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AP Physics
II.A – Fluid Mechanics
11.1 – Mass Density
Ex. What is the mass of a solid iron wrecking ball of radius 18 cm?
The density of iron is 7800 kg/cubic meter.
11.2 Pressure
Consider the lowly tire
The force perpendicular to a
given surface area is . . .
Increase pressure by
• Increasing force
• Decreasing area
For a static fluid, the force must
be perpendicular, not parallel.
Note that pressure is scalar.
Ex. A square water bed is 2.00 m on a side and 30.0 cm deep. Find
the pressure the bed exerts on the floor.
p. 337: 10, 13-17
10. 1.1 EE 3 N
14. 3.3 EE 4 n
15. Hint – to use the fewest number of bricks, use the
face of the brick with the least area
16. 2400 Pa
17. Note – pressure each exerts on the ground is the
same. Set pressures equal to each other, make
massive subs. and cancel happy.
Atmospheric pressure
11.3 Pressure and Depth in a
Static Fluid
Proof please
Absolute and gauge pressure
The Hoover Dam
Ex. Find the total force exerted on the outside of a 0.30 m
diameter circular window at an ocean depth of 1.00 EE 3 m.
Ex. Find the value by the which the blood pressure in the
anterior tibial artery exceeds the blood pressure in the heart
when the patient is a) reclining and b) standing. The density of
blood is 1060 kg/m3.
Pumping water
11.5 Pascal’s Principle
Amazing artwork and the Squidy
Key point – a change in pressure
at point one changes the pressure
at any point in the fluid.
Pascal’s Principle – a change in
pressure applied to a completely
enclosed fluid is transmitted
undiminished to all parts of the
fluid and its enclosing walls
As a formula . . .
Ex. To show his principle, Pascal placed a long thin tube of 0.30
cm radius vertically into a 20.0 cm radius barrel. He found that
when the barrel was filled with water and the tube was filled to a
height of 12 m the barrel burst. Find a) the mass of the fluid in the
tube and b) the net force on the lid of the barrel.
11.6 Archimedes Principle
(another incredible proof)
In words . . . Any fluid applies a
buoyant force to an object that is
partially or completely submerged
in the fluid. The magnitude of the
force is equal to the weight of the
water displaced by the object.
But what about other forces?
Ex. A 70.0 kg statue lies at the bottom of the sea. Its volume
is 3.00 EE 4 cubic cm. How much force is needed to lift the
statue? (the density of seawater is 1025 kg/cubic meter)
Ex. A crown of mass 14.7 kg is attached to a spring scale and
submerged in water. The scale reads 13.4 kg. The density of
gold is 19.3 EE 3 kg/cubic meter. Is the crown made of gold?
Comparing the weight to the
buoyant force
Ex. What volume of helium is needed to lift a balloon that has a
mass of 8.0 EE 2 kg? The density of air is 1.29 kg/cubic meter
and the density of helium is 0.18 kg/cubic meter.
11.8 – The Equation of
Continuity
Mass flow rate – the mass of fluid
that flows through a tube during a
given time interval
Another proof
Ex. What is the cross-sectional area of a heating duct if the air
moves through the duct at 3.0 m/s and can replenish the air every
15 min in a room with a volume of 3.0 EE 2 cubic meters?
Ex. The radius of the aorta is about 1.0 cm and the blood passing
through it has a speed of about 0.30 m/s. A typical capillary
has a radius of 4 EE –4 cm and the blood flows through it at
a speed of 5 EE –4 m/s. Estimate the number of capillaries
in the body.
p. 339: 39-40, 42-43, 52-53, 55
39. 59 N
40. 550 kg/m3
42. 2.7 EE –4 m3
43. 2.04 EE –3 m3
52. a) 0.18 m b) 0.14 m
53. a) 7.0 EE – 5 m3/s b) 2.5 EE – 4 m/s
55. a) 1.6 EE – 4 m3/s b) 2.0 EE 1 m/s
11.9-10 Bernoulli’s Equation –
complete with extended proof
Bernoulli’s Principle – pressure
exerted by a fluid is inversely
proportional to its speed.
Some practical applications and
astounding demos
Note that this horrible looking
equation reduces to something much
simpler when a) the velocities are
the same (or v = 0) or b) the fluid
conduit is horizontal
Ex. The water circulating in the water-heating system of a house
is pumped at a speed of 0.50 m/s through 4.0 cm diameter pipe
in the basement at a pressure of 3.0 atm. What will be the flow
speed and pressure in a 2.6 cm diameter pipe on the second floor
5.0 m above the basement?
Ex. Find the speed of water that leaves the spigot on a tank if the
spigot is 0.500 m below the surface of water in the tank and the
tank is open to the atmosphere.
Ex. An aneurysm in a certain aorta increases the crosssectional area of the aorta by a factor of 1.7. The velocity
through the normal part of the aorta is 0.40 m/s. If the person
lies so the aorta is horizontal, determine the amount by which
the pressure in the enlarged region exceeds the pressure in the
normal region. The density of blood is 1060 kg/m3.
p. 340: 56-59, 63-64; Rev. 03B6
56 86 m/s
57 150 Pa
58 470 Pa
59 1.92 EE 5 Pa
63 38 m/s
64 9500 N
03B6 a) 3.5EE 5 Pa b) 4.5 EE 5 Pa c) 1000 N
d) yours