1. AP Physics
II.A – Fluid Mechanics

2. 11.1 – Mass Density

3. Ex. What is the mass of a solid iron wrecking ball of radius 18 cm?
The density of iron is 7800 kg/cubic meter.

4. 11.2 Pressure

5. Consider the lowly tire

6. The force perpendicular to a given surface area is . . .

7. Increase pressure by
Increasing force
Decreasing area

8. For a static fluid, the force must be perpendicular, not parallel
For a static fluid, the force must be perpendicular, not parallel. Note that pressure is scalar.

9. 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.

10. p. 337: 10, 13-17
1.1 EE 3 N
EE 4 n
15. Hint – to use the fewest number of bricks, use the face of the brick with the least area Pa
17. Note – pressure each exerts on the ground is the same. Set pressures equal to each other, make massive subs. and cancel happy.

11. Atmospheric pressure

12. 11.3 Pressure and Depth in a Static Fluid

13. Proof please

14. Absolute and gauge pressure

15. The Hoover Dam

16. 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.

17. 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.

18. Pumping water

19. 11.5 Pascal’s Principle

20. Amazing artwork and the Squidy

21. Key point – a change in pressure at point one changes the pressure at any point in the fluid.

22. 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

23. As a formula . . .

24. Ex. To show his principle, Pascal placed a long thin tube of 0
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.

25. 11.6 Archimedes Principle (another incredible proof)

26. 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.

27. But what about other forces?

28. 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)

29. 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?

30. Comparing the weight to the buoyant force

31. 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.

32. 11.8 – The Equation of Continuity

33. Mass flow rate – the mass of fluid that flows through a tube during a given time interval

34. Another proof

35. 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?

36. 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.

37. p. 339: 39-40, 42-43, 52-53, 55
59 N
550 kg/m3
2.7 EE –4 m3
2.04 EE –3 m3
a) 0.18 m b) 0.14 m
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

38. 11.9-10 Bernoulli’s Equation – complete with extended proof

39. Bernoulli’s Principle – pressure exerted by a fluid is inversely proportional to its speed.

40. Some practical applications and astounding demos

41. 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

42. 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?

43. Ex. Find the speed of water that leaves the spigot on a tank if the
spigot is m below the surface of water in the tank and the
tank is open to the atmosphere.

44. Ex. An aneurysm in a certain aorta increases the cross-sectional area of the aorta by a factor of 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.

45. p. 340: 56-59, 63-64; Rev. 03B6 86 m/s 150 Pa 470 Pa 1.92 EE 5 PaN
03B6 a) 3.5EE 5 Pa b) 4.5 EE 5 Pa c) 1000 N
d) yours