Density,
Pressure
And
Buoyancy
Iceberg off Newfoundland
Density
The density of a substance of uniform
composition is defined as its mass per unit
volume:
m

V
Units are kg/m3 (SI)
or g/cm3 (cgs)
1 g/cm3 = 1000 kg/m3
PRESSURE
…is force per unit area.
F
P
A
N
Unit: 1 2 = 1 pascal (Pa)
m
Look at the force needed to burst a balloon.
FLUID PRESSURE
The force exerted by
a fluid on a
submerged object at
any point is
perpendicular to the
surface of the object
F
P
A
N
Unit: 1 2 = 1 pascal (Pa)
m
Variation of Pressure with Depth
If a fluid is at rest in a container, all portions of
the fluid must be in static equilibrium.
All points at the same depth must be at the
same pressure.
Otherwise, the fluid would not be in
equilibrium.
The fluid would flow from the higher
pressure region to the lower pressure region.
Examine the darker
region, assumed to
be a fluid.
It has a crosssectional area A
and extends to a
depth h below the
surface.
Three external forces
act on the region.
Look at
Pressure (P)
vs.
Depth (h)
data.
How does P depend on h?
Pressure vs. Depth equation
from theory and experiment:
P  Po   gh
Po is normal atmospheric pressure.
Po  1.013 105 Pa  14.7 lb in 2
The pressure does not depend upon the shape
of the container.
Absolute vs. Gauge Pressure
The pressure P is called the absolute pressure.
Remember, P = Po + gh
P – Po = gh is the gauge pressure.
Pressure Values in Various Units
One atmosphere of pressure is defined as the
pressure equivalent to a column of mercury
exactly 0.76 m tall at 0o C where
g = 9.806 65 m/s2
One atmosphere (1 atm) =
76.0 cm of mercury
1.013 x 105 Pa
14.7 lb/in2
Buoyancy
Three Observations:
1) Solid object on a spring
balance, submerged in a fluid.
2) Balancing water bottles.
3) Sink or float movie clip.
More on
Buoyancy
Iceberg off Newfoundland
Archimedes' Principle
Any object completely or partially submerged
in a fluid is buoyed up by a force whose
magnitude is equal to the weight of the fluid
displaced by the object.
Buoyant Force
The upward force is called the buoyant force.
The physical cause of the buoyant force is the
pressure difference between the top and the
bottom of the object.
The magnitude of the buoyant force (B) always
equals the weight of the displaced fluid:
B  fluidVfluid g  Wfluid
The buoyant force is the same for a totally
submerged object of any size, shape, or density.
Buoyancy – Three Possibilities
1. The object is less dense than the fluid.
The upward buoyant force is B = ρfluidVobj g
The downward gravitational force is
w = mg = ρobjVobj g
The net force is B-w = (ρfluid-ρobj)Vobj g
Buoyancy – Three Possibilities
1. The object is less dense than the fluid.
The net force B-w = (ρfluid-ρobj)Vobj g is upward.
Now the volume of displaced fluid is less than
the volume of the object. The object accelerates
upward and floats when the weight of the
displaced fluid equals the weight of the object.
Buoyancy – Three Possibilities
2. The object is more dense than the fluid.
The net force B-w = (ρfluid-ρobj)Vobj g is
downward and the object accelerates to the
bottom.
Buoyancy – Three Possibilitiess
3. Object and fluid densities are equal.
The net force is B-w = (ρfluid-ρobj)Vobj g = 0
Now the weight of displaced fluid equals the
weight of the object. The submerged object
remains stationary wherever it is placed.
How much of an Iceberg is Below the Surface?
Ask the Captain of
the Titanic!
B  fluidVfluid g
Vfluid is the volume of
the displaced fluid.
B  fluidVfluid g
Vfluid is the volume of
the displaced fluid.
For an iceberg,
Vfluid  .9Viceberg
because
ice  .9  water
B  fluidVfluid g
Vfluid is the volume of
the displaced fluid.
For an iceberg,
Vfluid  .9Viceberg
So about 9/10 of the
volume of the iceberg
is below the surface.
A static fluid in a container is subject to both
atmospheric pressure at its surface and Earth's
gravitation. The pressure at the bottom of the
container
A. is equal to the atmospheric pressure.
B. depends on the height of the fluid column.
C. depends on the shape of the container.
D. depends on the height of the fluid column and
the shape of the container.
A static fluid in a container is subject to both
atmospheric pressure at its surface and Earth's
gravitation. The pressure at the bottom of the
container
A. is equal to the atmospheric pressure.
B. depends on the height of the fluid column.
C. depends on the shape of the container.
D. depends on the height of the fluid column and
the shape of the container.
The buoyant force on an immersed body has the
same magnitude as
A. the difference between the weights of the
body and the displaced fluid.
B. the average pressure of the fluid times the
surface area of the body.
C. the weight of the fluid displaced by the body.
D. the weight of the body.
The buoyant force on an immersed body has the
same magnitude as
A. the difference between the weights of the
body and the displaced fluid.
B. the average pressure of the fluid times the
surface area of the body.
C. the weight of the fluid displaced by the body.
D. the weight of the body.
A block of aluminum and a block of iron have
equal volumes. If each block is completely
submerged in water,
A. the buoyant force on the aluminum will be
greater.
B. both blocks will experience the same buoyant
force.
C. the buoyant force on the iron will be greater.
A block of aluminum and a block of iron have
equal volumes. If each block is completely
submerged in water,
A. the buoyant force on the aluminum will be
greater.
B. both blocks will experience the same buoyant
force.
C. the buoyant force on the iron will be greater.
Imagine holding two bricks under water. Brick A
is just beneath the surface of the water, while
brick B is at a greater depth. The force needed to
hold brick B in place is
A. smaller than
B. larger than
C. the same as
than the force required to hold brick A in place.
Imagine holding two bricks under water. Brick A
is just beneath the surface of the water, while
brick B is at a greater depth. The force needed to
hold brick B in place is
A. smaller than
B. larger than
C. the same as
than the force required to hold brick A in place.
An ice cube is placed in a glass of water. As the ice
melts, the water level on the side of the glass
A. stays the same.
B. goes up.
C. goes down.
An ice cube is placed in a glass of water. As the ice
melts, the water level on the side of the glass
A. stays the same.
B. goes up.
C. goes down.
Buoyancy
Two more observations:
4) Barges on the river.
5) Recovering a damaged vessel.