Archimedes principle

Index

DensityBuoyancySpecific gravityArchimedes’ PrincipleSurface Equivalent air volumeLifting problems

Density

Definition 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.

Buoyancy

Force that allows an object to float.

Specific Gravity

Density of a substance vs. density of purewater.

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

When placed in seawater, what is the state of buoyancy for each of these objects?Where will they end up?

Positive_______________________________________________

Neutral

________________________________________________Negative_

32 lbs1 cu ft

64 lbs1 cu. Ft.

96 lbs1 cu. ft

States of Buoyancy

Positive buoyancy Specific Gravity of the object is less than that of the

fluidNeutral

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

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?

Answer to Example 1

Displaced wt.= .22 cu. ft. x 64 lbs. per cu. ft. 14.08 lbs.

-Dry wt. 100 lbs.

Buoyancy - 86 lbs

Example 2

How many 50 lb. lift bags will it take to liftan object with a volume of 3.1 cu. ft. and adry weight of 289 lbs.?

Each lift bag weighs 2 lbs. and the object isin fresh water.

Answer to Example 2

Displaced weight = 3.1 cu. ft. x 62.4 lbs./ cu. ft. 193.4 lbs.

-Dry weight 289 lbs.

Buoyancy - 95.6 lbs.

Lift capacity = 50 lbs - 2 lbs = 48 lbs of lift / bag.Use how many bags?

2 bags.

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?

Surface Equivalent Air Volume cont.

Buoyancy of the object -95.6 lbsHow much lifting force must be generated to

lift the object to the surface? 95.6 lbs

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

Surface Equivalent Air Volume cont.

How much air must we bring down from thesurface to displace 1.53 ft3 of fresh water ata 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

Lifting problemYou 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?

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 Object128 lbs – 900 lbs = -772 lbs

Calculate the Volume of Water to be Displaced

How much lifting force is necessary? 772 lbs

How much water must be displaced772 lbs / 64 lbs/ft3 = 12.06 ft3

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 12.06 ft3 = 48.24 ft3 How much air will be in the bag at thesurface?

Example 3

When properly weighted for diving in theocean, a diver and his gear weigh 224 lbs.How must the diver adjust the amount ofweight in his weight system to be properlyweighted in fresh water?

Answer to Example3

The volume of the diver and his equipment will not change

SW displacement = 224 lbs./64 lbs. per cu. ft. = 3.5 cu.ft.

FW displacement = 3.5 cu. ft. x 62.4 lbs./cu. ft. = 218.4 lbs.

Wt. system Adjustment = 224 lbs.- 218.4 lbs.

Answer:Remove 5.6 lbs

Shortcut Adjust up or down by 2.5% of total diver weight.This is the difference in density between ocean water andfresh water

Have we covered:

DensityBuoyancySpecific gravityArchimedes’ PrincipleSurface Equivalent air volumeLifting problems

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?

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.

Physics projectBY

ADITYA SANGWAN05 9D