Chapter 10: Fluid Mechanics

Chapter 10: Fluid Mechanics

What is a fluid?
What are examples of fluids? / Any material that flows and offers little resistance to changing its shape.
What is density?
How is the formula for density expressed on the AP test? / ·  An important property of matter is density.
·  Density is defined as mass per unit volume.
·  The symbol is r.

What is the density of water? / •  1.0 g/ml
•  1.0 g/cm3
•  1,000 kg/m3
Define pressure.
How is the formula for pressure expressed on the AP test?
What units will we be using to express pressure?
What is the value for standard pressure? / •  Force per unit area.


Measured in atm or Pascals (Pa)

Standard atmospheric pressure = force per 1 m2 of air at sea level.
1.01 x 105 Pa or 101 kPa
How does pressure change as you increase the depth of water? / The pressure due to fresh water (P=F/A) increases about 1 atm or about 100 kPa for every 10 m of water depth.
Which would exert a greater pressure, a large but shallow lake, or a small but deep lake? / Water pressure is greater in the deeper lake.

State Pascal’s Principle
What does this mean for an object that is completely immersed in a fluid? / The force exerted by a fluid on the walls of its container always acts perpendicular to the walls.
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? / The pressure of a liquid is the same at any depth regardless of the shape of its container. /
What is the formula for pressure in a column? / 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?
What is the formula for buoyancy on the AP test? / Buoyancy is an upward force that a fluid exerts on an object that is immersed in it. This is called the buoyant force.

State Archimedes’ Principle / An object is buoyed up by a force equal to the weight of the fluid it displaces
How is apparent weight different from buoyancy?
What is the formula for apparent weight? / 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 immersed in fresh water. The density of steel is 9.0 x 103 kg/m3. What is the buoyant force acting on the cube? /
FB = (1000 kg/m3)(0.05 m)3(9.8m/s2)
FB = 1.23 N
Problem (part 2)
What is the apparent weight of the steel? / => 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
Pascal’s Principle / 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.
Is Energy Conserved? / 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.
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.