Chapter
9
Solids,
Liquids, & Gases
The
Barometer:
The
atmospheric pressure is related to the height of fluid in the
tube by the relation .
Gauge
Pressure:
Absolute
pressure (P) is the sum of the gauge and atmospheric pressure.
(5)
Pascal's
Principle:
An
external pressure applied to a fluid confined within a closed
container is transmitted undiminished throughout the entire fluid.
Hydraulic
Machines:
The
force divided by the area of the piston determines the pressure.
Different piston areas and forces produce the same pressure.
(6)
If
you look at the change in height:
(7)
Example
10
In
a car lift used in a service station, compressed air exerts a
force on a small piston that has a circular cross section and
a radius of 5.00 cm. This pressure is transmitted by a liquid
to a piston that has a radius of 15.0 cm. What force must the
compressed air exert to lift a car weighing 13300 N? What air
pressure produces this force?
Solution:
Buoyant
Force:
Archimedes's
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.
(8)
Example
11
Archimedes
supposedly was asked to determine whether a crown made for the
king consisted of pure gold. Legend has it that he solved this
problem by weighing the crown first in air and then in water
as shown. Suppose the scale read 7.84 N in air and 6.86 N in
water. What should Archimedes have told the king?
Solution:
First
find the bouyant force:
Then
find the volume of the crown:
Then
find the density of the crown:
Compare
to the density of gold ():
The
denisty is much less therefore either hollow or not made of pure
gold.
Example
12
A
raft is constructed of wood having a density of .
Its surface area is ,
and its volume is .
When the raft is placed in fresh water of density ,
to what depth does the raft sink in the water?
Solution:
The
buoyant force must equal the weight of the raft.
Then
find the weight of the raft:
Then
solve for the height (h) and substitute the values:
On
to Fluid Dynamics
