AP Physics II.A – Fluid Mechanics. 11.1 – Mass Density

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. Findthe 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 volumeis 3.00 EE 4 cubic cm. How much force is needed to lift thestatue? (the density of seawater is 1025 kg/cubic meter)

Ex. A crown of mass 14.7 kg is attached to a spring scale andsubmerged in water. The scale reads 13.4 kg. The density ofgold 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 meterand 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 passingthrough it has a speed of about 0.30 m/s. A typical capillaryhas 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 capillariesin 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 houseis pumped at a speed of 0.50 m/s through 4.0 cm diameter pipein the basement at a pressure of 3.0 atm. What will be the flowspeed and pressure in a 2.6 cm diameter pipe on the second floor5.0 m above the basement?

Ex. Find the speed of water that leaves the spigot on a tank if thespigot is 0.500 m below the surface of water in the tank and thetank is open to the atmosphere.

Ex. An aneurysm in a certain aorta increases the cross-sectional 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. 03B656 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