Density

1
Density
Units kg/m3 Common unit g/cm3 Density water
1,000 kg/m3 1 g/cm3
Specific gravity density of substance/density
of water For example specific gravity of
wood 0.6 s.g. of
metals 7 See Active Figure 14.9 at pse6.com
2
Fluid Pressure
Units N/m2 Pascal (Pa) Other units psi
(lb./in.2) torr (mmHg)
3
Pascals Principles

• 1) Fluid pressure acts equally in all directions
  xyz ,
• 2) Fluid pressure in a homogeneous substance is
  the same at equal vertical depths below the fluid
  surface, and this doesnt depend on the shape of
  the container for example, the Pascals Arms
  demonstration ,
• 3) Fluid pressure increases with increasing depth
  below the fluid surface for example, scuba
  divers experience an increase of 1 atmosphere of
  pressure for each 10 m they descend below the
  water surface.

4
Pascals Demonstration

• The pressure doesnt depend on arms shape

5
Atmospheric Pressure(1)
Atmospheric pressure is due to the weight of the
earths atmosphere above our heads. The
atmosphere is substantial up to about 10 km .
Po 1 X 105 Pa 14.7 lb./in.2
760 mmHg
MAGDEBURG SPHERES
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Atmospheric Pressure (2)

• The mercury barometer was invented by Torricelli
  in the 1600s, and it measures current atmospheric
  pressure
• h 760 mmHg 760 torr 29.92 in.Hg

7
Atmospheric Pressure (3)
Suction occurs when one side of a surface is a
vacuum and the other side is at normal
atmospheric pressure. This causes a net force we
call suction. Question how deep can a well be
dug if we wish to use a suction pump to draw
water out?
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Absolute vs. Gauge Pressure

• Absolute pressure is the total pressure
• Gauge pressure is the pressure above atmospheric
  pressure .
• P P0 PG
• P absolute pressure
• P0 atmospheric pressure at sea level
• PG gauge pressure

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Hoover Dam

• Question Why is the Hoover Dam so much thicker
  on the bottom than on the top?

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Increase of pressure with depth
P Po rgh
HOOVER DAM
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Snorkeling

• Why is this situation ridiculous?

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Mercury Manometer
P Po rgh
13
Hydraulic Lift

• Principles of Hydraulics
• Pressure is the same throughout the system
• Force is proportional to the area of the piston
  F PA

14
Derivation of Archimedes Principle of Buoyancy
Archimedes Principle states that the
buoyancy force acting upward on an object
immersed in a fluid equals the weight of fluid
the object displaces. This concept goes back to
the ancient Greek scientist Archimedes.
Question How did Archimedes determine the
volume of a supposedly pure gold crown his king
gave him?
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Force Diagram for Buoyancy Problems
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Floating Object Archimedes example 1
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W Fb
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Floating Icebergs

• What of an icebergs volume is submerged under
  water?
• If icebergs melt, does
• that raise sea level?
• If glaciers melt, does
• that raise sea level?

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ISOSTATIC EQUILIBRIUM
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Suspended object Archimedes example 2
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Note the tension in the scale is less than the
true weight of the object.
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Weighted-down object Archimedes example 3