Ch 9 Fluid Mechanics & States of Matter

1. Ch9Fluid Mechanics & States of Matter Section 1 Pressure & Gas Laws

2. States of Matter • Solids – Definite shape, low KE • Liquids – Indefinite shape, Definite surface, higher KE • Vapor – Indefinite shape & surface, Takes shape of container, Increased KE • Plasma – High Energy/Temperature; Electrons stripped from orbits. Can Conduct Electricity. • EX: Lightning, Fire, Ionized Gas (Composition of Stars, therefore Most common state)

3. Matter can cause pressure by… • Changing Volume, • Mass or weight • Temperature • Conservation of Energy can be applied to Fluids, if we consider Pressure

4. Pressure • P = F/A • Units • Pascal (Pa) • kiloPascal (kPa) often used since Pa is so small • Also: 1 Pa = 1 N/m2 ** Convert to kPa (usually) • When a force is applied to an Area • Force assumed to be at 90o To the area F

5. Pressure key concepts • Generally, heavier objects (more force) = more pressure • F on a smaller area = more pressure • Higher KE = more pressure • Faster moving gas particles bounce off container walls = Δ momentum = causes more Pressure.

6. When determining area • For Rectangular surfaces use A = LW • For circular surfaces use A = πr2 ***For any other shape surface, Determine the Area by it’s own equation.

7. Section Properties of Fluids 13.1 Atmospheric Pressure • On Earth AT Sea Level:Atmosphericpressure is about 10 N per 1 cm2 (10−4 m2), ( ~ 1.0 x 105N/m2, or 100 kPa. ) • OTHER PLANETS: the pressure at the surface of Venus is about 92 times the pressure at the surface of Earth, SO: Venus has thicker atmosphere • While the pressure at the surface of Mars is less than 1 percent of Earth’s. SO: Mars’ has thinner atmosphere

8. GAS LAWS – explain relationships between changes in P, V, and T BOYLE’S Charle’s Law V1 = V2 T1 T2 Assumes constant Pressure CONVERT TO KELVIN!!! P1V1 = P2V2 Assumes constant Temperature

9. More Gas laws Combined Gas Law IDEAL GAS LAW From the Kinetic-molecular theory to show how the constant in the combined gas law depends on number of particles (N) PV = kN T P1V1 = P2V2 T1 T2 Used for Fixed amount of an ideal gas CONVERT TO KELVIN!!!

10. IDEAL GAS LAW This leads to the ACCEPTED IDEAL GAS LAW equation PV = nRT n = number of moles R = 8.31 Pa m3 /K Volume MUST be in (m) Temp MUST be in (K) PV = kN T k = Boltzmann’s constant = 1.38 x 10-23 Pa m3 /K N = Number of particles (mole) 1 mole = 6.022 x 1023 particles (Avogadro’s #) (use to convert between mass & moles)

11. Ideal Gas Law Key Concept • If V and T are constant… • And the # of particles increases, then the # of collisions increase, therefore P increases. • Removing particles decreases collisions, therefore P decreases.

12. Gas Law concepts • THERMAL EXPANSION--All matter , when heated becomes less dense and expands to fill more space. (ex: boiling water fills the room) • EXCEPTION: WATER ICE • It contracts due to strength of water bonds. • Water MOST dense at 4 degrees Celsius. • IMPORTANCE: If Ice sank, then bottoms of lakes, oceans, (etc..) would freeze & kill life

13. Section 2 Forces within Liquids

14. Properties of Water • Cohesive Forces- electromagnetic force of attraction • surface tension, seeks out smallest volume; forms spherical shapes • Water attracted down and to sides, never up. • Objects more dense than water can float • Some liquids are stronger (Hg); Some are weaker (Alcohol, etc…)

15. 18) Condensation Nuclei- Solid particles that water collects on. Ex: Dust, pollution, ash,

16. Condensation Nuclei

17. Viscosity- Depends on Temp & Composition (mainly) • Resistance to Flow • MORE Viscous = Slower movement • EX: Syrup more viscous • Heat weakens bonds = less viscous = faster • EX: HOT syrup is less viscous than cool syrup http://www.youtube.com/watch?v=7Ft9VDDPWb4 • More Viscous allows more build up in pressure • EXPLOSIVE volcanoes have MORE viscous Lava http://dsc.discovery.com/convergence/pompeii/interactive/interactive.html

18. Adhesive Forces • Electromagnetic attractive force between particles of different substances. • (water inside glass tube rises due to adhesive forces) • Capillary Action– causes fluid to rise

19. Evaporation • Allows a cooling effect • When a water particle leaves a lake (etc..), the KE of the lake decreases. • temperature decreases. • Combine with CONDENSATION, Clouds form • “why is it generally cooler on coasts or near water?”

20. 20) Fog- Stratus clouds that form at ground level  when WARM Air rises from water/ground & mixes with cold air (via convection) OR When warm, moist air moves over cooler ground

21. Pascal’s Principle: • Pressure depends on depth of fluid, NOT the shape of container • ANY change in Pressure at ANY point in confined fluid is transmitted throughout the fluid (ex: Brake lines) http://wn.com/Pascal%27s_law • P1 = F1 and P2 = F2 A1 A2 • LEADS to Force exerted by hydraulic lift : • F2= F1 A2 A1

22. http://www.youtube.com/watch?v=TL3DcMZQEog&feature=related

23. Pressure of water on a body: • We know P = Fg ; Fg = mg ; m = ρV A (ρ = density) Leads to P = ρV g and: V = lwh ; A = lw A Leads to P = ρlwhg lw SO: P = ρhg

24. P = ρhg • Tells us the Pressure that a column of water exerts is determined by the height of the column (depth) and density. • Also works for ANY fluid (air, He, oil, etc…) • http://www.i-am-bored.com/bored_link.cfm?link_id=47264

25. Pressure of water on a body:P = ρhg • Depends on density of fluid, depth, & gravity • Pressures at bottom of ocean up to 1000 times standard atmosphere pressure. • Pressure increases as the body sinks into water. • What force allows the body to float??

26. Buoyant Force • The increase in pressure with increasing depth creates an upward force (Buoyant Force) • Determine whether it will sink or float by comparing weight of object to its buoyant force. • Fbuoyant = ρfluidVg Show derivation---

28. Fbuoyant = ρfluidVg • Archimede’s Principle: • An object immersed in a fluid has an upward force on it that is equal to the weight of the fluid displaced by the object. • ** The force does NOT depend on weight of object but on weight of the displaced Fluid**

29. F apparent determines if object sinks or floats… • F apparent = Fg – F buoyant • Fg is the weight of the object. • F buoyant is the buoyant force ( Draw Diagrams– of float/sink) • If Fg > F buoyant then object sinks • If Fg = F buoyant then object remains where it is placed (no net force) • If Fg < F buoyant then object floats

30. SO….Examples of Archimede’s Principle in action… • Continents floating, • More dense ships are able to float. (how?) • Make average density of ship less than water density. • Fish, you, submarines are able to change their depth in water (how?) • By inhaling/exhaling, the buoyant force is changed

31. Wasserstraßenkreuz in Germany which is the longest navigable aqueduct in the world with a length of 918 meters

32. Q?: Did that bridge have to be designed to withstand the additional weight of ship and barge traffic, or just the weight of the water? • Answer: It only needs to be designed to withstand the weight of the water!   • Why? A ship always displaces an amount of water that weighs the same as the ship, regardless of how heavily a ship may be loaded.

33. IN CLASS Bridge project

34. Bernoulli’s Principlehttp://wn.com/bernoulli%27s_principle • Follows Law of Conservation of Energy • As Velocity of fluid increases, KE increases, but Pressure decreases • Since KE increases, Work is done (follows Work-Energy Theorem) • Work is proportional to Force (dependent on Pressure)

35. 5) If W is + , then P at input end is Higher than at output end INPUT Lower Velocity Higher P OUTPUT High Velocity Lower P

36. Applied to Rockets…

37. Bernoulli via Law of Conservation of Energy • PE1 + KE1 = PE2 + KE2 • (mgh)1 + 1/2 mv12 = (mgh)2 + 1/2 mv22 • Energy dispersed in Volume (divide by V) & ρ = m/V so… • (ρgh)1 + 1/2 ρv12 = (ρgh)2 + 1/2 ρv22 • But now there is Pressure Energy, so… • P1 + (ρgh)1 + 1/2 ρv12 = P2 + (ρgh)2 + 1/2 ρv22 • But assuming height is constant • P1 + 1/2 ρv12 = P2 + 1/2 ρv22

39. Applied to airplanes/helicopters…air has to travel faster on top to cover more distance in same time.

40. ‘angle of attack’ determines lift ability

41. Goal: to achieve a STREAMLINE motion for fluids STREAMLINED/ LAMINAR TURBULENT

43. Planes stay airborne due to Net force = zero Planes change altitude by … changing forward Thrust & angle of wing

44. Bernoulli applied to Kicking a ball (hang time)…OR…. Blood flow

45. Carbuerator • Low pressure pulls Gasoline into carbuerator • Air & gas mix • Engine continues to run • You get to your destination.

47. Thermal Expansion • Adding heat to material and it’s length or volume increases. • As Temperature increases, • KE increases • Particles vibrate more • Average separation of particles Increases and • Solid expands

48. Coefficients of Expansion LINEAR EXPANSION (α) VOLUME EXPANSION (β) β= ΔV V1 ΔT V1= original length ΔT = change in temperature Units for β = 1/oC α= ΔL L1 ΔT L1= original length ΔT = change in temperature Units for α = 1/oC

49. Why ‘Thermal Expansion’ important • Expansion Joints must be built into bridges • Stealth jets allow for expansion of it’s skin • Railroad tracks must allow for expansion • Telescope mirrors made so NO expansion occurs