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Chapter 10: Fluid Mechanics
What is a fluid?
What are examples of fluids?
What is density?
How is the formula for
density expressed on the AP
test?
What is the density of water?
Define pressure.
How is the formula for
pressure expressed on the AP
test?
What units will we be using
to express pressure?
Any material that flows and offers little resistance to changing its
shape.
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An important property of matter is density.
Density is defined as mass per unit volume.
The symbol is .
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1.0 g/ml
1.0 g/cm3
1,000 kg/m3
Force per unit area.
What is the value for
standard pressure?
Measured in atm or Pascals (Pa)
How does pressure change as
you increase the depth of
water?
Which would exert a greater
pressure, a large but shallow
lake, or a small but deep
lake?
Standard atmospheric pressure = force per 1 m2 of air at sea level.
1.01 x 105 Pa or 101 kPa
The pressure due to fresh water (P=F/A) increases about 1 atm or
about 100 kPa for every 10 m of water depth.
Water pressure is greater in the deeper lake.
State Pascal’s Principle
The force exerted by a fluid on the walls of its container always acts
perpendicular to the walls.
What does this mean for an
object that is completely
immersed in a fluid?
When you are under water the water’s pressure pushes in on you from
all sides. The force is perpendicular to your body.
Describe a Pascal vase.
How does it demonstrate
pressure exerted by a liquid?
What is the formula for
pressure in a column?
The pressure of a liquid is the
same at any depth regardless of
the shape of its container.
The pressure in a fluid column can be found using this equation:
AP test version of the same equation:
What is the pressure exerted
by water at a depth of 45 m?
P = (1000 kg/m3)(9.8 m/s2)(45 m)
P = 4.41 x105 Pa or 441 kPa
What is buoyancy?
Buoyancy is an upward force that a fluid exerts on an object that is
immersed in it. This is called the buoyant force.
What is the formula for
buoyancy on the AP test?
State Archimedes’ Principle
How is apparent weight
different from buoyancy?
What is the formula for
apparent weight?
An object is buoyed up by a force equal to the weight of the fluid it
displaces
If the object’s weight is less than the buoyant force, the
object will float. If the object’s weight is greater than
the buoyant force, the object will sink, but it will weigh
less.
The apparent weight, FA, is the difference between its
actual weight and the buoyant force.
Problem (part 1)
A cube of steel that measures
5.0 cm on each side is
FB = (1000 kg/m3)(0.05 m)3(9.8m/s2)
immersed in fresh water. The FB = 1.23 N
density of steel is 9.0 x 103
kg/m3. What is the buoyant
force acting on the cube?
Problem (part 2)
What is the apparent weight
of the steel?
Pascal’s Principle
=> m = ρV
FW = (9.0 x 103 kg/m3)(0.05 m)3(9.8m/s2)
FA = W – FB
FA = 11.03 N – 1.23 N = 9.8 N
The force exerted by a fluid on the walls of its container always acts
perpendicular to the walls.
It also says that the pressure on a fluid is transmitted unchanged
throughout the fluid.
Pressure on a fluid is transmitted unchanged throughout the fluid.
A hydraulic press uses this principle. If you apply 10 lbs of pressure to
one end, 10 lbs of pressure will be experience on the other end.
If the tube is wider on the other side, that pressure is exerted
throughout the liquid on the other side.
If a 1 N/cm2 pressure were exerted on one side, the other side would
also experience a 1N force for every square centimeter.
Is Energy Conserved?
Energy is always conserved! The distance moved on one side will be
proportional the distance on the other side. In this scenario, the final
distance would be 1/50 of the original distance.