IB PhysicsFluid Mechanics Syllabus

Chapter 10A/B Class Due on this class:1

Mar 17/18

DI-DemosIW-10.1 #1-3 Pressure, force, areaIW-10.1 #27-31 DensityIW-10.1 #37-44 Hydrostatic Pressure

VF 10A, 10 B, 10C, 10F Read: 10.1-4

2Mar

19/20

DI-DemosIW-10.1 #32-36 Pascal's PrincipleIW-10.1 #45-55 Buoyancy

VF 10G, 10H Read: 10.5-7

SpringBreakYaySpringBreakYaySpringBreakYaySpringBreakYaySpringBreak3

Mar 31/Apr 1

IW-10.1 #45-55 BuoyancyIW-10.2 #6-10 ContinuityThinking Physics quandaries

VF 10I Read: 10.

4Apr 2/3

DI-DemosIW-10.2 #11-20 BernoulliGW-FA10.1

VF 10 J Read: 10.9-10

5Apr 6/7

SA10.1 (first 30 minutes)VF-10K ViscosityDI-Stokes Law (10L)

Read: 10.11

6Apr 8/9

DI-DemosIW-10.2 #21-25 Stokes LawIW-10.2 #26-30 Reynolds numbers

VF 10M

7Apr

13/14

GW-IB Fluids questionsBernoulli PHET LabGW-FA10.2

8Apr

15/16

SA10.2 (first 30 minutes)IW-IB Fluids QuestionsGW-IB Fluids Questions

Apr 17/20 Vaves! Ja!

2 Formative/ Summative Assessments: (10 pts) 10.1 - Fluid Statics 10.2 - Fluid Dynamics

One Lab: Bernoulli PHET lab (20 pts)

Handouts: Worksheet-10.2-FluidDynamics Worksheet-10.1-FluidStatics FA10.1 FA10.2

Videos 10B - Density Name

Example – What is the mass of an iron cannon ball that is 17 cm in diameter?

Whiteboards:1. What is the destiny of a fluid if 2.00 liters of it has a mass of 1.58 kg? (1000 liters = 1 m3) (790 kg m-3 )

2. What volume (in m3) of mercury has a mass of 1.00 kg? (ρ = 13.6x103 kgm-3) How many ml is this? (1 m3 = 106 ml) (7.4x10-5 m3, 74 ml)

3. What would be the mass of a gold brick that measures the same as a standard building brick?(A regular building brick has a mass of about 2 kg)(92 x 57 x 203 mm, ρ = 19.3x103 kgm-3)

Videos 10C - Pressure, Force, Area Name

Example - A 2.4 kg box measures 15 cm by 25 cm on the base. What is the pressure under the box?

Whiteboards:1. What is the pressure of 42 N on a 20. cm x 32 cm plate? (660 Pa)

2. What force does 3.200 kPa exert on a 78.0 cm x 182 cm pane of glass? (4540 N)

3. A hydraulic jack lifts a 31,360 N car using a pressure of 1.38 MPa (M = x 106) What is the diameter of the cylinder?(0.170 m)

Videos 10F - Hydrostatic Pressure Name

Example – What is the gauge pressure 3800 m (12,500 ft) deep in the ocean where the wreck of the Titanic lies? Calculate it in Pa, PSI and atm. (ρ = 1.025x103 kg m-3)

Example – At what depth below fresh water is the absolute pressure 100. PSI? (Po = 1.013x105 Pa, ρ = 1.00x103 kg m-3)

Whiteboards:1. The water level in a water tower is 30. m above the point where a faucet is. What is the absolute pressure in Pa and PSI? (Po = 1.013x105 Pa, ρ = 1.00x103 kg m-3) What is the gauge pressure in PSI? P = Po + ρgh (4.0E5 Pa, 57 psi, 43 psi)

2. The density of air at STP is 1.29 kg m-3. What is the difference in air pressure between the top and the bottom of the 381 m tall Empire State Building in Pa? (assume the density is constant….) ΔP = ρghIf the pressure is 1.025x105 Pa at the bottom, what is the pressure at the top? (4.82E3 Pa, 0.977E5 Pa (9.77E4 Pa))

3. At what depth in mercury is the gauge pressure equal to one atmosphere? (ρ = 13.6x103 kg m-3) (answer in m and mm)P = ρgh1 atm = 1.013 x 105 Pa = 101.3 kPa = 760 Torr = 14.7 psi(0.759 m, 760 mm)

Videos 10G – Pascal’s Principle Name

Example – A hydraulic jack has an input piston with a diameter of 8.20 mm, and an output piston diameter of 95.0 mm. What force in Newtons do you need to apply to lift a ton? (8900 N) What is the pressure in Pa? How far must you move the input cylinder to raise the car 10.0 cm?

Whiteboards:1. A car has a master cylinder bore size of 2.50 cm, and a caliper bore of 4.40 cm. What force does the caliper exert if you press on the master cylinder with a force of 150 N?(465 N)

2. A hydraulic jack has an output cylinder with a 5.2 cm bore, and needs to lift a 53,400 N weight with an input force of 356 N. What is the diameter of the input cylinder needed?(0.0042 m or 0.42 cm)

Videos 10H – Buoyancy Name

Example – What is the buoyant force on a 3.0 cm diameter air bubble under water? ρH2O = 1.0E3 kg m-3

Example - What is the buoyant force on a 5.45 kg iron shot submerged in water? What is the weight of the shot in air, and what is its apparent weight submerged? ρFe = 7.8E3 kg m-3, ρH2O = 1.0E3 kg m-3, ρ = m/V so V = m/ρ

Example - The King’s crown has a mass of 14.7 kg, but appears to have a mass of only 13.4 kg when weighed when it is submerged in water. What is the density of the crown? Is it gold? ρAu = 19.3E3 kg m-3, ρH2O = 1.0E3 kg m-3, ρ = m/V so V = m/ρ

Over for whiteboards

Whiteboards:1. What is the buoyant force on a rectangular block of wood that measures 12x23x15 cm if it is submerged in the Dead Sea where the density of the water is 1240 kg m-3?(convert cm to m first)(50. N)

2. A 15x15x5.0 cm piece of wood floats in water (1000. kg m-3) face down in the water with the waterline 3.1 cm up the 5.0 cm side:What is its mass?What is its density?

(620 kg m-3)

3. A 5.0x4.0x4.0 cm piece of wood with a density of 530 kg m-3 is tied to the bottom of a pail of water (1000. kg m-3) with a string and held completely submerged. What is the tension on the string? (0.37 N)

4. A 25x25x10 cm block of iron (7.80x103 kg m-3) floats on mercury (13.6x103 kg m-3) If one of the 25x25 cm faces is down into the mercury, how far into the mercury does the block sink before coming to equilibrium? (5.7 cm)

Worksheet 10.1: Fluid Mechanics - Statics

Pressure: P = F/A (memorize area of circle, and rectangle)1. A force of 23,450 N is exerted on a rectangular window that measures 2.30 m

by 0.980 m. What is the pressure? (1.04E4 Pa)2. What is the force of 2100. psi over a circular flange with a radius of 8.5 inches? (476658

lbs ≈ 4.8E5 lbs)3. What is the total area in m2 of some snowshoes, if a 75 kg person does not

exert a pressure greater than 1.2 x 103 Pa? (0.61 m2)

Pressure conversionsConverting units of pressure. 1.00 atm = 1.013x105 Pa = 101.3 kPa = 760. Torr = 14.7 psi4. Convert 450. Torr to Pa. (6.00E4 Pa) 7. Convert 35 psi to Pa. (2.4E5 Pa)5. Convert 3.20 ATM to Pa. (3.24E5 Pa) 8. Convert 16.7 kPa to Pa. (1.67E4 Pa)6. Convert 835 Torr to psi (16.2 psi) 9. Convert 2350 Pa to psi (0.341 psi)

Gauge and absolute pressure: P = PG + 1 atm10. What is 0.45 atm gauge in absolute? (1.45 atm) 14. What is 3.60 atm absolute in gauge? (2.60 atm)11. What is 34.0 psi gauge in absolute? (48.7 psi) 15. What is 45.0 psi absolute in gauge (30.3 psi)12. What is 4.50 psi absolute in gauge? (-10.2 psi) 16. What is 34,500 Pa gauge in absolute? (1.358E5 Pa)13. What is 3.415 x 105 Pa in absolute in gauge? (2.402E5 Pa)

Gauge and unit conversions (on the assessments)17. What is 12.0 psi gauge in Pa absolute? (1.84E5 Pa) 22. What is 34,500 Pa absolute in atm gauge? (-0.659 atm)

18. What is 78.0 kPa absolute in Torr gauge? (-175 Torr) 23. What is 1.30 atm gauge in kPa absolute? (233 kPa)19. What is 34.5 psi gauge in atm absolute? (3.35 atm) 24. What is 7810 Pa absolute in kPa gauge? (-93.5 kPa)20. What is 0.835 atm absolute in Torr gauge? (-125 Torr) 25. What is -34.9 kPa gauge in psi absolute? (9.64 psi)21. What is 8.45 psi gauge in kPa absolute? (160. kPa) 26. What is 512,000 Pa absolute in Torr gauge? (3081 Torr)

Density ρ = m/V (memorize volume of rectangular solids, cylinder)27. What is the density (in kg m-3) of a cube that is 11.0 cm on a side, and has a mass

of 894 grams? (672 kgm-3)28. What is the mass of a gold brick that measures 26.0 cm x 8.00 cm x 12.0

cm? (ρ = 19.3x103 kgm-3) (48.2 kg)29. A sphere that contained 45.0 kg of air would have what radius? (ρ = 1.29

kgm-3) (2.03 m)30. What is the density of a shot put that has a diameter of 12.0 cm and a mass

of 7.26 kg? (8020 kgm-3)31. What is the mass of mercury (ρ = 13.6x103 kgm-3) in a (cylindrical) cup that

is 9.00 cm tall, and 11.0 cm in diameter? (11.6 kg)

Pascal's Principle: F/A = F/A 32. An engineer designs a hydraulic jack to lift 4560 kg. If the output cylinder is

8.20 cm in diameter, and the input cylinder is 0.420 cm in diameter, what input force is required? (117 N)

33. A hydraulic jack lifts 620. kg of mass with an input force of 24.0 N. What is the diameter of the input cylinder if the output cylinder has a diameter of 12.6 cm? (0.791 cm)

34. If you exert 4.45 N on the 0.920 cm diameter input cylinder of a hydraulic jack, what force does the 6.80 cm diameter output cylinder exert? (243 N)

35. A brake cylinder exerts 342 N of force with an input force of 55.2 N. What is the diameter of the brake cylinder if the master cylinder has a diameter of 1.21 cm? (3.01 cm)

36. A brake cylinder exerts 416 N of force on the rotor. What is the input force if the master cylinder has a radius of 2.30 cm, and the brake cylinder is 4.50 cm in diameter? (109 N)

Hydrostatic Pressure: P = Po + ρgd Simple:37.What is the pressure at a depth of 125 m in the ocean? (ρ = 1025 kgm -3) Assume there

is 1 atm above the water. (1.36x106 Pa)38.What is the gauge pressure at a depth of 1.67 m in mercury? (ρ = 13.6x103 kgm-3)

Assume there is 1 atm above the surface. (2.23x105 Pa)39.At what depth in fresh water (ρ = 1000. kgm -3) is the absolute pressure 2.31x106 Pa.

Assume there is 1 atm above the water. (225 m)More Complex: (These are like the assessment questions. Use Pa, and P = F/A)40.At what depth below the ocean (ρ = 1025 kgm-3) is the absolute pressure 100. psi?

(Assume the pressure above the surface is 1 atm) (58.5 m)41.A submarine is 45.2 m below the surface of a lake (ρ = 1000. kgm -3). What is the net

force exerted on a 85.0 cm diameter hatch. Assume there is 1 atm above the water, and in the submarine? (2.52x105 N)

42.There is a gauge pressure of 812 Torr at a depth of 14.2 m in a fluid. What is the density of the fluid? Assume there is 1 atm above the fluid. (777 kgm-3)

43.At what depth in the dead sea (ρ = 1240 kgm-3) does the water exert a force of 23,500 N on a 9.20 cm diameter porthole? Assume there is 1 atm above the water. (282 m)

44.A tank contains Liquid nitrogen (ρ = 808 kgm-3). At a depth of 13.5 m there is an absolute pressure of 313.7 kPa. What is the pressure at the top of the liquid in psi? (30.0 psi)

Buoyancy (B = ρfVfg)Simple: (I walk you through all the steps with separate questions)45.What is the buoyant force on a block of wood that is 2.95 cm x 4.50 cm x 4.50 cm

submerged in fresh water? (ρ = 1000. kgm-3) If the wood has a density of 362 kgm-3, what is its mass? What is its weight? What downward force would you need to exert to hold it under the water? (0.586 N, 0.0216 kg, 0.212 N, 0.374 N)

46.A 0.120 kg aluminium (ρ = 2680 kgm-3) mass is submerged in alcohol with a density of 789 kgm-3. What is the volume of the aluminium mass? What is the buoyant force acting on the mass? What is the weight of the mass? If the mass is resting on the bottom of the beaker, what is the normal force the beaker exerts on the mass? What is the apparent "mass" of the aluminium? (The mass that would weigh what the normal force is...) (4.48E-5 m3, 0.347 N, 1.18 N, 0.831 N, 0.0847 kg)

47.A rectangular block of wood has a density of 345 kgm -3 and measures 85.2 cm x 64.2 cm x 20.0 cm. It floats in water (ρ = 1000. kgm -3) with a large face down in the water. What is its mass? What volume of water must it displace to float? (What is the volume of water that has this mass?) How far up the 20.0 cm side does the water come so that the block displaces this volume of water? (85.2 cm x 64.2 cm x X = volume) How much of the 20.0 cm dimension sticks up above the water? (37.7 kg, 0.0377 m3, 0.069 m or 6.90 cm, or 13.1 above)

More Complex - I just ask you the last part.48.What downward force would you need to exert to keep a 14.0 cm radius sphere with a

density of 253 kgm-3 submerged in a fluid with a density of 965 kgm-3? (80.3 N)49.What upward force would you need to exert on a 52.1 kg piece of basalt (2920 kgm -3)

submerged in the dead sea where the water has a density of 1240 kgm -3 to keep it from sinking? (294 N)

50.A 13.25 gram hydrometer is a 1.12 cm diameter tube weighted on one end so it floats upright in a liquid. If it is 25.0 cm long, but floats with 7.80 cm exposed to air, what is the density of the liquid? (782 kgm-3)

51.A hot air balloon is 8.74 m in radius (assume it is spherical) and contains hot air with a mean density of 0.9486 kgm-3. Calculate the lifting capacity of the hot air if it is surrounded by air with a density of 1.34 kgm-3. (10,740 N)

52.A glass (2580 kgm-3) cylindrical stirring rod is 5.02 mm in diameter and 18.0 cm long. What force do I need to exert on it to hold it vertically at rest with the tip submerged in acetone (791 kgm-3) to a depth of 11.0 cm? (7.33x10-2 N)

53.A rectangular piece of wood that measures 13.0 cm x 15.2 cm x 3.78 cm floats face down in a fluid with a density of 893 kgm -3 with 2.93 cm of the 3.78 cm dimension submerged. What is the density of the wood? (692 kgm-3)

54.A 5.34 kg piece of rock can be supported by a force of 40.4 N when submerged in water with a density of 1008 kgm-3. What is the density of the rock? (4406 kgm-3)

55.A 1.28 kg piece of Styrofoam float material can be held under water (ρ = 1000. kgm -3) with a downward force of 328.7 N. What is the density of the Styrofoam? (36.8 kgm-3)

Videos 10I – Continuity Name

Concept 0Volume flow rate = Av

Example - What is the volume flow rate of air moving at 1.30 m/s down a hallway that measures 3.20 m by 4.10 m? What time will it take to change the air in a room that measures 10.2 m x 14.0 m x 5.20 m?

Concept 1A1v1 = A2v2 A = Area (m2)

v = Velocity (m/s)A 12.0 cm inner diameter pipe with water flowing at 1.18 m/s narrows to 5.00 cm inner diameter. What is the velocity in the narrow part? What is the volume flow rate in m3/s?

Whiteboards:1. Water is going at 1.45 m/s down a fire hose with a 6.20 cm inner diameter. If the water leaves the hose at a speed of 17.3 m/s, what is the inner diameter of the nozzle? (1.79 cm)

2. All the air going down a 3.0x4.0 m hallway goes through a doorway that measures 74 cm by 203 cm. If the air in the doorway is going 1.8 m/s, what is the speed of the air in the hallway? (0.23 m/s )

3. A hydraulicking monitor or giant discharges water at 44.0 m/s from a 3.0 cm diameter nozzle. What is the flow rate in m3/s, and what is the velocity in the 12 cm diameter supply pipe?What recoil force does it exert? (0.031 m3/s, 2.75 m/s, 1400 N, don't worry about the force so much)

Videos 10J – Bernoulli Name

Write down the derivation:

(data packet)

Whiteboards.1. The wind is moving horizontally at 12.0 m/s over a level rectangular roof that measures 4.50 m by 8.00 m. A. What is the pressure difference between the bottom (still air) and the top (moving air) of the roof surface? Use 1.29 kg m-3 for the density of the air, neglect the change in height, and assume (if you need to) that the pressure underneath is 1.013x105 Pa. B. What is the net upward force on the roof? (92.9 Pa, 3340 N (751 lbs) )

2. A very large Nitrogen tank is at 2000. PSI. If nitrogen at STP has a density of 1.17 kg m-3, how fast is the gas going if the valve breaks off when the tank is horizontal(assume P1 is 2000 PSI (convert), v1 is zero?, P2 is 1.013E5 Pa, solve for v2. Ignore change in height.) 1 atm = 14.7 PSI(4835.9 or roughly 4840 m/s, 3090 N (695 lbs) )

3. What pressure is needed in a fountain if it is spraying water straight up to a height of 23.2 m? What is the gauge pressure?ρ = 1000. kg m-3, P2 = 1.013E5 Pa (3.29x105 Pa, 2.28x105 Pa)

4. A water faucet breaks in the Physics room, spraying water upwards. If the gauge pressure in the water mains is 21.0 PSI, (at v = 0) with what speed does the water hit the ceiling 4.80 m above the faucet? How much time does it take a custodian to come down and fix the leak? ρ = 1000. kg m-3, P2 = 1atm = 1.013E5 Pa. 1 atm = 14.7 PSI(14.0 m/s )

5. Water flows at 2.00 m/s at ground level with a pressure of 1.15x105 Pa through a 10.0 cm diameter pipe. What is the pressure if it is at an elevation of 3.50 m going through a 6.00 cm diameter pipe? (Find the second speed first. ρ = 1000. kg m-3) (6.72x104 Pa )

Videos 10K, L, M – Viscosity, Stokes, and Reynolds Numbers Name

10K

10L

10M

Whiteboards.1. What force is needed to move a 0.85 cm diameter marble through Karo corn syrup at 1.00 cm/s? η = 2.350 Pa s (1.9 mN)

2. A water droplet has a terminal velocity of 0.00350 m/s falling through air. What is its radius? (ignore the buoyant force)Water: ρ = 1000. kg m-3

Air: η = 1.81x10-5 Pa s (5.39 microns)

3. What would be the terminal velocity of a 8.20 μm diameter piece of basalt silt (ρ = 2920 kg m-3) sinking in water with a density of 1025 kg m-3 and a viscosity of 1.72x10-3 Pa s. (You can’t ignore the buoyant force on the particle) What time would it take in minutes and seconds to settle in a test tube that is 5.40 cm tall?(4.04x10-5 m/s, 22 minutes 17 s – demo centrifuge)

4. What is the Reynolds number for a ping pong ball going through the air at 5.10 m/s? Use r = 0.0200 m. Is the flow around it laminar? (R<1000)ρ = 1.29 kg m-3

η = 1.81x10-5 Pa s(7270 – so no)

5. What is the maximum speed air could move down a 12.2 cm diameter duct and have laminar flow? (R < 1000)ρ = 1.29 kg m-3

η = 1.81x10-5 Pa s (0.230 m/s)

Worksheet 10.2: Fluid Mechanics - Dynamics

Volume flow rate. (Av = ΔV/t) (memorize volumes of cylinders, spheres, and rectangular solids)1. Water flows at 0.854 m/s down a 1.59 cm diameter hose. What time will it take

to fill a circular kiddie pool that is 1.75 m in diameter to a depth of 37.0 cm? (5250 s)

2. An HVAC duct that is 1.02 m in diameter supplies air to a 10.0 m x 4.20 m x 21.0 m room at a rate of 3.50 ACH. What is the air speed in the duct? (3.50 ACH means it replaces the air 3.50 times per hour, so it does it once in (3600 s)/3.5 seconds) (1.05 m/s)

3. A pump delivers 180. liters per minute. What speed does the water travel through its 4.15 cm diameter outlet pipe? What time would it take for the pump to fill a rectangular tank that is 2.1 m x 3.3 m x 5.4 m? (2.22 m/s, 12,500 s)

4. A classroom is 32.0 feet by 58.5 feet and 8.10 feet high. If air flows 8.65 f/s down a 1.50 foot x 1.00 foot air duct, what time in minutes does it take to replace the air in the room? (19.5 minutes)

5. A pipe bursts in a classroom that is 12.0 m x 35.0 m in floor area. If it is a 5.08 cm diameter pipe, and the water is going 20.3 m/s, what depth will the water be in a hour if it does not leak? (35.3 cm)

Continuity (Av = Av)6. A 0.75 inch pipe with water going 4.5 inches per second narrows to 0.50 inches

inner diameter. What is the velocity in the narrow part? (10. inches/sec)7. Air flows at 0.450 m/s down a duct that is 24.0 cm x 62.0 cm. If it widens to

35.0 x 62.0 cm, what is the air velocity there? (0.309 m/s)8. A circular 2.50 cm diameter pipe has a flow velocity of 56.0 cm/s. What is the

diameter of the pipe if the flow velocity slows to 13.0 cm/s? (5.19 cm)9. A fire hose sprays water at 34.0 m/s out of a nozzle that is 2.50 cm in diameter.

What is the diameter of the supply line if the velocity is 3.68 m/s (7.60 cm)10. A river with a strangely rectangular channel is 20.0 m wide. At a spot where

it is 6.30 m deep, the water moves at a stately 0.0850 m/s. Later there is a rapids where the water moves at 3.20 m/s. How deep is it there on the average? (Assume the channel is more or less rectangular in cross section) (0.167 m)

Bernoulli - 2 or 3 terms: (P + ρgh + ½ρv2 = P + ρgh + ½ρv2)1.00 atm = 1.013x105 Pa = 101.3 kPa = 760. Torr = 14.7 psi, ρwater = 1000. kgm-3, ρair = 1.29 kgm-3

11. Water issues from hole in the side of a water tank at 12.0 m/s. What is the height of the water in the tank above the hole? (ρ = 1000. kgm -3) Assume atmospheric pressure above the water in the tank and at the hole. (7.34 m)

12. Air (ρ = 1.29 kgm-3) streams at 6.70 m/s through a hole in a wall. What is the pressure difference from one side to the other? (29.0 Pa)

13. The air is traveling at 45.0 m/s over the top of a wing, and 43.0 m/s over the bottom of a wing. What is the pressure difference from one side to the other? (114 Pa)

14. Water is at 1.035x105 Pa in a level pipe where the velocity is 2.40 m/s. If the pressure drops to 1.024x105 Pa, what is the velocity? (2.82 m/s)

15. Water moves at 1.70 m/s down a level pipe at a pressure of 1.015x105 Pa. What is the pressure if the water speeds up to 4.92 m/s? (9.08x104 Pa)

Bernoulli - complex16. Water flows at 4.50 m/s down a 2.10 cm diameter pipe at a pressure of

9.92x104 Pa in the crawlspace. When the pipe is 1.20 m higher than this the pressure is 9.52x104 Pa. What is the velocity of the water in the pipe? What is the pipe diameter? (2.17 m/s, 3.02 cm)

17. Water moves at 3.50 m/s down a 4.80 cm diameter pipe at an elevation of 3.80 m and a pressure of 1.26x105 Pa. At a different elevation the pipe narrows to 3.60 cm in diameter and is at a pressure of 1.36x105 Pa. What is the elevation here? (1.43 m)

18. A 5.40 cm diameter pipe carries water at 3.70 m/s at an elevation of 3.40 m and a pressure of 1.56x105 Pa. At an elevation of 4.60 m the pipe narrows to 4.20 cm in diameter. What is the pressure in this part of the pipe? (1.32x105 Pa)

19. A 3.50 cm diameter pipe carries water at 4.10 m/s at an elevation of 6.30 m and a pressure of 1.24x105 Pa. The pipe widens out at an elevation of 5.10 m where the pressure is 1.43x105 Pa. What is the velocity here and the diameter of the pipe? (1.53 m/s and 5.72 cm)

20. Water moves at 4.90 m/s down a 4.70 cm diameter pipe at an elevation of 3.80 m and a pressure of 1.21x105 Pa. At a different elevation the pipe widens to 5.90 cm in diameter and is at a pressure of 1.37x105 Pa. What is the elevation here? (2.90 m)

Stokes law: FD = 6ηrv, at terminal velocity = mg = ρVg. (Ignore the buoyant force of air, but not the buoyant force of water.)1 micron = 1x10-6 m = 1 µmWater: ρ = 1000. kgm-3, η = 1.002x10-3 Pa s. Air: ρ = 1.29 kgm-3, η = 1.81x10-5 Pa s at 20 oC21. A droplet of water is 6.12 µm in diameter. What is its mass? What is its

weight? What speed must it fall through air so that its Stokes drag is equal to its weight? (This is its terminal velocity) (1.20x10-13 kg, 1.18x10-12 N, 0.00113 m/s)

22. A droplet of mist falls through air with a terminal velocity of 0.00156 m/s. What is its radius? (Ignore the buoyant force of the air) (3.60 μm)

23. A tiny grain of basalt (ρ = 2920 kgm-3) is 2.20 microns in diameter. What speed does it settle in water? (Don't ignore the buoyant force of water) (5.05x10-6

m/s)24. A tiny grain of basalt (ρ = 2920 kgm-3) takes 27.0 minutes to settle from the

top of a 8.50 cm tall test tube full of water to the bottom. What is its speed? What is its radius? What time would it take to settle in a 5.40 cm radius centrifuge spinning at 1200 RPM? (5.25x10-5 m/s, 3.54x10-6 m, 18.6 s)

25. A 3.60 micron diameter particle falls through air with a terminal velocity of 0.00130 m/s. What is its density? (3330 kgm-3)

Reynolds number Re_r = vrρ/η26. Syrup with a viscosity of 1.20 Pa s and a density of 1080 kgm-3 needs to have

turbulent flow down a pipe where it is heated. What speed must it go down a pipe that is 68.0 cm in diameter to ensure that it has a Re_r of 1200? (3.92 m/s)

27. What is the Re_r of water flowing at 0.130 m/s down a tube that is 8.01 mm in diameter? (520.)

28. What is the maximum speed air can flow down a 24.0 cm diameter duct to have a Re_r of 850? (9.94 cm/s)

29. What is the Re_r of air flowing at 0.935 m/s down a duct with a diameter of 1.20 m? (4.00x104)

30. What maximum diameter pipe can water flow down at 0.890 m/s to have a Re_r of 950? (2.14 mm)