fresh water.

13. Answer to Example 2 Displaced weight =
3.1 cu. ft. x 62.4 lbs./ cu. ft lbs.
-Dry weight
289 lbs.
Buoyancy
lbs.
Lift capacity = 50 lbs - 2 lbs = 48 lbs of lift / bag.
Use how many bags?
2 bags.

14. Surface Equivalent Air Volume
How much air must you bring down from the surface if the object in example 2 is located at a depth of 120 ffw?

15. Surface Equivalent Air Volume cont.
Buoyancy of the object lbs
How much lifting force must be generated to lift the object to the surface?
95.6 lbs

16. Surface Equivalent Air Volume cont.
How much freshwater must be displaced to generate the required lifting force?
How is this calculated?
Force required/density of fresh water
Density of fresh water
62.4 lbs. per cu. ft.
95.6 lbs/62.4 lbs. per cu. ft. =
1.53 cu. Ft. of water must be displaced

17. Surface Equivalent Air Volume cont.
How much air must we bring down from the
surface to displace 1.53 ft3 of fresh water at
a depth of 120 ffw.?
Calculate Pata at a depth of 120 ffw.?
{Depth + 34}/34 = atm
{120+34}/ 34 = 4.5 atm
Multiply Pata x Vol h20 to be displaced
1.53 x 4.5 = 6.93 cu. ft. at the surface

18. Lifting problem
You have been enlisted to salvage an outboard motor lost at sea. You locate the outboard, which displaces 2 ft3 of water and weighs 900 lbs in air, at a depth of 66 ft. How much air will you need to add to a lift bag to bring the outboard to the surface? How much air will be in the lift bag once at the surface?

19. Calculate the Buoyancy of the Object
Volume =
2 ft3
Weight of the water displaced =
2 ft3 x 64 lbs/ft3 = 128 lbs
Dry weight =
900 lbs
Buoyancy of the Object
128 lbs – 900 lbs = -772 lbs

20. Calculate the Volume of Water to be Displaced
How much lifting force is necessary?
772 lbs
How much water must be displaced
772 lbs / 64 lbs/ft3 = ft3

21. Calculate How Much Air You Need to Bring Down from the surface
Calculate Pata
(66 / 33) + 1 = 4 ata
Multiply P ata x volume H20 to be displaced
4 ata x ft3 = ft3
How much air will be in the bag at the
surface?

22. Example 3 When properly weighted for diving in the
ocean, a diver and his gear weigh 224 lbs.
How must the diver adjust the amount of
weight in his weight system to be properly
weighted in fresh water?

23. Answer to Example3
The volume of the diver and his equipment will not change
SW displacement =
224 lbs./64 lbs. per cu. ft. = cu.ft.
FW displacement =
3.5 cu. ft. x 62.4 lbs./cu. ft. = lbs.
Wt. system Adjustment =
224 lbs lbs.
Answer:
Remove lbs
Shortcut
Adjust up or down by 2.5% of total diver weight.
This is the difference in density between ocean water and
fresh water

24. Have we covered: Density Buoyancy Specific gravity
Archimedes’ Principle
Surface Equivalent air volume
Lifting problems

25. Can You Describe Archimedes’ Principle?
Define density, buoyancy, and specific gravity?
Correctly calculate the buoyancy of an object in either fresh or salt water?
Correctly solve a lifting problem?
Correctly calculate Surface Air Volume Equivalents?

26. Last Thoughts
Understanding and applying Archimedes’ Principle enables you to weight yourself properly and to achieve and maintain the appropriate state of buoyancy.
Combining Archimedes’ Principal with Boyle’s Law enables you to correctly calculate the volume of gas and number of lift bags you will need to bring from the surface to ensure you can lift and object off the bottom.